Induction through deduction?

Metaphysics and Epistemology
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I am confused. In Introduction to Objectivist Epistemology Rand says that applying concepts is basically a process of deduction. I quote the Lexicon:

"The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

“The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.”

http://aynrandlexicon.com/lexicon/induction_and_deduction.html

However, in The Logical Leap Peikoff-Harriman says that applying concepts is what makes a generalization, i.e., induction, possible. I think I understand this point.

Let me quote The Logical Leap: “In *utilizing concepts* as his cognitive tools, he is thereby omitting the measurements of the particular causal connection he perceives. ‘Fire’ relates the yellow-orange flames he perceives to all such, regardless of their varying measurements; the same applies to ‘paper’ and to the process of ‘burning.’ Hence his first statement of his concrete observation: ‘Fire burns paper.’ This statement is simply a *conceptualization* of the perceived data-which is what makes it a generalization.” What is “a conceptualization”? The book seems to define it as both the “the forming and *using* [of] concepts.” And: “New instances are *conceptualized*, i.e., placed under the appropriate concept, as and when they are encountered.” Induction is also described as the conceptulization process “in action”. As opposed to deduction which takes for granted the product of this conceptualization.

Let us now go back to the quote from Introduction to Objectivist Epistemology: “The process of subsuming new instances under a known concept is, in essence, a process of deduction.” So conceptualization, i.e., identifying something in conceptual terms, by applying the concepts, i.e., by placing new instances under the known concepts, is what makes possible the generalization. Yet the whole process is in essence a process of deduction, according to Rand.

So if I understand _all of this_ correctly, then it SOUNDS like Peikoff is saying that deduction makes induction possible. And that sounds like pure nonsense. Especially since Peikoff-Harriman argues in the book, and elsewhere, convincingly that induction comes first. I also happen to think so. But if so, then it nevertheless leaves me confused.

I am pretty sure _I_ am missing something. But I do not know what. Hence my frustration with myself. Any suggestions?

science is a priori
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‘Fire burns paper’ is the generalization of the causal relationship here.

Seeing a lit candle, or a lit burner on a stove, and/or a campfire gives rise to the induction of the concept of ‘fire’. Then seeing a house burn down, a match lit, or the burning ember on a cigar can be deductively subsumed under the previously formed concept of ‘fire’.

Seeing ‘fire burn paper’ is the inductive recognition that ‘paper burns when fire is present’. Further induction that ‘fire burns wood’, ‘fire burns coal’ can be later identifications.

One then, can further induce the concept of ‘fuel’ or ‘combustable materials’ from integrating that ‘paper’, ‘wood’ and ‘coal’ can interchangably be used for burning with fire, as earlier knowledge forms the base for later knowledge.

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If I understand you correctly, it is the different uses of the concept of generalization that is confusing.

When you form a concept, you generalize over them, abstracting what fundamentals they have in common. That is inductive-ish.

When you apply a concept, you see that a particular thing possesses the essential characteristics of a so-and-so, and you conclude it is indeed a so-and-so. That is deductive-ish.

In the second case, applying the concept to a new particular thing allows you to know a priori (so to speak) various things which earlier experience with the type so-and-so, taught you, to this particular one. In doing this, you are generalizing to it.

So, you can’t bind “generalize” to either the inductive or the deductive process. It is the key thing, which one forms and the other utilizes. Especially in the form, “generalize” and “generalization,” we should make it plain whether we mean “generalize from” or “generalize to,” and “generalization over” versus “generalization of.” A statement such as “makes generalization possible,” is ambiguous if the context doesn’t support one and only one possibility.

Mindy

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One instance of the book that can add to this confusion is from page 74:

“Concepts are what make induction possible and necessary.”

So how do you get the first concept - by deducing it from Plato’s ass?

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One instance of the book that can add to this confusion is from page 74:

“Concepts are what make induction possible and necessary.”

Although the quote is a bit confusing, it is possible to properly understand it:

“[The human need to form] concepts is what makes induction possible and necessary.”

Put another way:

“Conceptualization is necessary for a mind to more easily understand the world and retain knowledge. Induction is necessary for conceptualization.”

Really, I would say they go hand-in-hand. Obviously, conceptualization is the final goal, and induction is a necessary step down that path. But one part does not make sense without the other part, i.e. conceptualization apart from induction, or induction apart from conceptualization.

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So how do you get the first concept - by deducing it from Plato’s ass?

It would be safe say the context of first concepts is different because you do not require previously formed concepts at that first level. Concretes are self-evident and through good ol’ measurement omission, the percepts formed out of those concretes can then be used to form concepts. If you say ALL concepts must come from concepts, that would be blatant rationalism. At the very first level, concepts must be connected directly to percepts if they are to be objective.

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So if I understand _all of this_ correctly, then it SOUNDS like Peikoff is saying that deduction makes induction possible. And that sounds like pure nonsense. Especially since Peikoff-Harriman argues in the book, and elsewhere, convincingly that induction comes first. I also happen to think so. But if so, then it nevertheless leaves me confused.

Induction in essence “makes new knowledge”. Integrating referents into a new concept is in essence induction. Integrating two concepts into a new generalization is induction.

Consider “fire burns paper”. An inductive generalization (All S is P) makes a new integration between two existing concepts. Naming the fire and naming the paper are essentially deductive when fire and paper are already known concepts. No actual deduction appears here, only the essence of deduction. The essence of deduction is “making explicit what is already known implicitly.” What is new is knowing what fire does to paper, ‘burns’ is the causal connection newly induced to apply to all paper and all fire.

