Concept Formation and Induction

Metaphysics and Epistemology
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Concept Formation and Induction

04/09/2011

I’ve been giving some thought to the relationship of concept formation and induction, especially in light of “The Logical Leap” by David Harriman and his association with Dr. Peikoff. Concept formation is uniting two or more similar items by means of measurement omission, and in the history of induction there was as proposed relationship between concept formation and induction, but the writers of philosophy did not think that concepts were inductive primarily because they didn’t know how concepts were formed. Under Objectivism, concepts are first formed from observations and then get more abstract as the conceptual hierarchy is developed. Some people think this is an inductive process, but according to Harriman and Peikoff, induction is explicitly identifying a causal connection using a sentence that is abstract – and it is abstract because a sentence uses concepts. So, while it is necessary to have concepts to form an inductive generalization, the concept itself is not such a generalization. Induction is dependent on concept formation, but concept formation is not dependent on induction – it is dependent on observation at root, but a concept is not the identification of a causal connection. The identification of causal connections are also dependent on observations to come up with first-level inductive generalizations, but one must have many concepts first before the causal connection can be made explicit.

For example, if we take the first-level, directly observed, inductive generalization of “Flipping a switch will turn the lights on,” then this in and of itself is not a conceptualization, but is rather dependent on all the concepts of the sentence. One has to first have the concept of “flipping” and “switch” and “lights” before one can perform the inductive generalization. Otherwise I don’t think one could retain it in one’s consciousness for longer than it took one to observe that flipping a switch turns the lights on. It is the formation of concepts and organizing them into a sentence that can transform such observations into knowledge about how reality works.

I’ll have to give this more thought, but I think that is the delineation between concept formation and induction, at least in light of “The Logical Leap.”

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I take it that the two share the same fundamental root in measurement omission and the unit perspective. Concept formation applies this to entities to form classes of entities, whereas induction applies this to actions of entities to form classes of causal connections applicable to the classes of entities so observed acting. This indicates two things to me:

first, that while measurement-omission is crucial to both, concept-formation has the primacy (just as Identity is hierarchically superior to Causality), and

second, that after a short while the two must proceed together, often in lock-step fashion, where learning about cauasal connections increases one’s knowledge about the entities these connections relate to and also make possible the identification of more abstract entities (eg learning the concept of society properly, as opposed to a collection of unconnected men who happen to be congregated together for some accidental reason, is only possible after learning about causality in the interactions among certain men as well as commonalities in social institutions etc).

Thus I think that the need of discovering the method of concept formation before discovering the full answer to the question of induction comes from identifying their common root as part of the discovery of that method. Does this help?

JJM

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I don’t think I agree with that, since you seem to be saying both involve the unit perspective. Induction is not forming a unit, it is identifying a causal connection that is not a unit – i.e. “Typing on the keyboard brings letters into the edit box” is not a unit, at least not in the sense that a particular cat is a unit of the concept “cat.” So, unless you can make the case that a sentence is a unit, I can’t agree with what you are trying to do.One would have to show that a particular instance of typing into an edit box is a unit of an abstraction, and I think that violates ITOE and what Miss Rand meant by the term "unit"since typing into an edit box is not one thing.Unless you can show that it is, but then wouldn’t the sentence be reducible to one concept?

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I think it important to distinguish between individual instances of causal sequences and a causal connection as an abstraction, just as one distinguishes between individual entities and concepts for entities as abstractions. Induction for causality (IIRC) is not simply the identification of individual causal sequences, but recognising that the individual sequences one observes are instances of universals: all S does P under conditions X. It is not that individual event B happened to follow individual stimulus A, but that A causes B is a timeless principle of cause-and-effect that can recur again and again. That is, in induction you are looking at one or more individual causal sequences and recognising that each is a unit member of an open-ended class of such sequences, that each is identifiable a unit instance of the same cause under the same conditions having the same effect. One is dropping the measurements of each particular individual sequence observed and identifying a causal principle that unites them. So yes, induction, in forming universals from observations of concretes, is an instance of identifying individually observed cause-effect sequences as unit members of an abstraction.

