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Notes on "Induction in Physics and Philosophy"

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Notes on "Induction in Physics and Philosophy" Lecture 1

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Generalization - The inference of some member of a class to all. The inference moves from

  • from the observed to the unobserved
  • from the past to the future
  • from here to everywhere

Generalizing is the essence of human cognition and distinguishing feature of man from the animal.

Induction is the primary process of gaining knowledge that goes beyond perception. Deduction also moves beyond perception but presupposes premises; therefore is not primary.

Definition of Generalization - a proposition that ascribes a characteristic to every member of an unlimited class, however a member is placed in time and space. Format: "All S is P"

'unlimited' is in the definition to rule out simple inventory as an induction. Example: Inspecting every marble in a bag of marbles, seeing they are all red, then stating "All the marble in this bag are red" is not an induction despite the universal format. {this is not an open-ended universal}

side note - metaphysical axioms are not inductive generalizations. 'A is A' is not 'All S is P'.

Generalizations are made possible by man's conceptual faculty. S and P are concepts. {Definition of concept from the Lexicon}

Concepts are tools of knowledge, file-folders. They are not the claims to knowledge, they organize it and integrate it. Higher level concepts can presuppose knowledge but themselves state nothing.

'Table' is not true or false but valid or invalid.

'All S is P' is true or false and belongs in the S file-folder

Rand formulated rules for concept formation.

Aristotle formulated the rules of deduction.

This course formulates the rules for induction.

Statement of the "Problem of Induction"

Man is neither omniscient nor infallible. His generalizations are therefore not automatically correct. Thus the question: How can man know, across the whole scale of time and space, facts which he does not and can never perceive?"

Importance: false generalizations are contradictions in thought and a clash with reality in action

Motivational statement for students of philosophy: Except for a few axioms all the crucial principles of philosophy are reached and validated by induction.

use 'gen' for generalization

types of gen:

  • perceptual or abstract
  • narrow or wide in scope
  • quantitative or qualitative
  • pertain to consciousness or matter
  • descriptive or normative

Justification: Induction is not to be justified because it itself together with deduction are the means for justifying everything. Task is to explain how to perform induction.

Polemic: Must start with observation and focus on method for reaching a true gen. Cannot simply start with a gen and attempt to evaluate it without considering its genesis. Philosophers today concern themselves only with evaluating gens.

Constituents of gens are concepts and observations. How are gens formed and related to reality?

Method of enumeration is false. Enumeration is merely counting instances, and supposedly the bigger the count the greater the probability. No certainty possible. Subject to problem of the swan's. Enumeration provides no basis of moving from some to all. A true gen can be formed from a single observation, there are false gens based on millions of instances.

Investigative lead: science has used induction and made progress. Philosophers have made no progress. Therefore, induce a theory of induction by studying successful inducers. Abstract a general method from the method of physics.

3 Preliminary Points:

1) assumes familiarity with OPAR

2) am not claiming to be equal to Rand or Aristotle, this is my own application of Objectivism.

3) will assume audience is unschooled in physics. Examples taken from mechanics, electromagnetism and particle theory from Greece to late 19th century.


Science depends on prescientific knowledge. Must be able to identify conceptually the observed concretes around before forming gens. Tree, water, fire.

Early primitive generalizations are required, and a secular pro-reason pilosophy.

Generalizations are hierarchical: many gens are not available to perception, they require a context of previous gens

First level gens: are the empirical starting point for all generalizations.

Reduction identifies first level roots of a higher level product by traversing backward through the hierarchical structure involved, reverse of the order needed to reach the knowledge.

Ex. Galileo - horizontal motion is unaccelerated. Showed this by rolling balls on polished surfaces to remove friction. Had to know about friction first, perhaps by rolling a ball in tall grass and short grass and no grass. Also needs to know that 'pushing a ball causes it to roll'.

Ex. Modern idea that 'light travels in straight lines' requires realization that light travels. Not a perceptual fact until telescopes were invented. 'light travels in straight lines' is dependent on astronomy and telescopes depend on science of optics. Straight lines travel are perceived in via light rays that are tangential to the outline of an object thus producing a shadow. A shadow is a dark area with no tactile property, can disappear and appear, change with the light source, are produced when objects block light. Blocking comes from 'walls block balls', one can push or hammer on a wall with own hands to feel its resistance blocking motion through it.

Definition of First Level Gens - a generalization derived directly from perceptual observation , without need of any antecedent gen and as such is composed only of first-level concepts.

The perceptual is self-evident so first level gens are self-evident. Their status is axiomatic, not provable. "How do you know pushing a ball will make it roll?" has no answer except to push it and see. Observations such as this lead to the laws of motion, not the reverse.

First level gens are, like sense perception, invulnerable to overthrow by later knowledge.

A first level generalizer is not omniscient; contextuality applies.

Ex. A child learns pushing a ball makes it roll. Later he learns a ball won't roll if it is very large or glued to the floor or magnetically attracted. This does not make him wrong. That "A happens only under X conditions" presupposes that "A happens". Learning about the conditions expands knowledge.

Ex. Newtons Laws remain absolute in Newton's context and make possible the discovery of additional factors.

Knowledge possessed by a rational inducer is always limited but nonetheless real. Because it is limited it is open to further qualification. Because it is real, qualifications have no negative significance. A qualification is purely positive, an epistemological asset, a step forward.


Q: What is the role of volition in forming first-level gens?

A: Two things are self-evident in human cognition: 1) perception and 2) application of first level concepts. {Volition is involved in creating first level concepts}

Q: Relative versus absolute ignorance

A: Never use those terms. Hegel used omniscience for absolute. But all knowledge is absolute {without omniscience}. There is partial knowledge and fuller knowledge, but nothing is gained by restating that distinction.

Q: What if we don't have a full explanation?

A: What is a 'full explanation'? Explanations cannot infinitely regress.

Q: something about context

A: 'Context' is the knowledge that conditions and makes possible some cognitive item (concept or gen.) Using context as shorthand for 'the sum of all you know' is too broad.

Q: What is the standard for knowing that enough evidence exists for concluding a generalization is true (vs. merely possible or probable)?

A: OPAR development of possible\probable\certain still applies. There will be a bit more later for very broad gens.

Q: You said other sciences are reducible to physics. Overly reductionist?

A: Reducible in one direction does not mean deducible in the other direction. Ethics is reducible to the theory of man's nature, which itself could not be understood except on the basis of a certain epistemology, but ethics is not deducible from epistemology.

Q: Can one perceive a gen?

A: Next lecture

Q: When does one recognize the perception of the correct gen?

A: If you see the sun over there and feel the warmth on your skin over here, you are perceiving a correlation not a gen. You can perceive yourself pushing on a ball but perceive nothing about the sun, the sun example is an inference. Must perceive the 'why'.

Q: confused question

A: First level concepts have no prior gens.

Q: business method question

A: Can you establish a causal connection? Then ok.

Q: (Greg Salmieri) In Objectivism through Induction lectures you said "an induction of causality".

A: I reject that formulation now. Value of the lecture is still in the concretization of the ideas.

Q: Is a 'unit of red' a thing that is red?

A: No. 'Unit' is only used in epistemology, it refers to the attribute red abstracted away from the entity that is red.

Q: Reduction. Relationship of microscope to microbiology?

A: Reduction is not going to be a straight line, but a but a branching tree that also reduces all of the tools of measurement. Optics of microscopes is part of the reduction of microbiology.

Bonus question: Identify the error in the following argument.

An evil person is an irrational person.

An irrational person is an illogical person.

An illogical person is one who commits fallacies.

Therefore an evil person is one who commits fallacies.

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Notes on "Induction in Physics and Philosophy" Lecture 2

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}


The axioms of induction are first level gens.

All gens are statements of causality, direct or implied, from the first level on to the most abstract.

How does man learn causal connections? Only first level gens are being considered in this lecture.

Essential precondition of grasping particular causal connections is the grasp of the general law of causality.

In a Humean universe it is impossible to ask "Why?" of anything. Fact of causality and knowledge of that fact make possible the integration {of cause and effect}. Without both together only disconnected arbitrary data would be possible.

The law of identity and the corollary law of causality are implicit in all knowledge, even at the preconceptual and prelanguage stage of development. {see OPAR}

The question "what is it?" assumes the law of identity, "why" is likewise dependent upon law of causality.

How does a first level inducer grasp his first causal relations, and the explicit grasp of the concept 'cause'?

I Causality is perceived

A child's first causal discoveries flow from his own personal efficacy.

(this is not an original hypotheses)

(this is not necessarily universally true, it need merely be a likely or at least common path)

A child pushes away a ball and it rolls away. This is a pure experience of causation, it is ostensive and perceptual.

A child drinks water and thirst goes away. Perception of thirst quenching is a perception of causation.

We experience a direct connection between some events, not mere correlation.

First level gens are ostensive.

A child then turns from internal experience to the external world. "I make the ball roll" becomes "the wind makes the leaves flutter" "the fire makes the paper turn to ash" "the rain makes the ground wet"

These gens can be made after a single instance or experience because the causation is directly perceived as it is occurring.

The primary method of grasping a causal connection is to perceive it. Perception is essential, necessary and sufficient.

Scientific induction relies on indirect perception via instruments.

Thousands of instances of a disconnected regularity establish at most an hypothesis worthy of investigation

Ex. thousands of sunrises are witnessed by primitive man with no clue, inkling or sniff of causality as to why they happen. These observations do not permit a generalization, they are evidence for a gen that would be validated by later methods (Copernicus and Galileo)

Impersonal vs. Personal distinction must be learned. Default tendency is to construe personal experience outward and anthropomorphize motives onto inanimate (or animal) entities. This is the epistemological root behind animism and theism. Impersonal perspective was a Greek innovation and follows upon the law of identity. "Impersonal metaphysics"

II Passing from particular to universal

Problem posed is that percepts only ever reveal concretes. What mediates the passage from a causal connection between particulars to a universally applicable truth? The application of concepts.

Concepts are open-ended, formed based on only a few instances and then new instances are identified by the preexisting concept. In using concepts to identify the elements of a causal relation (fire, paper, burns) a "first level inducer" omits the measurements of the particular perceived causal connection. "Fire burns paper" is a conceptualization of perceived data, and is a generalization. Description in conceptual terms at once states a universal truth.

