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I thought it might be interesting to have a discussion on induction. Here's someone's notes on Peikoff's lecture course to get us started:

http://www.aynrandchat.com/induction.html

From the notes:

"Definition of induction: the primary process of reaching knowledge that goes beyond perception."

So to start this discussion off, does primary in this context mean "first" or "main?" I would assume it means the latter, because doesn't concept-formation come first? Or could it mean the former, since isn't concept-formation a form of induction? Please discuss ;)

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I thought it might be interesting to have a discussion on induction.  Here's someone's notes on Peikoff's lecture course to

"Definition of induction: the primary process of reaching knowledge that goes beyond perception."

So to start this discussion off, does primary in this context mean "first" or "main?"  I would assume it means the latter, because doesn't concept-formation come first?  Or could it mean the former, since isn't concept-formation a form of induction?  Please discuss

I think the first thing to mention is that induction is usually differentiated from deduction. Both are a process of inference (a leap from something that you already know to something new). Induction goes from knowledge about a set of particular concrete existents (considered as a member of group of other simliar existents) to knowledge about all members of that group. For example, "man A is mortal, man B is mortal, man C is mortal, man D is mortal, etc." and then concluding, "therefore ALL men are mortal". Induction is a process going from SOME to ALL. Deduction on is an inference as well, but its pattern is going from ALL to SOME (sometimes from SOME to SOME).

Induction is refered to as "Primary" because it is presupposed by deduction. The concepts used in the premises of a deductive inference are UNIVERSAL, the truth of which is dependent upon induction.

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I thought it might be interesting to have a discussion on induction.  Here's someone's notes on Peikoff's lecture course to get us started:

http://www.aynrandchat.com/induction.html

Since Peikoff's lectures are available from the Ayn Rand Bookstore, it would be preferable to discuss them rather than someone else's notes which may or may not be an accurate representation of the lectures.

Also be aware that Peikoff's work on induction is "work in process." Although the lectures sold by ARB are a combination of the 2002 Palo Alto lectures and the 2003 Pacific Palms lectures, I was present at both and he made some significant changes between the two series. He also acknowledges that he has more work to do before he will be ready to publish the material.

"Definition of induction: the primary process of reaching knowledge that goes beyond perception."

So to start this discussion off, does primary in this context mean "first" or "main?" 

It means "first." There are only two ways of reaching knowledge beyond sense perception: induction and deduction. Since deduction depends on induction for its premises, induction is the one that must come first.

BTW, this isn't a definition of induction since, while it states something true about induction, it doesn't demarcate exactly, in terms of the essential genus and differentia, exactly what induction IS.

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Supposing you're trying to grow bacterial cultures.

You set your petri dishes up and go to bed.

The next morning, you find that a spot of fungus has completely ruined one of your cultures.

You're about to throw it away in disgust when you notice that there's a circle of empty space between the fungus and the bacteria.

Being a true scientist, you take a look under the microscope to verify.

Sure enough, it's empty space. Not a trace of fungal fibre.

Now why is there nothing there?

Having already formed concepts of fungus and bacteria, you know that they will live wherever they have food and certain other resources to do so. You also know that certain plants can emit toxins preventing infection. Using your concepts, you analogize the present situation to past experience. Thus, you are able to think of several possible explanations:

1) the bacteria is preventing further encroachment by the fungus

2) the fungus is emiting something which prevents growth of the bacteria in the immediate area

3) the fungus is emiting something which kills the bacteria

After subsequent experiments, you determine that penicillin can kill bacteria.

Decades pass. Penicillin is used so much that there are resistant strains.

Clearly, you can't say penicillin ALWAYS kills that species of bacteria.

HOWEVER... you need a new proposition specifying the cellular characteristics distinguishing non-resistant bacteria from resistant ones. In other words, instead of saying "Penicillin kills all bacteria of species B", you say "Penicillin kills all bacteria of species B possessing (or lacking) the following cellular characteristics..."