This is the same method applied to casual sequences as is applied to entities. The point about the unit perspective is not that only entities or classes of entities can be units, but that one is looking at something - be that an entity or an action of an entity - and recognising that it is an instance of an abstraction one can form. It matters not whether this abstraction is of classes of entities (eg men) or classes of actions of entities (eg running) or classes of connections between causes and effects (eg when men run they soon begin to sweat).

As to reducing whole sentences to individual concepts, how is that necessary for all induction? It can be done as and when there is need - eg from “One element can be converted into another under the influence of high-speed impact or ionising radiation of the right kind” to “transmutation” - but I don’t see this being a required element of induction for it to qualify as an example of the unit perspective. What need is there for a single concept to denote the act of typing into an edit box to recognise the fact that there are such things as edit boxes and there is a universal causal connection between typing into one and seeing what one types becoming published? Each individual act of you doing so and seeing the results is identifiable a unit instance of this causal sequence, a whole sequence that after a series of observing instances of it in action, becomes for us a universal expectation taken for granted every time we see one and have occasion to use it - ie those individual uses are identifiable as units of a rudimentary principle of end-user computer usage. Again, you could do so if you wanted to - eg I could say “John is about to postpublish” where ‘postpublish’ is a concept I just invented that refers to the action of typing something into an edit box and submitting it for publication on a forum, a concept whose meaning is dependent on knowledge of a now-common causal sequence using computers - but what is the point in that?

JJM

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I think I agree with the general gist of what you are getting at, that there is a sense in which one can retain a sentence in one’s mind as one mental entity – maybe. The reason I say this is that Miss Rand discusses concept formation in ITOE, but she doesn’t discuss propositions or sentences, so I’m not sure she would agree with the “a sentence is a one thing in the mind” conjecture. And I think you would have to show this to stand by what you are saying. Otherwise, we have to say that a sentence is many mental entities (the concepts) tied together by the rules of grammar, but it isn’t an integration of concepts. An actual integration of concepts would be a concept, not a sentence. So, you would have to show that a sentence is a type of integration without it being formed into a single concept. But I think saying a sentence being integrated into a single concept would be a violation of the crow epistemology. You would have to form new concepts for each category of sentences,and then we would have far too many units in the mind to retain. I’ve heard there are people working on this problem of exactly how we retain sentences without it being a single concept, but the work hasn’t been finalized yet.

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I think that concept-formation and induction are two different cognitive processes.Concept designates an essential common denominator between two or more entities. The process of concept-formation is a process of omission of non-essential. Induction as like as deduction is a logical process. If “A” then “X”. Both processes are based on observations and concept-formation is prerequisite of both. Induction is essentially a process of anticipation. Robert Rosen defined an anticipatory system as follows:

“A system containing a predictive model of itself and/or its environment, which allows it to change state at an instant in accord with the model’s predictions pertaining to a later instant.”( Anticipatory Systems, Robert Rosen, 1985, Pergamon Press).

It is a vital process for any living organism, since it allows to project goals into the future and to act upon them. Animals have build-in mechanisms for this purpose, but man uses volition and conceptual cognition. Induction, thus, is an anticipatory process on conceptual level.

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Concept Formation and Induction

04/09/2011

The identification of causal connections are also dependent on observations to come up with first-level inductive generalizations, but one must have many concepts first before the causal connection can be made explicit.

You also need the right kinds of measurements. Consider the history of the concept of burning. The idea of phlogiston raced ahead of measurement and claimed burning was a type of separation. A simple closed chamber and careful measurements would have informed them that ash was more massive than the original substance burned and that therefore burning involved *combination*, not separation.

It is the formation of concepts and organizing them into a sentence that can transform such observations into knowledge about how reality works.

And propositions “work” by taking open-ended classifications based on measurement omission, specifying some of the measurements, and predicating a fact about it.

e.g.:

“My floor is hard”

The phrase “my floor” specifies a smaller set of units than “carpeted floors”.

The phrase “is hard” identifies a connection between some observable quality abstracted from the background and a physical entity that is capable of being hard.