In contrast: "I see shimmering orange yellow turning those square sheets into a pile of hot white ash" is an nonconceptual description, and generalization is impossible from this description. The generalization actually comes before a descriptive account when first level concepts are at hand because the application of first level concepts is automatized. The gen is a direct product of applying the conceptual apparatus to the perceived connection.

Universality comes from the open-ended nature of concepts, which subsume all instances of the referents past, future, local, remote.

Summary: Our child inducer in the very act of naming what he perceives automatically drops the measurements of the perceived cause and effect, and thereby gains knowledge transcending the given context.

Animals perceive the same raw data but having no conceptual faculty cannot set aside particularity.

A gen in essence is no more than a percept of cause and effect conceptualized.

Induction is measurement omission applied to causal connections.

Validation of first level gens:

Perception is self-evident.

Application of first level concepts is self-evident.

Therefore there lay at the base of all future inductions absolutely certain first level gens which extend beyond all possible perception and which follow self-evidently from man's highly limited perceptual experience as and when this is processed by his conceptual faculty.

III Necessity in Induction

(discussion no longer restricted to first level gens)

Why is there a "problem of induction" but never a "problem of deduction"? Necessity.

Reasoning (all kinds) is inferring a conclusion from earlier knowledge. Conclusion follows from premises necessarily. If necessity is not present, the conclusion is a non sequitor and invalid. Necessity applies to all reasoning.

Ayn Rand taught "logic is the art of noncontradictory identification". Denying a necessary conclusion is a contradiction (of a premise or of logic itself).

In deduction the conclusion is implicit in the premise, there is nothing "logically new".

In induction, moving from "Tom, Dick and Harry are mortal" to "All men are mortal" is logically new. The conclusion is not implicit in the data about the named individuals.

Q: How then can it apply/be true that an inductive generalization is necessary? What contradiction manifests in denying a generalization?

First level gens are validated by perception and conceptualizing. How to validate higher level gens?

Long illustrative example: Benjamin Franklin's identifiction of lightning as electricity. Necessary conclusion drawn after a single experiment.

{Franklin background}

Franklin saw sparks to the Leyden jar, parts of the wet kite string repel each other, was later able to draw sparks from the Leyden jar, felt a shock while touching the jar and wire. The series of sparks and shocks would mean nothing to a child or savage, or even an ordinary educated adult of Franklin's day. The causation at work is not perceivable.

Franklin required concepts to identify what was happening. He needed these concepts: electricity, discharge, conductor, insulator, condenser. That conceptual framework enabled identification of what he witnessed: "Electricity discharged down a conductor to an insulated condenser."

"Lightning is an electrical discharge" is a necessary conclusion. A denial would contradict either his observations or a valid conceptual framework.

Perception and conceptual identification are constants for all induction from a child to a scientist. The difference lay in the scientist's complex conceptual framework.

The total conceptual framework is necessary to make the identification. Franklin drew up a catalog of everything known about electricity and lightning before forming his hypotheses.

Structure of Inductive reasoning


application of total conceptual framework

generalization out of necessity

Deduction is simple because it starts with a complex causal relation as a premise, taken for granted. "All men are mortal" takes concepts for granted.

Induction is the conceptualization process in action. An inductive argument is not self-contained series of premises leading to a conclusion. The bridge leading from observation to a necessary gen is not one premise (or 10 premises or 10,000) but a total conceptual framework.

Induction has been insoluble for so long because the nature of human consciousness has been misunderstood so long. A is A solves deduction. Rand's theory of concept formation solves induction.


First,thanks to Greg Salmieri who suggested a child experiences his personal efficacy in pushing a ball at previous year's OCON during the question period.

Q: Einstein doesn't know what gravity is, he merely looks for mathematical patterns. Is this like the primitive counting sunrises?

A: Not commenting on Einstein, who said many things at different times. Look forward to David Harriman's upcoming book the "Anti-Copernican Revolution" General pattern of modern science is to find a mathematical formalism that seems to describe a particular phenomenon well enough for successful predictions. Tinker with the formula when something comes up that doesn't fit. If you ask them what is the cause of this phenomenon they will throw out the idea of cause and effect and just say that there are events succeeding one another. Kant sets the epistemology. Quote from university days: "Physicists are not concerned with what "really" happens only with observed quantities."

Q: How to bridge from personal to impersonal understanding of causation?

A: Don't know, not as philosophically significant as the fact that there are these two perspectives. There is a problem in concretizing what is a first level concept in that it is contextual (baby raised in a furniture store example in appendix to ITOE). There are also options here, analogous situation.

Q: Will this material appear in a book?

A: The first two lectures are the first two chapters of a book called "Induction in Physics and Philosophy". Was in such constant consultation with David Harriman that he is now a co-author, and in fact the primary author. No time-frame. "Ominous Parallels" took fourteen years.

Q: (Christine) ??

A: Franklin is not deducing his conclusion that lightning is an instance of electricity.

Q: Is there additional measurement omission is forming gens above and beyond that of forming concepts?

A: No. Measurement omission of the gen comes from the union of the measurement omission in the concepts.

Q: Where do Mill's methods become involved in induction?

A: Mill's methods are involved as soon as you have to analyze to reach causality and not perceive it. Next lecture.

Q: What about critics based on "but you forgot about this factor"

A: Mistakes are always possible with any method, that does not inject uncertainty without a reason to suspect a particular mistake. Reject the arbitrary. And if we had critics that would accept reason, concepts etc. and just nit-pick that would be great.

Q: (Dave) What does it mean "The conclusion of deduction is not logically new"?

A: It may be new to you in the sense that you never thought of it before. Deduction is an important method of gaining knowledge. I am not deprecating deduction. "Not logically new" means the conclusion is not implicit in the premises. Induction and deduction have different relationships between premises and conclusion.

Q: Franklin and certainty. Franklin sees the sparks, knows of nothing else that could explain the sparks, so concludes that lightning is electricity.

A: Correct, but you make it sound like he is doing a lot of thinking. Once Franklin has the concept of electricity, it is not a matter of "electricity is the only thing that will explain what I saw" but rather "this is electricity", an identification not a selection of a most probable cause.

Q: Yesterday's bonus question:


An evil person is an irrational person.

An irrational person is an illogical person.

An illogical person is one who commits fallacies.

Therefore an evil person is one who commits fallacies.

This is the word play of rationalism. A thought progression that transforms one word to another and another is completely cut off from reality.

Many equivocations glossing over important distinctions. Irrational can be misusing reason or not using reason. Reason is the faculty of being rational, logic is the method of being rational. A child needs to be rational as much as anyone but doesn't know the method. A child can be illogical while being rational. Stringing together words like this is ridiculous.

This is a pure example of misuse of deduction. Starts with the word 'evil', combined with a pronouncement from an authority figure (Miss Rand). Then equate reason with logic, both are opposite to faith. Going wrong in the process of logic, which evil must, is called fallacy. Its just all up in the air like that.

If you learn nothing else in life, it is better to have no mental processes at all than to engage in this one. Rationalism gives the illusion of clarity, thought , precision when it is all day dreaming and free associating.

An inductive approach would be to look at some instances of evil. Then see if you can generalize and make a general principle based on integrated observations. As an example, consider Peter Keating in relationship to the virtue of independence. Keating does not walk around committing petitio, or stolen concept, or argmentum ad hominem. He looks to other people for answers. Nonthinking makes him dependent. He evades contradictions. Not being conscious is the essence of Keating's evil. That is independence, what out integrity and justice and so on? He you have to keep concretizing. And then you'd have to go into the relation between thinking and virtue. Only then could you talk about the negative side of unthinking and evil. How could you know thinking was a virtue without a standard of value? You would need a whole system of ethics as a conceptual framework within which to make identifications. That ethical conceptual framework can't stand by itself it depends on epistemology and metaphysics and those in turn grow out of observation.

If you did all this you would have no temptation to say evil is just fallacies. Some evil people commit fallacies and others just as evil don't bother to cover up evil with fallacies. Dr. Ferris doesn't bother equivocating to himself, he just evades.

Do you get the difference between the easy rationalistic floating along with no content and no relation to reality at all versus the tremendous challenge of an inductive approach which when you have you really then know what relates to rationality and what relates to logic. The whole field would be clear to you.

Sliding from one word to another without any concretes, without any individuals is just a little world of its own, and is wrong no matter where you start or where you end. It has nothing to do with cognition and is very harmful to your own mental processes and thinking. It is better to live and die confused than to try to untangle that confusion by drawing little lines in your mind that are disconnected from reality.

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Grames, I am very thankful for your notes. They are great!

But I have one question concerning this: "Application of first level concepts is self-evident." When you/Peikoff say that the application is "self-evident", what does that actually mean? Is this another way of saying that the application of first level concepts is automatized?

Furthermore, once a complex conceptual framework is established, is then the application of this framework "self-evident" in the sense that it is automatized?

I, for instance, do not have to tell myself, over and over again, when I read about a new statist scheme, that it will have bad consequences. I know it will and, given the total of my knowledge, I regard it as "self-evident". (I also react automatically emotionally because I immediately grasp the implication of what I am reading.) Of course, I am fully aware of the fact that without this knowledge it is not "self-evident" at all, why I am not suprised that other people do not necessarily draw the same conclusion from reading the same article as I do.

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"Application of first level concepts is self-evident." is true because everything needed to make the identification is presented via perception. All of the "evidence" is presented by the perceived entity itself in the act of perceiving it, no further proof or argument is needed.

In the Art of Thinking lecture 4 on Certainty Dr. Peikoff addresses the question "Must one preface all statements with "In the present context of knowledge."" The answer is no, one exception is the self-evident because that always "carries around with it" enough context which is directly perceivable that "the present context of knowledge" has nothing to refer to that could change an identification. If any additional context is needed beyond the directly perceivable that would constitute "further proof or argument" and preclude being self-evident.

A "complex conceptual framework" is complex because it is comprised of high level concepts. These can become automatized with familiarity and frequent use but can never be self-evident because not everything needed to make the identification is directly perceived. The similarity in applying first level concepts and applying complex conceptual frameworks is in the necessity to make the identification. However, that necessity is not what makes an identification self-evident. That common necessity can actually be 'felt' sometimes because of the automatization. Automatized and self-evident are not equivalent even though they can feel the same.

That was a good question and a useful distinction to make.

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Notes on "Induction in Physics and Philosophy" Lecture 3

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}


Science rises level to level through a hierarchy of gens.