Observe that this example divides scientific induction into several steps:

1) pattern-recognition

2) selecting a concept to subsume perceived cases

3) hypothesis-formation based on the selected concept

4) testing the hypothesis:

  • If hypothesis holds for all observed cases, exhaust the ranges of your instruments. For example, Newton's math is "good enough" for low massees and velocities but starts to fail more and more noticeably as you raise the bar
  • If hypothesis sometimes holds but sometimes doesn't, then either there is some hidden factor at work affecting the outcome or your hypothesis isn't a factor.
  • If hypothesis doesn't hold for any other cases, it's DOA

5) identifying logical consequences if hypothesis is true

6) testing predictions:

  • If prediction holds throughout the range of your instruments, it's probably true
  • If prediction doesn't always hold, then there is some hidden factor affecting the outcome.

7) formulating a new proposition to include the set of conditions under which the proposition always holds

Are we done or is there a step missing here?

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Observe that this example divides scientific induction into several steps:

1) pattern-recognition

2) selecting a concept to subsume perceived cases

3) hypothesis-formation based on the selected concept

4) testing the hypothesis:

  • If hypothesis holds for all observed cases, exhaust the ranges of your instruments.  For example, Newton's math is "good enough" for low massees and velocities but starts to fail more and more noticeably as you raise the bar




  • If hypothesis sometimes holds but sometimes doesn't, then either there is some hidden factor at work affecting the outcome or your hypothesis isn't a factor.




  • If hypothesis doesn't hold for any other cases, it's DOA

5) identifying logical consequences if hypothesis is true

6) testing predictions:

  • If prediction holds throughout the range of your instruments, it's probably true




  • If prediction doesn't always hold, then there is some hidden factor affecting the outcome.

7) formulating a new proposition to include the set of conditions under which the proposition always holds

Are we done or is there a step missing here?

YES! You missed the most important step of all.

To have a valid and certain induction, you must identify the CAUSE. You must determine what properties of the entities in question reduce your inductive conclusions to a statement of identity.

What characteristics of the bacteria and the fungus are responsible for the observed results? What characteristics of the bacteria give rise to resistance? What difference in characteristics accounts for the difference in resistance? WHY?

Causes identify what it IS about the entities that makes them be what they are and do what they do. Until you have a CAUSE, all you have is a correlation with a given degree of probability. When you have a cause you know that what they are accounts for what they are -- A is A -- and you can be certain of it.

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Since Peikoff's lectures are available from the Ayn Rand Bookstore, it would be preferable to discuss them rather than someone else's notes which may or may not be an accurate representation of the lectures.

Also be aware that Peikoff's work on induction is "work in process."  Although the lectures sold by ARB are a combination of the 2002 Palo Alto lectures and the 2003 Pacific Palms lectures, I was present at both and he made some significant changes between the two series.  He also acknowledges that he has more work to do before he will be ready to publish the material.

They also cost $210, so the notes are better than nothing :P

Any idea when he'll publish the material? Also, how much physics is in it?

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When we form a concept we omit measurements of commensurable characteristics. We don't do so consciously (we don't consciously think "well...erm... I'll omit this, no wait - this!") we just look at enough objects and our mind forms a concept subconsciously, all we have to do on the conscious level is pay attention to or focus on enough similar objects. Consciously we also give the abstraction a name.

So doesn't the validity of an induction depend on what exactly our mind did subconsciously? It omitted certain measurements - is there any concievable value for those measurements which could make the induction false?

For example, I concentrate on a lot of similar objects causing my subconconscious to create a new file folder which I label "table."

The first five tables I encounter I throw in the river and they all float, so I induce that "all tables float." Then later I see a metal table. I recognize it as a "table" even though it is made of metal. I throw it in the river and it sinks.

How could I have known before that point, that my induction was wrong? If I consciously identified what measurements my subconscious had omitted, I would have realized that it had isolated the bizarre spider like shape of tables and that it wouldn't care what the thing was made of. If I also knew, from work in another field, that shape combined with material effects whether a thing floats I could have known in advance that "all tables float" was a false induction.

Wait a sec... am I being rationalistic here? The only difference being speaking in terms of the subconscious formula instead of the conscious defintion, but still saying the equivalent of "if its not in the definition then it can change?" Because even though the subconscious formula allows for a metal table (it contains a "variable" in the material slot) - that is not proof that there is any such table. So I still could not know in advance that the induction was false.