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I think it important to distinguish between individual instances of causal sequences and a causal connection as an abstraction, just as one distinguishes between individual entities and concepts for entities as abstractions. Induction for causality (IIRC) is not simply the identification of individual causal sequences, but recognising that the individual sequences one observes are instances of universals: all S does P under conditions X. It is not that individual event B happened to follow individual stimulus A, but that A causes B is a timeless principle of cause-and-effect that can recur again and again.

And if you want to determine whether the sequences are instances of universals, you look at P units, not the sequences per se.

You examine specific instances of P, hoping to find a unit that teaches you about the entities and constitutive properties responsible for P.

e.g.:

Instances of biological development in a chicken egg indicate stages in a process.

Instances of color have nothing in common but color, meaning that color depends on arrangement of parts rather than chemical components or other aspects.

Instances of fields tell us that we have found an attribute dependent on nothing but the entities themselves.

Instances of thresholds, such as phase transition of water into vapor, tells you that two things thought to be different have a common quantitative basis in entity-interaction independent of entity-composition.

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The reason I say this is that Miss Rand discusses concept formation in ITOE, but she doesn’t discuss propositions or sentences, so I’m not sure she would agree with the “a sentence is a one thing in the mind” conjecture.

ITOE’]

He organizes concepts into propositions—and the truth or falsehood of his propositions rests, not only on their relation to the facts he asserts, but also on the truth or falsehood of the definitions of the concepts he uses to assert them, which rests on the truth or falsehood of his designations of essential characteristics.

Every concept stands for a number of propositions. A concept identifying perceptual concretes stands for some implicit propositions; but on the higher levels of abstraction, a concept stands for chains and paragraphs and pages of explicit propositions referring to complex factual data.

While it is not a proposition explicitly being held as a single unit in the mind, the converse is certainly touched upon.

Also, she discusses that there are words that are developed to specifically aide us within the context of grammar.

ITOE’]

Grammar is a science dealing with the formulation of the proper methods of verbal expression and communication, i.e., the methods of organizing words (concepts) into sentences. Grammar pertains to the actions of consciousness, and involves a number of special concepts—such as conjunctions, which are concepts denoting relationships among thoughts (“and,” “but,” “or,” etc.). These concepts are formed by retaining the distinguishing characteristics of the relationship and omitting the particular thoughts involved. The purpose of conjunctions is verbal economy: they serve to integrate and/or condense the content of certain thoughts.

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Thanks for your input. Some further thoughts:

04/09/2011

Some further thoughts on the relationship between concept formation and inductive generalizations is I think one would have to show that an inductive generalization is definitional for a concept to perform an integration similar to a concept. In other words, to have an actual integration, which I am saying is reducing mental content to one mental entity, one would have to form a concept. This can be done for some inductive generalizations, but I think one would have to show that it is true for all inductive generalizations.

For example, take the following inductive generalization: “Upheavals in the ocean bottom during an earthquake leads to large waves hitting the shoreline.” This could be definitional for the concept of “tsunami.” Or let’s take: “Connecting wires to the ends of a battery and to the ends of a motor will operate the motor.” This could almost be definitional of “electric current,” but not quite, since “electric current” is actually broader than the inductive generalization given. Also take the following inductive generalization: “Rapidly slapping hands together makes a sound,” which could be definitional of “clapping.” But is this true of all inductive generalizations? Do all inductive generalizations lead to new concepts or re-definitions of old concepts? Otherwise I think it would have to be shown that the human mind can deal with a sentence in the form of an inductive generalization as one mental entity, for my definition of an integration.

Or put the question another way, can the identification of a causal sequence be retained in the mind as one thing, perhaps one event? Is ”Scratching oneself can relieve itching” one mental entity? I’ve argued before that it is not one mental entity unless one can form a concept from it, otherwise it is many concepts united together via grammar. But I think this would have to be shown for one to say that concept formation and inductive generalizations have a similarity such that they can be integrated together into the same concept – i.e. ”induction.”

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Or let’s take: “Connecting wires to the ends of a battery and to the ends of a motor will operate the motor.” This could almost be definitional of “electric current,” but not quite, since “electric current” is actually broader than the inductive generalization given.