Scientific knowledge is continuous with prescientific knowledge beginning with first level concepts and first level gens.

Science begins with the use of experiment.

definition of experiment - the method of establishing causal relationships by controlling variables

method comprises:

1) hypothesize all relevant factors (relevant based on other knowledge, contextual, reject arbitrary guesses)

2) eliminate all but one cause. two methods of elimination are Difference and Agreement

Difference - find "the difference that makes a difference" against a background a similarities

From Mill:

"Whenever there are two cases, the effect occurring in one case and not the other, and the only relevant antecedent difference is a certain factor which is present when the effect is present and absent when the effect is absent then conclude the antecedent factor A caused the effect B".

  • From lectures 1&2 conceptualizing A and B leads to the generalization 'A causes B'.
  • People know the method of difference implicitly; corollary of causality which is implicit
  • Difference is a valid method at any level of hierarchy; proper application is not necessarily obvious or easy
  • Differences against a background of similarities is parallel to concept formation. Nothing is more primary than similarity and difference
  • Again notice that number of observations is irrelevant
  • All generalizations are implicitly statements of causal connection reducible to form "Entities of a certain kind act in a certain way" or "All S is P"

ex. "The Sun rises in the east and sets in the west whereas the North Star does not." is equivalent to

"Something about the Sun is different from the North Star and that is why it behaves differently" - a statement of Difference

Agreement - find a similarity among relevant possible causes in a number of different cases exhibiting the same effect, conclude "same cause, same effect"

  • Also a valid method at any level of hierarchy
  • Again number of observations is irrelevant
  • Similarities against a background of differences is also parallel to concept formation.
  • Difference and Agreement can work hand in hand to confirm each other, but either alone is sufficient

J.S. Mill identified 5 methods, but Difference and Agreement capture the essentials. For example, concomitant variation can be understood as successive application of Difference.

Galileo - father of the experimental method, used here in an extended example of inductive scientific generalization about motion

Principle of Inertia - an object in motion remains in motion without needing additional force. Greek idea was rest is the natural and normal state.

Force causes changes in motion; falling objects all accelerate at the same rate. Greek idea was heavy objects fall faster.

Galileo was able to speedily make valid inferences about what was and what was not a causal factor because he worked within context. Philosophers of science bemoaning the difficulty

Discovery of these principles via a series of experiments (abbreviated presentation here):

Pendulum experiments - started with observing swaying of chandeliers in church, timing the swings. At home, noticed period of time required to swing is constant regardless of amplitude (length of swing, or angle at greatest height measured from straight vertical) Varied bob sizes, weights, strings, rods, amplitudes to eliminate possible causes of the relation between amplitude and period. Neglected color as arbitrary, neglected air resistance but there was no reason to think it wasn't constant.

Pendulum period is a function of length of rod/string - Galileo had to make a water clock for sufficiently accurate time measurements. He used method of difference to establish that the length L was proportional to the period squared t2.

Compared free fall to pendulum motion - adjust pendulum amplitude and height of fall h for simultaneous impact at blocking planks at bottom of pendulum swing and under the falling weight. Does this for a variety of pendulum lengths L. This sets one quarter of pendulum period t equal to time to fall. Found that distance fallen d was proportional to length of pendulum L.




d~t2 (and in fact from later experimentation d=16t2 using feet, the acceleration due to gravity is 32 ft/s2)

This last is Galileo's law of free fall, that falling is accelerated motion.

Galileo also knew from horizontally rolling balls no acceleration occurred.

Galileo predicts from the above two gens that a variety of moving objects not moving purely horizontally or vertically have a trajectory caused by a mixed motion of two components. Mathematically projectiles move in parabolas.

Quoting from book "Birth of a New Physics" Cohen pg. 112:

These analyses of parabolic trajectories are all based on the Galilean principle of separating a complex motion into two motions, or components at right angles to each other. It is certainly a measure of his genius that he saw that a body could simultaneously have a uniform nonaccelerated horizontal component of velocity and an accelerated vertical component, neither one in any way affecting the other.

Galilean component analysis is an abstract perspective on motion which is perceived as a single unitary action.

Philosophical comments:

metaphysics - every gen, law, equation, proportion is necessarily a causal statement. Galileo doesn't know why the things happen but he does know they happen and something in nature causes it to happen. That is a causal knowledge.

epistemology -

** Galileo's conclusions are dependent on the concepts he forms. He needs new concepts to think up the experiments and to understand the results. 'Speed' prior to Galileo was 'intensity of motion' or sometimes 'rapidity of motion', an unquantifiable idea. Galileo redefined speed as distance traveled over a given time interval.

**A concept is a green light to induction A concept makes induction possible and necessary. A properly formed concept uniting concretes by clearly defined essentials permits any attribute discovered of some instances to be inferred to exist in all instances of the concept.

Example of not inducing concept when necessary:

A child has concept of man as beings that walk around and make sounds. Then he learns the sounds are the men passing messages to each other. Then he goes to the next village, sees some more beings which he names men because they are moving and making sounds also. The child is asked "why are the men making sounds?" and he replies "I have no idea, I've never seen these particular men before".

{ see also “Anti-Conceptual Mentality” }

To emphasize the point: A concept is a green light to induction, a necessary precondition and a commandment to pass from some to all.

** An invalid concept or even imprecise concept (intensity of motion) is a red light. It inhibits, stultifies the process or leads to false generalizations.

** Any claim to conceptual knowledge involve two complementary process: reduction and integration. {OPAR Ch 4. Objectivity & 'Art of Thinking'}

Reduction of an experimental conclusion is pretty obvious, the data is available and the concepts that organize them. An integration for Galileo at this early stage could be the following:

Galileo knows a very high object is falling really fast when it hits the ground as opposed to dropping it from his hand. This can integrate with his experiments with pendulum amplitudes. Larger amplitudes start from higher points, so the bob ought to be moving faster through its arc. Faster travel through a longer distance could balance out with slower travel through a shorter arc to produce the constant amplitudes observed.

** Galileo's series of experiments reinforce each other through continuous integration. All point to the same conclusions because the same principles are at work. The series forms an overarching structure using the method of Agreement.

** Galileo integrated the principle of inertia with Copernicus' heliocentrism. Previous objections to heliocentrism were "why does a falling object drop straight down instead of being displaced?" and "why don't we feel a wind as the earth moves through the air?" Galileo's answer was to apply inertia and say the whole system of the earth and everything on it moves together with no additional force needed to push it along.

Integration is essential, not because the result of any of the experiments was uncertain, but because no element of knowledge no matter how well reduced can qualify as full cognition until it has been integrated to the full extent possible with the rest of knowledge.

Warning to Rationalists:

The process of induction does not consist in grasping some gens from experience and then sitting back in an armchair and doing some thinking. Observation is not merely the beginning, observation is needed afresh at every level of the hierarchy of knowledge. No matter how highly abstract our reasoning may be perception remains our means of remaining in contact with reality. The result of each of Galileo's experiments suggested another experiment. Sense-data are not a "jumping off point"

Quantitative Relations, Measurement, Mathematics

  1. Concepts used by a scientist must be defined in terms susceptible to numerical measurement
  2. Procedure of experiment consists in taking measurement (often need to invent new measurement devices)
  3. Results of an experiment are expressed in some mathematical relation
  4. Integration necessary to fully validate inductions in physics is made possible by their common formulation in quantitative mathematical terms. {Compatibility} Mathematics is the language of science.

("A is A" never "A=A" which is ridiculous)

Deep question: Why is it the case that measurement and number is so important and indispensable to induction in physics? Answer at end of course.


Q: Why would Aristotle not ever do an experiment as simple as dropping two bodies?

A: Action is characteristically modern attitude. Even the Christian God has plans, damns people, is a hubbub of activity. Active is good. Greek ideal is motionless. Motion is a sign of imperfection because the motion is toward something better. This is one good difference between the ancient and modern.

Q: If we heard a crashing sound behind the curtain behind you, could or must we conclude the sound was caused by entities?

A: Yes, but not necessarily entities located behind the curtain.

Q: Suppose the anti-conceptual child from the lecture had a reason to hesitate to induce in the new village. Say, everybody wore black pants in the old village, but nobody does in the new village.

A: Still wrong behavior, what child does not realize pants are not essential to being human? Pants can come off, separate from the person wearing them. Pants can be washed or thrown out without washing or throwing out the person owning or wearing the pants. Only a professor of philosophy could have this problem.

Q: Founding fathers of U.S. did not apply concept of man to slaves. What caused the error?

A: Contextual error based on evaluation of entire culture of european vs. african, imputing the present achievement level they saw as the best they could ever do, since they hadn't throughout history. Division of people into two types goes way back. 'Barbar' is greek root for barbarian meaning foreigner. Freedom was the antidote to this because former slaves (or women for that matter) that could read, write, work and achieve {Frederick Douglas} wiped out the myth of inferiority and the basis of racism. (Homosexual behavior would have been less prevalent among the Greeks if they hadn't derogated women as a class). Relating question to induction: Free blacks enabled induction to occur {Agreement? same effects, caused by same humanity?}

Q: Will you address generalizations in psychology such as metaphysical value judgements?

A: No. Psychologists should be able to follow the philosophical principles of induction, as other scientists follow the principles of induction found in physics. I am not a psychologist.

Q: First level concepts like "man is an entity that makes sounds", isn't this already a generalization? Chicken/egg situation which comes first concept or gen?

A: First level concepts are not at first formed on the basis of definitions in words, they are ostensive. "Man" must be first before "Man makes sounds". Generalizations must be explicit because they are conscious inference, while concepts can be implicit.

Q: Is lack of measurement in social science responsible for their lack of progress compared to natural science?

A: No. Measurement does not have as central a role in social science. See last lecture.

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Notes on "Induction in Physics and Philosophy" Lecture 4

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Supplemental course material.


Micheal Faraday creates the new concept of 'field' and enables a host of inductions leading to James Clerk Maxwell and all of modern technology.

When an apple falls to the ground its motion is due to two factors, the apple's mass and its position relative to the Earth.

Since the mass is constant, the force varies depending on the apple's position in a 'force field', the potential net force exerted on a body located at a particular spot by all surrounding bodies. Fields apply to gravity, electrostatics, magnetics. Fields enable rejection of "action at a distance".