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How could I have known before that point, that my induction was wrong?

You weren't wrong! That is the line that anti-inductivists take. Consider this from OPAR (pp. 172-3):

  Man is a being of limited knowledge—and he must, therefore, identify the cognitive context of his conclusions. In any situation where there is reason to suspect that a variety of factors is relevant to the truth, only some of which are presently known, he is obliged to acknowledge this fact. The implicit or explicit preamble to his conclusion must be: "On the basis of the available evidence, i.e., within the context of the factors so far discovered, the following is the proper conclusion to draw." Thereafter, the individual must continue to observe and identify; should new information warrant it, he must qualify his conclusion accordingly.

  If a man follows this policy, he will find that his knowledge at one stage is not contradicted by later discoveries. He will find that the discoveries expand his understanding; that he learns more about the conditions on which his conclusions depend; that he moves from relatively generalized, primitive observations to increasingly detailed, sophisticated formulations. He will also find that the process is free of epistemological trauma. The advanced conclusions augment and enhance his earlier knowledge; they do not clash with or annul it.

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You weren't wrong! That is the line that anti-inductivists take. Consider this from OPAR (pp. 172-3) ...

Bowzer,

If claiming context is all that is needed to validate induction, then what has Leonard Peikoff been working on all this time? "On the basis of all available evidence" I have to conclude that there is more going on here...

Regards

Ian

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If claiming context is all that is needed to validate induction, then what has Leonard Peikoff been working on all this time?

One doesn't just "claim" a context as an addendum to one's conclusions. Dr. Peikoff's explanation holds true only when one's context of knowledge is actively held and plays a role in the inductive process. This translates mainly into relating (without contradiction) any new item of knowledge to every other relevant piece of knowledge in addition to reducing your conclusions, step by step through the hierarchy, to the facts that gave rise to the conclusion. This takes a significant amount of work but it is the reason why new knowledge does not contradict old knowledge.

As to what can be said about induction in addition to the point that knowledge is contextual, I suggest Dr. Peikoff's outstanding courses on the subject of induction: (Objectivism through Induction and Induction in Physics and Philosophy.

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When we form a concept we omit measurements of commensurable characteristics. We don't do so consciously (we don't consciously think "well...erm... I'll omit this, no wait - this!") we just look at enough objects and our mind forms a concept subconsciously, all we have to do on the conscious level is pay attention to or focus on enough similar objects.

That's because we don't really "omit measurements." Instead, we seek similarity.

The element of similarity is crucially involved in the formation of every concept; similarity, in this context, is the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree.

We focus on the common characteristics and IGNORE the measurements.

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For example, I concentrate on a lot of similar objects causing my subconconscious to create a new file folder which I label "table."

That's not how people form concepts. They deliberately and consciously have a cognitive PURPOSE in mind. Maybe they are looking for "things I can put other things on." Maybe they are looking for "things that float."

The first five tables I encounter I throw in the river and they all float, so I induce that "all tables float."
No, you hypothesize that all tables float. All you really know is that something about the 5 tables makes them float. Is it the table shape? Is it that they are made of wood? Since you don't know the cause of the floating, you don't have a valid and certain induction yet.

Then later I see a metal table. I recognize it as a "table" even though it is made of metal. I throw it in the river and it sinks.

That experiment shows that your hypothesis about table-shaped objects floating was wrong. Shape is not the cause of floating.

How could I have known before that point, that my induction was wrong?
Until you identify a cause, you can't validly know that your hypothesis is right. It could be or it might be wrong. It is only by testing reality and observing the actual actions of actual entities (like the metal table) that you can know if your hypothesis is wrong -- i.e., contradicted by the actual actions of actual entities.

If I consciously identified what measurements my subconscious had omitted, I would have realized that it had isolated the bizarre spider like shape of tables and that it wouldn't care what the thing was made of. If I also knew, from work in another field, that shape combined with material effects whether a thing floats I could have known in advance that  "all tables float" was a false induction.

It is not a matter of omitted measurements but of causal characteristics. Proper induction requires identifying the characteristics of entities that cause their properties and actions.