It describes what a motor will do given a closed-loop current.

If I knew nothing of motors but what happened when I strung components together, I might regard your formulation as a working definition for “motor-current”. It would be fine for *that* stage of knowledge, but new discoveries would prompt new concepts and new definitions.

After I discovered that current can exist without a motor, I’d arrive at “electric current” as such. I might define it in terms of continuity of an effect given variation in certain measurable quantities.

But once I had the concept of “voltage-gradient”, my definition of electric current would become something like “charged particles with a net direction of motion due to a potential gradient”. If I wanted a mathematically rigorous definition, I’d talk about the time derivative of charge. Whatever is appropriate for the level of knowledge involved.

Also take the following inductive generalization: “Rapidly slapping hands together makes a sound,” which could be definitional of “clapping.” But is this true of all inductive generalizations? Do all inductive generalizations lead to new concepts or re-definitions of old concepts? Otherwise I think it would have to be shown that the human mind can deal with a sentence in the form of an inductive generalization as one mental entity, for my definition of an integration.

Not that you need a concept for the sentence. Just a concept of the *relationship* being asserted about the subject. Then you apply your concepts to narrow the units of the main concept in the subject and specify the relationship those units are in.

Or put the question another way, can the identification of a causal sequence be retained in the mind as one thing, perhaps one event? Is ”Scratching oneself can relieve itching” one mental entity? I’ve argued before that it is not one mental entity unless one can form a concept from it, otherwise it is many concepts united together via grammar. But I think this would have to be shown for one to say that concept formation and inductive generalizations have a similarity such that they can be integrated together into the same concept – i.e. ”induction.”

You can regard the specific entity described in any true proposition as a unit of a certain kind. After all, you aren’t advocating that we form a concepts as narrow as blue-eyed girls shorter than 5’ 4" walking through the grocery aisle. You’re just asking whether we can regard something that narrowly defined as a unit. And we can.

It sounds like you’re trying to get a better understanding of what exactly propositions do with concepts.

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Do all inductive generalizations lead to new concepts or re-definitions of old concepts?

Generalization involves ascribing a characteristic to every member of an open-ended set.

Given that open-endedness, I am not sure how you can avoid *something* conceptual.

In some cases we separate and unite previous identifications, arriving at new concepts which demand new definitions of old concepts. I indicated how this might work in the previous post.

Sometimes we see that an old concept actually applies somewhere we didn’t and THAT leads to rethinking a subject. But I’m not sure whether such a process should be considered *inductive* so much as a *logical refinement*.

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Or put the question another way, can the identification of a causal sequence be retained in the mind as one thing, perhaps one event?

I would say no - neither a causal sequence nor a sentence is retained in the mind as “one thing”. Entities and events are in fact “one thing”, but their description/explantion occurs through propositional statements that are bound by both the “crow” limitations of the mind and time.

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Do all inductive generalizations lead to new concepts or re-definitions of old concepts?

Be careful, Thomas. You are starting to sound like Whewell. :slight_smile:

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Be careful, Thomas. You are starting to sound like Whewell. :slight_smile:

I don’t know much about Whewell, but I am against his argument that we have innate ideas that lead to the possibility of knowing fundamental aspects of reality – i.e. like “causality.” And I’m also against his idea that God puts these fundamental ideas into our heads so they cannot be wrong, God being the creator of the universe and being all-knowing. So, on the fundamentals of philosophy, he was very wrong, but I am not going to deny that he might have had something good to say about the scientific process. Many philosophers of science were not consistent with their fundamental ideas. I will have to read more on Whewell, so I’ll just state that I am against his explicit fundamentals. All the philosophical fundamentals are given in perception – they still require forming an abstraction, which has to be done volitionally, but all the evidence is given in perception or observation. I posted my essay “Causation as a Corollary of Identity” to this board and to FaceBook,if you would like to take a look at it, and see the Objectivist approach to the axioms.

http://www.facebook.com/note.php?note_id=135728633151785

Causation as a Corollary to Identity