What underlies the field? There must be something really there. Ether - underlying and all encompassing material comprising the universe. Jocular definition of ether used by Rand: "that which is where nothing isn't".

definition of field: the continuous state of some physical stuff that gives rise to a net force when a body occupies a given location.

epistemological result of the 'field' concept: two bodies apparently separated and distant from each other are connected by a field between them, a cause which should lead to certain effects.

illustration: handout diagram on magnetic lines of force around a bar magnet. Iron filings will line up along these lines. Fields are real, not just a construct.

With an idea of a physical mechanism to communicate forces, Faraday is on the lookout for examples of that connection in action. It was already known that current in a wire had magnetic effects (deflected a compass needle). Faraday theorized a magnetic field could cause a current.

Skipping to Faraday's decisive experiment, he found a moving magnet and changing magnetic field created a current in a perpendicular loop of wire. Also found direction of motion changed the direction of the current. Relative motion was significant: same effect could be generated by a static magnetic field and a moving loop of wire.

Philosophic comments on this experiment:

  • has reduction to percepts
  • numbers, measurement, math are everywhere. magnitudes, velocities, angles. Results were proportionalities.
  • integration to other knowledge - field makes possible understanding the two phenomena. Without field, the observer is looking at a "black swan", an incomprehensible concrete. {a miracle? magic? Arthur Clarke comment on tech and magic}
  • use of method of difference
  • speed, confidence and certainty of the induction reached. Totally unlike the presentation of scientific process in LP's philosophy classes. No agonizing over arbitrary 'other factors' Experiment takes place in an established context of knowledge that defines and delimits possible relevant factors.


Mathematical Derivation of the Inverse Square Law for Gravity by Isaac Newton

Force is proportional to 1/R2

Mathematics is the science of measurement. Also: Mathematics is the relation of some quantities to other quantities, or of some measurements to other measurements.

Pattern of Math "an immense deductive structure"

In the calculus, Newton formulates methods to determine a quantity at an infinitesimal, split-instant of time. Also provides a method to sum up a series of infinitesimals into a whole. Both methods necessary for measurement of a continuously varying quantity {an analog vs. a discrete quantity}

Newton generalizes from "force causes acceleration" to "force causes a change in direction". Newton formulates the Law of Inertia: "an object at rest continues at rest and an object in motion continues to move in a straight line, unless acted upon by an external force." This is Newton's First Law of Motion.

Newton then considers circular motion, such as a planet in orbit. There must be a continuous force acting centrally. Empirical test was a rock on a string, he could feel the centripetal and centrifugal forces.

Note: this refuted the Greek idea that circular motion was natural. Now it was straight linear motion that was natural and circular motion only occurs under acceleration.

Note: circular vs. elliptical orbits. Kepler had earlier proved orbit were ellipses, but Newton simplified, then later revisited the issue for the general case of elliptical orbits.

Newton needed a new concept of motion to refer to both changes in speed and direction as accelerations. He created the concept of a vector

definition of vector - a quantity which is a magnitude and a direction. (Contrast with Scalar - a magnitude)

Vector makes possible an explanation of the motion of the moon and a falling apple as obeying the same principle.

A valid concept is a green light and commandment for induction. An invalid concept is a redlight and obstacle to induction.

Example: early chemistry considered all gases forms of air, regardless of composition. Leads to wrong conclusions such as "steam is a gas which can be breathed"

Example: alchemists named compounds by how they were formed. Refining antimony by removing sulfur from its ore can be accomplished in a nummber of ways.

heating with iron created "Regulus of Mars"

heating with lead created "Regulus of Saturn"

heating with tin created "Regulus of Jupiter"

heating with copper created "Regulus of Venus"

Natural consequence of the multiplicity of names is to hesitate to claim that the properties of any of the substances are the properties of any of the others.

Lavoisier quote - "A well composed language will not allow the teachers of chemistry to deviate from the course of nature. Either they must reject the nomenclature or they must irresistibly follow the course marked out by it. The logic of the scientists is essentially dependent upon their language." Brilliant statement about the concepts behind the words.

Return to Newton's derivation of the ISL

{summary: derives a force law for uniform circular motion; derives an similar expression from Kepler's first law; substitutes and concludes F proportional to 1/R2}

Unresolved issue was could the inverse square law apply to the Earth's moon and a falling apple on the Earth's surface? Direct observation could not prove anything as the moon does not vary its distance from the Earth. But the acceleration of the apple and the acceleration of the moon could be compared.

Newton assumed apple is 1 Earth radius from the Earth's center (proved the point source approximation later). Greek Aristarchus proved moon was 60R from the Earth.

For apple F ~ aapple ~ 1/R2

For moon F ~ amoon ~ 1/(60R)2

aapple/amoon ~ 3600R2/R2 = 3600

aapple = 32ft/s2 from Galileo

amoon = aapple/3600 = 32/3600 assuming ISL holds.

Verified without assuming ISL by using the Law of Circular Acceleration.

At this stage Newton regarded his conclusion as probable, not certain. A number of approximations were left to be proven later: circular orbits vs. elliptical, point source. But those were done.

All these: Galileo's observation of the horizontal component of motion, Newton' inference to the law of inertia, the concept of vector, the law of uniform circular motion, Kepler's third law, moon's distance from the Earth, an apple's accelaration, all of it was integrated into the I.S.L. by mathematics. This is not a straight line mathematical deduction, but a stop and go, import more observation, then deduce more, process.

Math is more abstract than physics, which is why it is so important. Gives hypotheticals to a scientist "If you have this, then that and that follow". Math subsumes a physical situation under a more abstract model. On the other hand, by doing this it enables the physicist to be more specific than otherwise possible. Qualitative statements are dead ends for integration while equations and proportionalities can be combined and integrated into new statements.

Q: Definition of field used 'continuous'. Also referred to ether. How is this established?

A: Will answer question "Is the universe a plenum?" Answer is yes, established by metaphysics. Parmenides. "What is, is. What is not, is not. What is not can neither be nor be conceived." There are no little areas of 'what is not' peppered throughout existence, there is just a solid spread of 'what is'.

Q: Kepler - how did he generalize from 'Mars moved in elliptical orbit' to 'all the planets moved in elliptical orbits'.

A: Kepler did not have a clear idea of what was happening, but he did have the idea that some force from the Sun kept the planets in their orbits. Since the Sun is the common factor in all the orbits, then it is causing all the planets to have similar orbits.

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Grames , There are parts of this lecture that have been abandoned by Dr Peikoff. I recognized certain problems immediately. I'm wondering if you did too? I started transcribing the whole lecture in order to dissect and confront it ,but thought to email Dr. Peikoff first, as he mentioned that he didnt think it was his final word on the subject. He confirmed my position openly.

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Yes, this current version of the course comprises the later parts of an old course and two new lectures at the front. There are continuity problems. The first two new lectures are vital and lay out how induction is accomplished in principle. The middle lectures are a tour through the history of science, and can't change much. The final lectures on how induction works in philosophy are not coordinated with the new content of the first two lectures so he could be making different points if he revisisted the topic, or the same points more strongly.

That is just what is internal to this course, if he has made other comments in more recent venues I wouldn't know of them. I would be grateful if you could indicate which points are up for revision, particularly so if they involved the first two lectures.

The next lecture is ready for typing up as a post.

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Notes on "Induction in Physics and Philosophy" Lecture 5

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Supplemental course material.


James Clerk (pronounced Clark) Maxwell is to electromagnetism as Newton was to mechanics.

Discovered a changing electric field creates a magnetic field. ex. magnetic field around a charging capacitor (only while charging/discharging)

J.C. M. reached this discovery by mathematics alone. Verifying observations came from later experiments.

Follow-on discovery that changing E-field causing changing B-field {B is magnetic}which causes a changing E-field ... led to description and discovery of electromagnetic waves. Wave properties such as propagation, reflection, refraction, interference all can be inferred from the e.m. wave equation.

Speed of propagation was found to be 186,000 mph, the same as optical light. Enabled identification of light as an example of e.m. waves.

E.M. and Optics were integrated and the means of integration was mathematics.

In physics math is essential and of the deepest importance. "Why?" is answered decisively in the last lecture.


How can the last, widest fundamentals in a field be proved or validated? They cannot be perceived or verified by experiment because they are too abstract, too far removed from concretes. No chain of mathematics can do it.

What says the Inverse Square Law applies to the entire universe?

These principles are primaries, they cannot be derived or deduced from anything bigger or deeper {universe is the biggest concept there is}

{see Notes on "The Art of Thinking" for a fuller explanation of primaries}

A wrong answer is the hypothetical deductive fallacy. "If theory predicts all the observed data it must be true"

If you are a man, you are mortal.

The pig is mortal.

Therefore the pig is a man.

What is necessary is the statement "ONLY this theory predicts all the observed data."

How can we know no other theory will ever be possible? Maybe what you think is impossible is just the result of a poverty of imagination or a limitation of knowledge?

"A broad theory is true when it represents an integration of diverse fundamentals within an intensively studied area."

Fundamentals from at least two different fields, then integrated together.

An intensively studied area is required to ensure enough context has been acquired to reach a fundamental.

All along the ascent of greater integrations the lesser fundamentals eliminate possible competing theories until at last only one possibility remains.

Alternate candidate theories are not just subjectively inconceivable but objectively arbitrary and must be dismissed.

Analogy: Author writing a novel. At the beginning a novel could go in a hundred different directions even with the same characters and theme. Further along the writing process, choices are made and future possibilities narrow. Near the end, the writing races along because there are few choices to make. Established characters and prior circumstances constrain what can happen at the conclusion.

An integration of fundamentals is a super-integration.

Ex. Newton's Laws of Motion and of Gravity explain and integrate all of the discoveries in astronomy and physics. They are super-integrations.

Passage from possible, probable, certain is apparent.

On early, lower levels and identification with certainty can be made in one leap.

Coordinating results from multiple fields typically takes time for the fundamentals to be established.

Ex. ATOMISM - validating a universal

Atomism is the theory that matter is particulate, all matter throughout the universe.

(will skip the math, we already studied the role of math in physics)

(atoms/molecules considered equivalent, molecules are made of atoms)

Didn't Democritus prove atomism by pure philosophic deduction? No. Democritus rationalized by taking for granted unproven and even false principles, such as his principle that "motion is impossible in a plenum"

FACT: Count Rumford while having some cannon bored out while submerged in water noticed the water temperature increase and steam formation. That is all that changed by the drilling. (Difference) The motion of the drilling did not cause the vat of water to move as a whole, it must be that some internal parts of the water are in motion. If heat was a continuous fluid, how could drilling introduce an endless supply of this fluid?