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Until you identify a cause, you can't validly know that your hypothesis is right.  It could be or it might be wrong.  It is only by testing reality and observing the actual actions of actual entities (like the metal table) that you can know if your hypothesis is wrong -- i.e., contradicted by the actual actions of actual entities.

Betsy, could you clarify what you mean by identifying a cause please? When I drop an apple I've no idea what causes it to fall to the ground - I know very little about modern physics and current explanations of gravity (as far as I know, theres no current consensus amongst physcists regarding what causes gravity, although I could be wrong). I just know that apples fall to the ground when dropped. The same applies to most other things in my day to day life - when I've got a sore head I take aspirin and I feel better. I don't know why this is the case - I'm sure someone with a degree in medicine could explain it to me, but at present it is beyond the boundaries current knowledge. Does this mean that my inductive inference that aspirin cures headaches is invalid?

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I was wrong when I said, "You weren't wrong! " The conclusion "all tables float" was not a valid induction for the reason that Betsy cites: you had not identified a causal connection. My point would stand if you had approached the issue more cautiously with a conclusion like, "the few tables that I have seen so far have all floated." This qualified induction would be the outcome of contextualizing your knowledge of tables with other things that float (tables being more unlike rubber duckies and boats than they are alike).

I should have read the post that I was responding to more carefully, d'oh!

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Betsy, could you clarify what you mean by identifying a cause please? When I drop an apple I've no idea what causes it to fall to the ground - I know very little about modern physics and current explanations of gravity (as far as I know, theres no current consensus amongst physcists regarding what causes gravity, although I could be wrong). I just know that apples fall to the ground when dropped.

Me too. My husband is the physicist in the family. When it comes to gravity, highly probable hypotheses are as far as I can go. I know a little more about aspirin and how it works, but not all the connections.

In other areas, I can say a lot more. Here is how I identify the cause of "All men are mortal" which reduces that generalization to an identity:

Let's take the proposition "All men are mortal."  Another way of

saying this is that there is something about being a man which causes

all men to eventually die.

We know that all men have certain biological characteristics in common

with all other men (and all higher animals):  we are composed of

cells which can die or malfunction, our bodies consist of complex

interrelated systems with some vital, irreplaceable components and

moving parts which wear out with time and use, etc., etc.

Once we know enough about what we _are_, we know how what we are

_causes_ our mortality.  Since causality is the law of identity

applied to actions, we have established a relationship of _identity_

between humanity and mortality.  The characteristics which make an

entity human are the _same_ characteristics which make him mortal.

Observe that this explanation not only shows the identity involved, but it also delimits the context. "All men are mortal" is true only so long as body parts wear out, can't be replaced, etc.

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My point would stand if you had approached the issue more cautiously with a conclusion like, "the few tables that I have seen so far have all floated." This qualified induction would be the outcome of contextualizing your knowledge of tables with other things that float (tables being more unlike rubber duckies and boats than they are alike).

"The few tables that I have seen so far have all floated" is not really an induction. It is only an observation which is the raw material for induction.

I regard the first step in induction to be hypothsizing a causal connection, even if the cause is only a place-holder like "something."

"These objects that people call "tables" have something in common."

"Something makes things fall down."

"The Dean and Peter Keating are alike in some way that makes them act like that."

The next step is to gather enough knowledge about the relevant entities to suggest what the cause might be. Then you have a testable hypothesis. You then test the hypothesis, learning more and more about the entities and how they act, as you search for the cause. If all goes well, you eventually find it.

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But surely you're then committed to the claim that 99.99% of people on this earth, including you and I, dont actually 'know' that all apples fall to the ground, since they cant identify the cause underlying the inductive inference? This seems completely absurd...

We know THAT things fall down. We don't know WHY.

We know a great deal, on a common sense level, about the cause. We know that things which are heavy fall down. In fact, "gravity" literally means "heaviness." Still, as a non-physicist, I am only at the level of "something" makes things fall down, mathematical descriptions of the behavior which hold experimentally with an extremely high degree of probability, etc.

Fortunately, that is sufficient for my purposes.

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regarding the causal approach to induction:

Bacteria cultures b1, b2, and b3 are not resistant to penicillin.

Bacteria cultures b1, b2, and b3 possess (or lack) cellular characteristics ABC.