STATUS: AMBIGUOUS. "Possible" requires movement toward a defined proof, which is still unknown. Unexplained is the water transforming to steam. Contradictory evidence existed that was explained nicely by the fluid theory of heat (mixing liquids at different temperatures produced a mixture at an intermediate temperature). Conservation of heat is easily comprehensible if it is a substance, but how can motion be conserved?

FACT: Discovery of "Law of Definite Proportions" in chemistry. Complete reactions were always the result of integer ratios of substances measured by weight. If matter were continuous why would elements do this? But if elements are made of atoms then the nonexistence of half-atoms or fractional atoms explains the impossibility of fractional reactions.

STATUS: POSSIBILITY Congruent evidence from 2 diverse fields, heat and chemistry. No evidence from mechanics or e.m.

(jumping ahead in the history)

FACT: Avogadro solved a certain problem in the chemistry of gases by hypothesizing equal volumes of gases contained equal numbers of molecules. This enabled a determination of relative atomic weights. Also sorted out which gases are diatomic. Big step forward for atomic theory because it allowed measurement within the theory.

FACT: Electrolysis of hydrogen bearing compounds showed hydrogen was electropositive (it collected around the negative plate) This created a question: how could two like substances form into one compound in violation of the 'opposites attract' principle of electricity?


FACT: "Law of Constant Heat Capacity" discovered. Heat capacity is the amount of work required to raise one gram of substance by one degree ©. "Law of Constant Heat Capacity" is that measured heat capacity of a substance multiplied by the atomic weight of that substance is a constant. Explanation from atomic theory was that each molecule absorbs the same amount of heat.

STATUS: PROBABILITY Fluid theory of heat is incompatible with the idea of atomic weight, so is a real problem for that competing idea.

FACT: Isomers discovered in chemistry. Different compounds can be made from combining the same elements in the same proportions. Atomic explanation was a different internal structures among compounds. Methyl Alcohol and Methyl Ether

FACT: Faraday's electrolysis experiments showed electricity comes in discrete units.

FACT: J.J. Waterston discovered the "Ideal Gas Law". This has universal implications because it is known that all substances become gases if heated enough. PV~nmv2 P pressure V volume n number of atoms m atomic mass v velocity of atoms. Charles' Law established PV~T where T is temperature. Thus T~nmv2 establishing temperature is a form of kinetic energy of the atoms.

STATUS: PROBABILITY Not a certainty because the 'billiard ball model of gases' behind the Ideal Gas Law is an assumption still unproven. An independent demonstration of the Ideal Gas Law was needed.

FACT: Slow dispersion of gases was a problem. Computed velocity of atoms is very fast, but gases that can be smelled can be perceived to cross a given distance much slower than that. J.C. Maxwell working on pendulum damping found that damping was a constant as a function of air density. This was deduced from the Ideal Gas Law in 1867 and verified later experimentally.

FACT: Mendeleyev's Periodic Table of the elements was organized by atomic mass and valence. Predicted 6 new elements based on holes in the table. 6 new elements were found.

STATUS: Atomic theory explained Avogadro's Law, temperature, Ideal Gas Law. Avogadro's Law explained chemistry, valence, periodic table of elements.

By the 1870's enough evidence had gathered to regard atomic theory as proven jointly by chemistry and physics. Waiting until Brownian motion is too late.

Transition points are debatable within limits and are not quantifiable. The need for an overarching super-integration of fundamentals is indispensable.

Philosophers have claimed such integrations are impossible but they have been accomplished and withstood the test of time and later discoveries.


1. At every stage of science, valid concept formation is essential because valid concepts are the only green light to valid induction.

2. Induction begins with self-evident, first level generalizations, to which all other generalizations must ultimately be reduced.

3. Induction requires the contextual discovery of causal connections, using methods of Difference and Agreement.

4. Induction at every level beyond the first level requires integration with other knowledge - and on the highest levels requires the discovery of principles which integrate fundamentals from a diversity of fields.

5. In the physical sciences, after their early stage, the above steps depend on and are performed through and only through mathematics.

Note parallels to rules for concept formation

1. Valid concepts

2. Reduction to first level concepts

3. Definition by similarities and difference in essentials

4. Integrate hierarchically and horizontally

5. Measurement omission


Science is self corrective so long as the correct method is followed.

Honest Errors by Scientists

Overgeneralization - corrected when new contexts and qualifications are discovered

Imperfect fit - corrected by a better theory. Newton fixed Kepler's 3rd Law

Mistaken explanations - when other theories are still possible. corrected when new unexplainable data appears

Premature Integration - refuted by later data. Ex. Kepler's attribution of the Laws of planetary motion to magnetic influence from the sun

Committing fallacies in deduction is not a 'problem of deduction' or an attack on deduction, neither are errors in induction a special problem for induction.

Errors at Large

Absence of any defined method, leading to reliance on emotions and authority. No other explanation is possible for the absurd "inductions" in racist and rationalist generalizations. Always the pretense of evidence in these cases is enumerative swan counting, not causation discovering. Emotionalist and authoritarian corruption is not confined to induction but is a general problem for all thought.

Philosophical Issues

- this presentation has been based on Objectivism

- intrincism, skepticism, empiricism, mysticism will cut the thinker off from reality

ex. Progress was rapid in electrical phenomenon once discovered because the Bible had no dogma about electromagnetism

Worst enemy of science today is not 'religionists' but the skeptics who only want to 'save the appearances' and give up theorizing about reality.

from textbook "Modern Physics" by Van {somebody} in a relativity chapter:

"The question might now be raised as to whether or not a moving rod is really shortened by its motion and a moving clock really slowed down. The answer of course is that motion has no effect on the properties of a measuring rod or clock. However the real length of a rod plays no part in physical theory, only measured quantities are of interest."

Logical positivism and empiricism rejects any conceptually reached knowledge of reality. Uninterpreted formalisms are the favored method. LP as a student in a quantum mechanics class watches a professor come in and put a big T and a lowercase t on the board. Prof says "For every big T there is a little t". LP asks "What does T stand for?" Prof responds "The terms are uninterpreted at this stage, they have no meaning."

Quote from Professor of Evolutionary Genetics @ University of Leeds, England from Apr 16, 2000 NYT Book Review.

"Personally I like to think of the universe not as a machine but as a bus network in which the identity of the buses and the reason they keep running are ultimately unknowable. Science is like a bus time table. Forget truth. If you can put together a good timetable you will have a much better chance of catching a bus."

Occam's Razor - "Entities are not to be multiplied beyond necessity." Utterly invalid, truth is not necessarily simple. "Correspondence to reality" is superior to "fewest elements". At best, Occam's Razor is a misguided way to state "avoid the arbitrary". Using Occam's, reality can be discarded because it complicates the equations. Reality is not simple enough.

Q: How do I know a first level gen is really first level?

A: Self-evidency, which is perceptual. There is no further test for 'perceptual or not' than 'can you perceive it?'

Q: Atomic theory was applied to explain things before it was proven.

A: Even before reaching proven status it has evidence in its favor so is not arbitrary. {A theory can only be proven or disproven by attempting to use it}

Q: How can calculus and continuous variables validate a theory of discrete phenomena such as atomism or QM?

A: Pass {answered next lecture}

Q: Why are your proffered Razors valid. "Gens are not to be multiplied beyond necessity."

A: Context was specified, not left at mere simplicity. All 'Razors' state that something should not be multiplied beyond necessity. The difference is what is necessary. Occam's supplies no context beyond counting elements. Rand's Razor is not arbitrary like that. {this question revisited again next lecture}

Q: Modern science textbooks

A: Separate the first handed info from some authority's theory. David Harriman is preparing a text based on a hierarchy. Ayn Rnd used to say to me "Your classes are not a total waste because you can learn in reverse. Keep asking yourself "What is wrong with what this guy is saying?""

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I would be grateful if you could indicate which points are up for revision, particularly so if they involved the first two lectures.

Basically the parts of the lecture that involve "super-integration" are no longer a part of his thesis.

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Hey Grames, when can we expect more notes? :) I am so eager to see where this is going.

Soon. I'm finding it difficult to avoid the pitfall of writing a transcript with this lecture. I hate mangling his points but I have to get over it.

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Soon. I'm finding it difficult to avoid the pitfall of writing a transcript with this lecture. I hate mangling his points but I have to get over it.

Here is a suggestion: write your notes as usual and then only quote him (extensively) once or twice, if you do not know how to present a very important point in a short and concise way.

Edited by knast

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Notes on "Induction in Physics and Philosophy" Lecture 6

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Supplemental course material.

Lecture 6 Induction in Philosophy

Similarities and Differences between Philosophy and Physics

Physics - science that studies the nature and laws of matter and energy

Philosophy - science that defines the proper relationship between a volitional consciousness and reality

"proper relationship" means a consciousness in contact with reality and guided by it in all its choices

The essential question of philosophy is "how is one to be guided by reality?"

The absence or silence of philosophy permits all of the following claims:

Pope claims to be in contact with reality through God

A liar claims to be in contact with reality, he recognizes lying is a means of survival. All men are crooks, strike first.

A dictator claims to be in contact with reality, the reality being man creates reality and if he doesn't set the terms someone else will.

A modern artist claims to be in contact with reality, a subconscious nonrational dimension made of nonentities.

John Galt claims to be in contact with reality, and reality requires him to go on strike to assert his rights.

Who is right, who gets to decide, how do we know the method?

Differences of philosophy from physics:

1. Philosophy deals with consciousness, physics omits it

2. Philosophy is normative, physics descriptive

3. Philosophy is broader than physics

4. Philosophy is known by everyone (at least implicitly) physics can be ignored for a lifetime

Which is broader, "inverse square law" or "man's life requires independence"? Independence has as its context and content man's relation to reality, the total of reality, everything that exists including matter, energy and the inverse square law. The Law of Gravity must be understood first-handedly, not through conforming to consensus or faith in your science teacher.

One can't pursue knowledge in a narrow field without knowing what counts as knowledge in any area, and how to gain it. Same for values and ethics, as values are a type of knowledge for man. Philosophy is fundamental to all knowledge, fundamental as in 'makes possible'. Philosophy provides guidance on how to stay in contact with reality at every point where there is choice and action.