If cellular characteristics ABC account for the death of bacteria in the presence of penicillin, then penicillin will kill any bacteria possessing cellular characteristics ABC.

Likewise, if mass accounts for gravitational attraction, then all bodies possessing mass will exhibit gravitational attraction with other bodies possessing mass (as per Einstein).

Both examples hinge upon the assumption that a certain characteristic or set of characteristics causes a phenomenon.

But how can we know that? How can we know that they are sufficient?

After all, causal inference is a species of inductive inference.

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I am only at the level of "something" makes things fall down, mathematical descriptions of the behavior which hold experimentally with an extremely high degree of probability, etc.

Fortunately, that is sufficient for my purposes.

But isnt this essentially what Hume said? I'm unsure of what you've actually added - a solution to the problem of induction which means that I only have a "high degree of probability" that an apple I drop will fall doesnt seem to have advanced us much further beyond Hume's "custom and habit"...

To borrow an example Fred Weiss often uses, we surely _know_ for certain that a cow wont jump over the moon. If our induction only gives us a 'high degree of probability" that it won't, due to us not knowing how gravity actually works, then surely this is not the case?

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But isnt this essentially what Hume said? I'm unsure of what you've actually added - a solution to the problem of induction which means that I only have a "high degree of probability" than an apple I drop will fall doesnt seem to have advanced us much further beyond Hume's "custom and habit"...

To borrow an example Fred Weiss often uses, we surely _know_ for certain that a cow wont jump over the moon. If our induction only gives us a 'high degree of probability" that it won't, due to us not knowing how gravity actually works, then surely this is not the case?

For one thing, Hume's point, if I understand it correctly, was that certainty is impossible, not that uncertainty is possible. Betsy has added the fact to the problem of induction that you can be certain.

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For one thing, Hume's point, if I understand it correctly, was that certainty is impossible, not that uncertainty is possible.  Betsy has added the fact to the problem of induction that you can be certain.

Hume claimed that we only ever witness 2 events happening in sequence, and never the 'necessary connection' between them, therefore we cannot logically justify the claim that these events will always occur together in the future. Betsy, as I understand her, is claiming that causation _is_ this necessary connection, and that once we have grasped this cause we are then entirely justified in claiming that these events will always occur together, due to the law of identity. I'm not entirely sure what "grasping this cause" consists of however, since we technically havent grasped the cause of why apples fall to the ground, or the cause of the majority of things which we witness in daily life.

If I've mistated Betsy's position I'm sure she will correct me.

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Both examples hinge upon the assumption that a certain characteristic or set of characteristics causes a phenomenon.

But how can we know that?  How can we know that they are sufficient?

After all, causal inference is a species of inductive inference.

The Objectivist view of causality is that causality is a corollary of identity and it consists of things acting in accordance with their natures.

In my view of induction, in order to show causality, you have to be able to state the generalization as an identity or as a chain of identities.

As an example, here is Darwin's Theory stated as chain of identities:

Organisms which are, by their nature, unable to survive in a particular environment, are not able to survive in that environment.

Organisms which, by their nature, unable to survive long enough to reproduce will not survive long enough to reproduce.

All organisms currently alive are the progeny of organisms which survived long enough to reproduce.

Etc.

This all seems obvious and tautological NOW, but it wasn't always so.

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But isnt this essentially what Hume said?

No. Hume had a completely different view -- an INVALID view -- of what causality is.

I'm unsure of what you've actually added - a solution to the problem of induction which means that I only have a "high degree of probability" that an apple I drop will fall doesnt seem to have advanced us much further beyond Hume's "custom and habit"...
It doesn't because that is not MY solution to the Problem of Induction. My solution requires reducing the generalization to an identity which we can and have done in many areas of knowledge. If and when we can show the generalization is an identity, we can be 100% certain. A IS A is as certain as anything can get.

To borrow an example Fred Weiss often uses, we surely _know_ for certain that a cow wont jump over the moon. If our induction only gives us a 'high degree of probability" that it won't, due to us not knowing how gravity actually works, then surely this is not the case?

Proper induction gives us certainty. See how, "The cow can't jump over the moon" is reduced to a chain of identities on the Hume thread here.

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