Philosophy is hierarchically prior to all other sciences. Philosophy gives us reality, a means to knowledge, knowledge of the nature of values. These enable pursuit of special sciences.

Similarities of philosophy to physics:

1. Philosophy is an inductive science, just like physics (except metaphysical axioms see ITOE and OPAR)

Philosophy is just another type of knowledge, so is subject to the methods of all knowledge. Philosophic norms are not innate or self-evident, they are learned in painstaking hierarchical fashion starting from perception, just as in discovering physics principles. Nothing is deduced or deducible from metaphysical axioms.

All knowledge comes from observation, including knowledge about the method of knowledge.

Conumdrum: we need the method of induction to induce the method of induction

Resolution: there are first level philosophic gens available because they are self-evident. Thses form the starting point for climbing up the hierarchy of philosophical knowledge.

ex. Choice/free will is discovered in the same way as pushing a ball makes it move. Will makes the arm move, it is the same before and after. Method of Difference singles out the phenomenon called will'.

gen - "My decisions move my limbs"

gen - "My decisions move my thoughts"

gen - "My thoughts cause my actions"

observation - "others move their limbs, act as I do"

gen - "Man is a being of volitional consciousness" by method of Agreement

All of this is as certain as first level gens in physics. No proof necessary or possible. Any analysis of other possible causes of moving your arm assumes the freedom to direct your thoughts.

ex. Senses

observations - a child closes eyes and world dissappears. Holds nose and smells disappear. Fingers in ears make sounds disappear.

gen - "My senses are my only contact with what is out there". will lead to validity of the senses

gen - "The objects of perception fall into patterns of similarity and difference." leads to basis of valid concept formation

gen - "There are no pure similarities, only similarites against a background of differences" leads to context

ex. Ethics

observations - pleasure and pain

gen - "pleasure is positive & to be desired. pain is negative and to be avoided" self-evident, true for animals as well as humans, forms basis of all values because they are hierarchically later than pleasure & pain.

Corollaries as horizontal integrations

Some self-evident gens can at a later stage of understanding be recognized as corollaries of axioms. Even corollaries must first be grasped independently and inductively. Only after knowing first level philosophical gens for years and taking them for granted can then some of them be integrated with the metaphysical axioms by recognizing their corollary relation.

NOTHING IS EVER DEDUCED FROM THE METAPHYSICAL AXIOMS. 'Cause and effect' does not fall out of 'A is A' no matter how long one stares at it. Objectivists are not rationalists. Let this expurgate the last temptation to rationalism in Objectivist thought.

2. Philosophy and Physics both use the methods of Agreement and Difference.

Philosophy does not use controlled experiments because

- human rights prohibit the manipulation of people

- volition means there is always an uncontrolled factor at play

- since a partly correct philosophy is necessary to live at all, it is impossible to make a conclusive experiment in Difference where one group has a purely wrong philosophy

Projecting ideals in art or creating Auschwitz are in a sense experiments in philosophy, but they do not originate knowledge as physics eperiments do. Ayn Rand had to know her philosophy before writing Atlas Shrugged. Nazis had to know what they were doing in creating Auschwitz. LP needed to know Objectivism to identify what they were doing.

Personal experience and history both provide a bounty of opportunities to use Difference and Agreement to reach philosophical gens.

ex. Honesty {long example omitted}

ex. Politics {long example omitted}

ex. Epistemology {long example omitted}

ex. more Epistemology

obs - You fear something will happen, but it doesn't

obs - You want something badly, but it turned out hurtful

obs - You followed God's commandments and ended up in the gutter.

obs - You followed society's commandments and ended up in a psychiatrists office.

gen - "I can't trust emotions or authority, I need something better to come to conclusions"

4 sources of data from which to make 1st level philosophical gens:

- own personal life, introspection and observation of others

- history, "the laboratory of philosophy"

- litrature, the great novels and plays, Objectivist or not

- news & current events, least valuable because not essentialized by historians, bad journalism

3. Philosophical gens are integrated into principles, just as in physics

All the gens about lying are integrated into the principle of honesty. Suppose our inducer has also learned sbout justice and other virtues. He can integrate these into rationality, an integration of principles. "If man acts according to reason he achieves his values, if not not." This will not be a floating abstraction because his context is jammed full of gn about lying, work, punishments, rewards, etc. This is not rationalistically deduced from "Reason is man's means of survival."

All gens about FCC regulations, labor laws, ancient pharoahs, the United States integrate into the principle that "man must be left free to achieve"

Gens about untrustworthy emotions, no infallible authorities, needing a method for gaining knowledge, Aristotle's logic, integrate together into Ayn Rand formulation of Objectivity.

The necessity for rationality in action, individual thinking even in society, objectivity in thinking all integrate into "reason is man''s means of survival and fundamental attribute"

Early gens alone are dead ends unless integrated (empiricism)

Principles are arbitrary without their lower level gens (rationalism)

Principles are known to be objective when they are proven inductively. (inductively, not just 'proven')

Objectivity in both physics and philosophy means reducibility to perceptual observation and first level gens.


Being able to give examples is not enough understand a principle. You must be able to derive the principle step by step from first level gens. {For the same reason derivations are taught in physics and math} Gravity is self-evident to everybody but no one understood it until it was approached hierarchically by Newton. Independence has exemplars in Roark and Keating, but if being able to identify the referents is all you can do then you miss everything that deriving independence hierarchically and inductively would have taught you. One cannot claim to understand independence while lacking its context, its forms and varieties, the consequences of having it or not, relation to other virtues and principles, etc...

Concretizing an abstraction is only a good first step in the long marathon of traversing the hierarchy of knowledge.

4. Concepts are a green light to induction

ex. Ayn Rand's original formulation of objectivity

objectivity in art - representationalism

objectivity in rights - rights are not sourced or subject to collective or supernatural decree

objectivity in laws - selective interpretation and enforcement as in anti-trust law is evil

objectivity in nature - only that reducible to sense data is real so goodbye to God

Contrast with Hegelian objectivity which means collective. Then consensus is an infallible authority, individuals should obey and conform to others even if it means sacrifice.

ex. invalid definition of man as 'the social animal'

this cuts off all inductions and integrations based on rationality "Man needs love" has truth when understood as needing to share rational life-supporting values and to give and receive appreciation for achievement of those values. If man is essentially social not rational then all men are Peter Keating and unconditional love is the ideal.

Only valid concepts are green lights to induction. Abstract thinkers that can form new valid concepts are critically important.

Recall the alchemists many names for antimony based on how it was produced. We have the same situation today in politics where people cannot recognize the similarity of Soviet communism to the modern welfare state, or that conservatives and liberals are essentially authoritarian because one is produced by religion and one produced by Marxism.

All gasses were called 'air' and no progress was possible until that package deal was broken up. Same occurs when all satisfactions of any desire no matter how are equated with 'selfishness'. Same occurs when all frustrations caused by others no matter how are packaged together as 'enslavement'.

5. True fundamentals are irreducible

There cannot be an infinite series of "whys?" "It is" terminates every inquiry.

ex. Existence is irreducible. Heidigger's ludicrous "The main question of philosophy is why is there anything at all rather than nothing."

ex. Man has a conceptual consciousness. Why? "It is." Nothing learned about the brain will answer this 'why' because all lower level observations, gens and principles are all united in this fundamental.

Physics and Philosophy both seek the fundamentals. If fundamentality is the basis of scientific validity, then philosophic theories are the most scientific of all theories.

6. Validation of an idea is the combination of both reducibility and integration.

{testing for reality and noncontradiction. See Notes on Art of Thinking}

7. Inductive errors in philosophy

Same as in physics, but due to lack of any method there is far more emotionalism and authoritarianism.

When approached factually philosophical errors are also self-correcting. Greeks thought democracy was the opposite of theocracy and autocracy. Locke and Jefferson identified what was wrong with democracy.

Next lecture: Physics is a science because it uses math. Philosophy does not, cannot use math. How can philosophy be inductive without math?


From previous lecture, Occam's Razor - "Entities are not to be multiplied beyond necessity." Utterly invalid. Versus "Concepts are not to be multiplied beyond necessity." Rand's Razor is epistemological while Occam's is metaphysical. Concepts are tools that serve the purpose of cognition, choose to create a new tool only when that purpose is advanced. But Occam says "something doesn't exist if something simpler can exist" ex. "there are no epicycles because we can get along without them" But foisting a criterion of simplicity upon reality is primacy of consciousness.

Q: How can calculus and continuous variables validate a theory of discrete phenomena such as atomism or QM?

A: The discrete things still move continouosly.

Q: (Betsy) Philosopher disputes with a physicist. "There is a contradiction" "But you haven't looked at my data"

A: Philosopher wins. Noncontradiction is the precondition of all knowledge.

Q: Can philosophy say anything positive in physics? {Entity ontology?}

A: No. Entities are perceptually given but that does not imply that entities are the ultimate constituents of matter. There must be something, an existent, but that says very little.

Q: How did concept of energy lead to inductions and discoveries?

A: Through conservation of energy. 3 examples

Radioactivity - surplus energy around radioactive materials theorized to be from nuclear decay

Heat from the sun - Sun produces far more energy than any known source could account for. theorized nuclear fusion

Nuetrino discovery - missing energy in certain particle interactions must have been carried off by a new particle

Q: Is space an entity?

A: Who gets space? Physics. Metaphysics does not cover time and space. Kant added that. {Did Kant get anything right?}

Q: (written submission) "I have understood for some time that an experimentation with no explicit hypothesis is invalid ..."

A: WRONG. It is not true that a prior hypothesis is required. It is a Kantian idea that we can't learn things from perception but must have some a priori category to guide us to a conclusion. All that is needed is a context. ex. Faraday by trial and error found lead borate could polarize light waves if he shined light along the crystal in one direction and applied a magnetic field in another direction. He had no idea if that would work until he tried it.

Edited by Grames

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Corollaries as horizontal integrations

Some self-evident gens can at a later stage of understanding be recognized as corollaries of axioms. Even corollaries must first be grasped independently and inductively. Only after knowing first level philosophical gens for years and taking them for granted can then some of them be integrated with the metaphysical axioms by recognizing their corollary relation.

NOTHING IS EVER DEDUCED FROM THE METAPHYSICAL AXIOMS. 'Cause and effect' does not fall out of 'A is A' no matter how long one stares at it. Objectivists are not rationalists. Let this expurgate the last temptation to rationalism in Objectivist thought.

Does Dr Peikoff explain how this relates to earlier his statement in OTI, that the law of cause and effect is induced, and his later statement, in this course, that it is not? Or is he only saying that the self-evident perceptual/axiomatic experience of causality is _later_ integrated with A is A and can then, as a result, be _explicitly_ viewed as a corollary to the law of identity?

Edited by knast

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I'm glad you picked that passage to quote. I think it is one of the more important statements about the Objectivist method of reasoning and I've erred exactly the way he described.

Salmeiri asked a similar question at the end of lecture one;

Q: (Greg Salmieri) In Objectivism Through Induction lectures you said "an induction of causality".

A: I reject that formulation now. Value of the lecture is still in the concretization of the ideas.

My understanding is that the Law of Identity and the Law of Causality can be and are grasped separately, and then it is a later act of horizontal integration that relates the two together. Or least that is the proper way to learn the relationship.

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Notes on "Induction in Physics and Philosophy" Lecture 7 (the last)

Not a transcript. These notes paraphrase the speaker's points and are not accurate quotes unless in quote tags. {Curly brackets denote my comments}

Supplemental course material.

Lecture 7 The Science of Philosophy

So far in this course we have established

  • what induction is and how it is done
  • induction is the same in physics and philosophy
  • mathematics is essential in physics
  • mathematics is inapplicable to philosophy

The conflicting role of mathematics in physics and philosophy is the "real problem of induction". How is this reconciled?

I: Mathematics is Inapplicable to Philosophy

Understand this point in the strongest possible sense. It is not merely a fact that philosophy does not and cannot use math, but rather a principle that a philosophy that did use math would be a contradiction.

Establish some context: From ITOE, all conscious processes are conceptualizable which implies they have measurements to be omitted. Therefore none of the following is to be understood as denying that conscious processes exist on a continua of magnitude: there are broader and narrower thoughts (based on how much they subsume), emotions are more or less intense. ITOE describes an approximate, implicit, qualitative measurement process applicable to thought.

Thesis: Numerical measurements will never apply to consciousness. Consciousness is not numerable.

1. Epistemological Argument

Consciousness integrates thoughts together, thereafter no part or single thought can be separated to use as a unit of thought. This state has no counterpart in the world of material objects where parts are always separable.

Ex. LP early on considered "existence exists" and "man needs capitalism" as two separate ideas, it was puzzling how Ayn Rand considered them related and even as one issue. Now after having written Ch. 11 of OPAR LP can no longer consider them in isolation, they are integrated, they are a one now.

Ex. Automatized recognition of tables. One no longer regards these objects as inexplicably unique concretes.

Ex. Ayn Rand thinks about the 'moral vs. practical' dichotomy. Then she considers the 'love vs. sex' dichotomy. Then she puts the two together saying "Aha! The mind-body dichotomy." Is the arithmetic here "1 + 1 = 1"?

Ex. Colloquial expressions about counting ideas cannot be understood literally. Consider 3 cases: a man with no ideas, a man with one idea, a man with dozens or tons of ideas. Possible interpretations are:

The man with no ideas merely never thought of 'X'.

The second man is obsessed, as Spinoza was with God.

The third man has an active mind.

Or alternatively,

The man with no ideas has many implicit ideas, as all men act on at least implicit philosophical premises.

The God obsesed Spinoza wrote out 5 volumes of numbered propositions, he has many ideas although related.

The fertile mind may be teeming with hundreds of variations within linguistic analysis, but since linguistic analysis is dedicated to negating the faculty of abstraction this is equivalent to having no ideas at all.

Summary: An arbitrary bit of identification cannot be isolated as a unit of identification.

Aside: This principle is why it is impossible to specify numbers in definitions of various epistemological terms.

Ex. How many attributes must an essential cause/explain? Can't say more specifically than 'most'.

2. Ethical Argument

Man pursues values only through the guidance of principles, implicitly or explicitly. Principles are not a matter of degree. Either a principle applied and you followed it or it didn't (or you didn't).

{Humorous double entendre here "There are no degrees in philosophy."}

Efficient causation in physics permits one to be hot and then even hotter.

Final or Teleological causation in ethics does not permit one to be free and then even free-er.

Ex. Related to the OPAR passages on integrity, one cannot be honest then even more honest. There may be bigger and smaller liars, but all liars are dishonest i.e. not honest.

ex. Reason and freedom are corollaries but no proportionality applies. Can't say if reason goes down by 7 then freedom will go down by 7, or 49 (a square law). A law in philosophy is utterly unlike a law in physics. {another reason fictional psychohistorian Hari Seldon is impossible}

3. Metaphysical Argument

Apply the 'primacy of existence' principle.

Consciousness is awareness of existence. Existence is a 'thing in itself' while consciousness is entirely derivative of and dependent upon existence. Consciousness has no innate or intrinsic contents to be aware of.

The identity of consciousness is its physical instrumentalities. (brain, senses). Nothing else to analyze, there is nothing there to be characterized numerically. Counting applies to entities and their attributes. States of consciousness are not entities, they are the awareness of entities.

Consciousness is (thoughts are) implicitly measurable only in relationship to matter. A broad thought subsumes more matter, and intense love is an action of valuing and intensity of action can be measured. See ITOE re: teleological measurement. Speech of a juror in announcing a verdict can be recorded, throat movements measured etc. but his justice is not quantifiable.

Summary: Conscious processes are quantifiable but not in numbers. Counting and math are inapplicable to consciousness. Philosophy is about consciousness therefore counting and math are inapplicable to philosophy.

II: Mathematics is Indispensable to Physics

Why? What does math do for physics that nothing else ever could?

"Math is exact but qualitative statements are inexact." is a false answer. "Man needs capitalism" is exact. "Qualitative statements are not reliable" is a qualitative statement, thus not reliable and self-refuting.

The subject matter of physics is the external world, including reality beyond the perceptual level. Induction is the primary means of gaining knowledge of what lies beyond the perceived. So, what does math do for induction about external reality?

Granting that consciousness cannot be numerically quantified, conceptual awareness is inherently quantitative.

"Human consciousness on the conceptual level is an inherently quantitative mechanism. It is an apparatus for processing quantity."

Our minds grasp reality - attributes, causal relations, - by grasping quantitative data. Qualities of things are fundamentally quantities. Quantity has epistemological primacy over quality in studying the external world. This is implicit in Ayn Rand's theory of concept formation. The referents of a concept are commensurable, reducible to the same unit. Instances are the same except for varying measurements. Quantitative relating brings the whole universe of immense and microscope distances into the human scale of perception by a perceivable unit.

Concept formation is quantitative.

Induction of causes is quantitative (as seen in physics)

A concept is a file folder formed by omitting measurements.

Induction relates between file-folders with an explicit conceptual measurement system and number system.

Measurement comes in two variants, preconceptual and implicit or conceptual and numerical. A concrete is to a perception as a numerical measurement is to a causal induction in physics.

If we could know everything about a quality by simple perception then we could know causal relations directly by perception. Early cognition with first level concepts and gens is just that. "Fire is hot" is ostensive, no measurement process required beyond sticking your finger in it. Higher levels require abstract conceptual measurement. Physics does not happen to be mathematical, it must be.

Why does human consciousness work through quantity? "It is" {By the law of identity only quantity exists?}

Another perspective on same idea: physics completes the job of concept formation.

Concept formation omits measurements

Physics adds the measurements back in, explicitly and numerically.

Summary: The nature of consciousness forbids numbers in the grasp of itself and its own states while mandating them in the study of the external world.

III: The Relation of Mathematics to Reality

Intrinsic theory the Plato - Pythagoras axis claims numbers are metaphysical

God thinks in equations so reality obeys equations.

"Why are the numbers in physics so often simple integers?" God thinks in integers. (or regular solids) God can do anything he wants, why not that?

ex. Einstein: "These equations form a part of the mind of God."

critique: supernatural explanation explain nothing; detaches physics from matter

Subjective theory exemplified in [Copenhagen style] quantum mechanics - numbers are arbitrary creations of consciousness

"Reality is silent", mathematics is convenient for physics. Why? "It is."

critique: reality is dropped from physics as an unnecessary complication. "Don't be metaphysical." {thanks Occam!}

Objective theory numbers are facts of reality as processed by our cognitive faculty

metaphysically given facts: entities are real, variations in quantity are real

action of consciousness: relating quantities to a unit makes possible counting, numbering, measuring

Numbers are epistemological and validated by being reducible to the perceived.

Numbers are the product of existence and consciousness.

ex. pi is the ratio of the circumference of a circle to its diameter.

Reality contributes two lengths. There are round things in reality.

Consciousness contributes the ratio-taking, relating the two lengths. The lengths are abstracted and then their quotient is an abstraction. Pi is objective.


Numbers are inapplicable to to their creator, consciousness.

Numbers are indispensable to physics.

Numbers are objective.

II: Philosophy Is A Science

Is philosophy inexact, nonobjective, noninductive and nonscientific because it does not use numbers? No!

Philosophy explains what numbers are and mandates their formation and use. Physics is hierarchically dependent on philosophy.

Since the Renaissance physics has been guided by an Aristotelian spirit but Aristotle never specified the use of numbers or experiments to know reality. Physics has merely stumbled upon its use of math without understanding why.

Philosophy has as its task and subject matter the norms of consciousness. Consciousness is not measurable. Non-numerable philosophy is the only science that can explain and validate the use of numbers in the special sciences. {and using numbers to validate numbers would be a circular argument, a begging of the question.}

Philosophy is the arbiter of measurement instructing when to take them and omit them, when to take them numerically and relate them, and when not to take them at all. Philosophy is the only validator of the physicist qua measurer.

Philosophy does not need and cannot use numbers because it is not concerned with relating objects to each other. Philosophy is concerned with relating consciousness to objects.

Philosophy is the same idea from beginning to end "perceive reality in order to stay in it". Since it is all one thing, an integrated unity, it has no need for an additional technique of integration.


Philosophy does everything inductive sciences do and what they use numbers for it accomplishes without numbers. It is false to say philosophy is not scientific because it is not mathematical. Philosophy defines and validates the scientific method therefore no inductions in physics can be better than the principles of philosophy, especially epistemology.

Philosophy is just as scientific as physics, just as inductive, hard-headedly factual, objective, inescapable and absolute. The proper methods and standards of thought, virtues and values for survival on a desert island or in society, the criteria of great art and literature, are laws and facts as ruthlessly scientific as the laws of Newton and Maxwell. This is one of the most crucial truths all of us must know and spread in order to save the world. Because in order to save the world you have to know the philosophy you are preaching is a science, and then your listeners have to discover it too.

The philosophies of the past, the philosophies that created the problem of induction, are dead. Long live philosophy, the science of philosophy, the inductive science of philosophy.


Q: What is David Harriman's comment on exponents?

A: Why is the law of circular accelaeration a=v2/r such a simple relation? Why not a=v2.9/r1.6 ? Because exponents are introduced by our own operations. If we have two relations equating quantities involving v, then by substitution we can equate them into a single expression. Then v will appear twice, which when terms are gathered results in an exponent of 2, an integer.

Q: Is animal consciousness quantitative?

A: No. {Perception may be but} they do not relate quantities to a unit. Our own dog's vocabulary of 27 words was learned by association, taught by humans.

Q: Does the crow have a little crow inside?

A: "Can the crow count?" no, the crow can hold in awareness a finite number of entities, but it is us looking at him that says that the crow can hold 3 units at most.

Q: You said consciousness is a continuous phenomena but it is also discrete in that you have it or don't, and the difference between animal and human consciousness is not one of degree.

A: No, certain conscious processes are on a continuous basis. That is a separate issue from "do you have consciousness or not?" An attribute exists or not, if it does it exists on a continuum. {Essentially the same question as L6 about using continuous mathematics and calculus to describe discretes as in atomic theory and QM.}

Q: Are numbers and counting essential to survival the way all men have an implicit philosophy, and would this make at least an elementary number theory part of philosophy?

A: No, and no. Man can survive at all levels of cognition. Concepts develop one at a time, in an individual [and in civilization.] Numbers are required to advance beyond a childhood level of civilization but survival is possible at the ostensive level. Philosophy of numbers is not number theory, philosophy of physics is not physics, the philosophy of any special science explains how the subject is objective.

Q: How do you relate the two standards of proof, the explicit prior standard which must be met as in the possible/probable/certain ascent given in OPAR, and the 'inductive discovery'

A: If you get certainty right away, proof is inherent. {I think he should not have said you can "get certainty right away". You can get proof right away. From OPAR - "Certainty is about knowledge from a certain perspective. It designates some complex items of knowledge. Not all complex items, and no simple items, considered in contrast to the complex transitional evidential states that precede them." The only standard of proof is reducibility and noncontradiction. There are two kinds of certainty, the formal one discussed in OPAR and the informal extension of certainty to all knowledge to indicate the presence or absence of the emotions of conviction and doubt. This last is ok but not essential to the epistemology considered here. See Art of Thinking lecture on certainty}

Q: Ayn Rand's last investigations?

A: LP thought she may have had as a hypothesis that just as algebra's relation to arithmetic was illuminating to concept formation, higher math might illuminate further elements in epistemology. Also wanted to integrated discoveries in neuro-science.

Q: (written) Great physicists immediately jump to the generalization once they recognize the pattern. This brought to mind a similarity with the story of how Ayn rand came upon her theory of concept formation. She knew she had it when she got it. Could you comment?

A: Yes. She didn't think it up out of the blue, she had a whole context. She had long dismissed the supernatural in any form. she had dismissed any form of subjectivism. She had held in arguing against skeptics that consciousness has identity and against "naive realism". She knew consciousness and reality each contribute to cognition. From Aristotle she knew and admired the idea that selective focus was essential to abstraction, and that concepts were our way of grouping or classifying percepts. She had a great respect for mathematics (Kira in We the Living thought math was the only subject where you didn't have to listen to lies.) She knew math was essential to measurement.

Given all this you can practically see her theory ripening in her mind. When she imagined looking for the rose-ness in roses she imagined a series of roses before her, one brighter, one duller, one sharper, one blunter, etc.. That the similarities and differences were quantitative, selectively focused upon, partly determined by personal perspective and environment (context), were all summed up in 'measurement omission'. She checked the theory out with all the categories of concepts but she knew she had it right when she got it. This is a good example of scientific thinking.

Q: Clarify that there are two forms of measurement, preconceptual and approximate.

A: No, preconceptual is approximate, conceptual is exact. The concept 'length' does not depend on any numbers, just bigger or smaller. You have to have the concept 'length' available before designating a unit of length and creating numbers. Philosophy does not use either method of measurement, it does not measure.

Q: (Betsy) What is the relation between an equation which fits the data and a causal explanation?

A: Not every equation reveals a causal relation. All scientific discovery of causality is in the form of an equation, but reverse is not necessarily true.

Q: Are first level generalizations in physics axiomatic like axioms in philosophy?

A: No. They do not have the quality of necessarily being used in an attempt to refute them. Physics studies concretes, different physicists may start from different concretes.

Q: Logic is the art of noncontradictory identification. How does logic apply to induction.

A: Do not equate logic with deduction. Induction is logic. [this question was posed before the newer lectures 1&2 thus the 'necessity in induction' passage is relevant but not available then]

Q: Can the rejection of the charge that philosophy is not scientific because it is inexact due to being not numerical be extended to other fields in the humanities, such as history?

A: Yes. All subjects that deal with man qua consciousness (i.e. not medicine, anatomy, evolutionary theory) come under the same rule as philosophy. Measurement and numbers are inapplicable for the same reason. The apparent exception of economics is not an exception, prices are 'teleological measurements' a grading of preferences as Ayn Rand used the term. Prices are not empirical measurements as in physics.

edit - fixed wrong bracket types for my own comments

Edited by Grames

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I'm glad you picked that passage to quote. I think it is one of the more important statements about the Objectivist method of reasoning and I've erred exactly the way he described.


Salmeiri asked a similar question at the end of lecture one;


Q: (Greg Salmieri) In Objectivism Through Induction lectures you said "an induction of causality".

A: I reject that formulation now. Value of the lecture is still in the concretization of the ideas.


My understanding is that the Law of Identity and the Law of Causality can be and are grasped separately, and then it is a later act of horizontal integration that relates the two together. Or least that is the proper way to learn the relationship.

I was not aware that Peikoff changed his mind about this.  This is causing me to have a few questions that I was hoping to get some answers to.

Is Peikoff basically saying that his inductive proof of causality that he goes over in a course called "An Inductive Approach to Philosophy" is wrong?

He mentions in the lecture that it essentially involves 3 concepts: entities, identity, and action i.e. entities with identities acting in a particular kind of way in accordance with their identities.  What is wrong with this understanding?  What is improper about this understanding of causality?  Did Peikoff ever mention what his reason was for later rejecting the proof that he himself gave?

And lastly, I suspect my understanding of "horizontal integration" is not up to par so could you explain what "horizontal integration" is?  Maybe give an example of it and how it differs from "vertical integration?"


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7 hours ago, [email protected] said:

Is Peikoff basically saying that his inductive proof of causality that he goes over in a course called "An Inductive Approach to Philosophy" is wrong?

He is saying that it is no proof.  Causality is axiomatic, and axioms are not proven.

His  given motivation for this correction was to combat rationalism.  Rationalism is word-thinking rather than concept-thinking (my description).

Vertical integration is when one relates a higher level concept to a lower level concept, possibly through additional concepts in between them, by demonstrating the hierarchical dependency of one upon the other.

Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

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2 hours ago, Grames said:

Vertical integration is when one relates a higher level concept to a lower level concept, possibly through additional concepts in between them, by demonstrating the hierarchical dependency of one upon the other.

Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

Fascinating, from your description it would seem that performing a horizontal integration of A and B (with hierarchically prior C) is the same as performing two vertical integrations (A and C well as B and C).

Is this correct?

If not, could you describe how integrating A and B with use of hierarchically prior C, is the different from vertically integrating A and C as well as vertically integrating B and C?

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Horizontal integration is performed between two concepts that are not hierarchically dependent upon each other.  They can be related through some other concept(s) are are hierarchically prior to both, and they should not contradict each other directly or indirectly.

If they are horizontally related through some other concepts that are hierarchically prior to both, how can causality and identity be horizontally relatable?  What concept is there that is "hierarchically prior" to identity?  I thought identity was the most fundamental concept anyone can form.  There shouldn't be anything hierarchically prior to "identity" right?

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6 hours ago, [email protected] said:


If they are horizontally related through some other concepts that are hierarchically prior to both, how can causality and identity be horizontally relatable?  

Remember that question you started with. the about Peikoff's so-called (at the time) proof of induction?  It is no proof but it does serve as a nifty horizontal integration. 

Higher level concepts can be related and integrated with two vertical integrations to something in common, but that is not applicable to axioms and first level concepts.  Horizontal integration also refers to checking for noncontradiction.  Noncontradiction always applies and is the chief means by which we become suspicious of perceptual illusions.  

Technically existence comes before identity.  But the placement of existence as prior to identity (the "primacy of existence principle" is not derived or proven, because it too is part of the mechanics that make logic and proof possible.

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10 hours ago, StrictlyLogical said:

Fascinating, from your description it would seem that performing a horizontal integration of A and B (with hierarchically prior C) is the same as performing two vertical integrations (A and C well as B and C).

Is this correct?

If not, could you describe how integrating A and B with use of hierarchically prior C, is the different from vertically integrating A and C as well as vertically integrating B and C?

Well, no.  The point of doing a horizontal integration is to make your knowledge a noncontradictory unity.  The two reductions don't themselves rule out the possibility of a contradiction.  It is good to be able to reduce a concept, and is a requirement of a well formed concept, but it could still be in contradiction to some other concept.  

Consider the recent memewar entrant "Islam is right about women".  This is an attempt to provoke horizontal integration in the reader.  It is quite possible for some feminist to able to identify Islam without actually knowing all of the attributes of the religion.  It is possible to have a concept but have it ordered around nonessentials.  To feminists, Islam and muslims are simply a non-white and non-christian ally in the fight against the white christian patriarchal power structure of America and the whole western tradition.  As one of the Abrahamic religions it is in fact patriarchal also, vehemently so when compared to Christianity.  The feminist concept of Islam is apparently no more than that group of people who claim to be muslims, and a feminist would reduce the concept to its referents and stop.  Horizontal integration is need to provoke the feminist into realizing this level of concept formation about Islam is inadequate.

Edited by Grames
missing word

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