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I have been thinking about this and I have realized that it was as I suspected: I made a serious mistake in my thinking. I looked my at the words, not at what actually happens in reality.

The basic CONFUSION (on my part) came out of this syllogism: Rand says that using a concept, to subsume a new instance under a concept, is in essence deduction. (This is true but as it turns out irrelevant.) Yet Peikoff says that we use and apply concepts to reach inductive generalizations. Therefore (this sounds like) we induce by deducing.

But I have realized one thing (with the help of primarily Roderick Fitts). Namely that to merely use concepts to describe, conceptually, what you are observing is NOT a process of DEDUCTION. Example: If you merely look at an apple and you use concepts to identify what you are observing: “That’s an apple.” Then you are obviously NOT deducing anything. If you see fire burn paper and you use concepts to identify what you are observing by saying: “What do you know, fire burns paper.” Then you are, again, NOT deducing anything.

So to USE or APPLY a concept to DESCRIBE or IDENTIFY what you OBSERVE is NOT to deduce. There is no deducing going on here. In fact, as Grames says, this is indeed induction since it gives me NEW knowledge, not some implications of OLD knowledge. The NEW knowledge consist of the conceptual identification and integration of a causal factor.

Now, ONCE you have conceptualized your observation and, therefore, generalized through a process of measurement omission, then you can say: “Fire burns paper. This is a fire. Therefore it (can) burn paper”. Now you are indeed deducing. I.e., subsuming everything you know about fire to this new fire. But to do this, you first had to induce, by conceptualizing the observed causal connection by using concepts.

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But I have realized one thing (with the help of primarily Roderick Fitts). Namely that to merely use concepts to describe, conceptually, what you are observing is NOT a process of DEDUCTION. Example: If you merely look at an apple and you use concepts to identify what you are observing: “That’s an apple.” Then you are obviously NOT deducing anything.

When you look at an apple, and, possessing the concept, “apple,” you realize that this object is an apple, you are performing a deductive-like process, just as Rand said. It is akin to deduction because the concept, “apple,” which you already possess, acts in the place of the “all S is P” premise, through its genus and differentia. Then, the perceptual evidence before you–red, round-ish, hanging from a short tree, etc. operates as the second premise “here is S,” and you end up categorizing the particular object as an apple, “therefore here is P.”

  1. “Apples are round, red/green/yellow fruit that grows on trees of this sort…” 2) “Here is a round, red, fruit growing on a tree like so and so…” 3)“Therefore this is an apple.”

Mindy

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So what’s the conclusion of this…?

This is what I think:

  • Any identification made by the use of concepts or concept-formation, is induction.
  • Any process of applying previously induced knowledge to an existent that you´ve identified as being an instance of a conecpt’s referent, is deduction.

Also, regarding my quotation earlier, I think now that concepts make induction necessary as a means to achieve them, and concepts also make induction possible on higher levels of abstraction.

Please comment.

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Any identification made by the use of concepts or concept-formation, is induction.

Any process of applying previously induced knowledge to an existent that you´ve identified as being an instance of a concept’s referent, is deduction.

I think “any identification” is pretty broad and would necessarily include deduction (“logic is the art of noncontradictory identification”). There has to be a better way of designating the common element in concept-formation and induction. Harriman relies on ‘conceptualizing’ for that purpose. The second statement on deduction I agree with completely.

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So what’s the conclusion of this…?

This is what I think:

  • Any identification made by the use of concepts or concept-formation, is induction.
  • Any process of applying previously induced knowledge to an existent that you´ve identified as being an instance of a conecpt’s referent, is deduction.

Also, regarding my quotation earlier, I think now that concepts make induction necessary as a means to achieve them, and concepts also make induction possible on higher levels of abstraction.

Please comment.

I suggest that it is misleading to call conceptualizing induction. The process is only akin to induction. Induction proper is the formation of general propositions like All S is P. Trying to form an undifferentiated concept of induction that applies equally to the process of forming such general propositions and to conceptualizing existents is a mistake.

Same, of course, for deduction. Applying concepts you alredy possess to a particular thing is akin to deduction, but only that. Don’t try to understand deduction as something that encompasses deductive logic and conceptual identification of new particulars.

It is worthwhile, to repeat myself, to understand how concept-formation is like induction, and how applying concepts is like deduction. It is a mistake to regard those similarities as defining. Keep the four concepts distinct. Know how they relate.

Mindy

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I’ve recently listened to Dr. Peikoff’s course, “Objectivism Through Induction,” and took some notes with respect to what he said concerning concept formation and induction.

Disc 10, Track 4, 01:00

Question: “I don’t understand the difference between concept formation and induction.”

Peikoff: "Well now those are radically different. I mean, not opposites, but a concept, think of as a single word, like “table,” “chair,” “man,” “star,“run,” “hit,” “red,” “green,” etc. Concept is like a file-folder which you designate a certain category, all the things which have this shape, for instance, table, or this structure, man, and then you put in that file-folder every piece of information you gather by studying a few men, and you say, ‘since it belongs to this category, what I have learned about the few men, that they are mortal, for instance, applies to all the rest in this category.’ So induction is, let’s say, is the cash value of concept formation. Concept formation, you form the single word which is the file-folder. Induction, you formulate a proposition, a sentence, a statement, all so-n-so is so-n-so, which consists of applying to every member in the category the things that you learned by studying some of them.”

And: ‘“Man” is a concept. “All men are mortal” is four concepts united into a proposition which is reached by induction.’

Question: “Is induction used in concept formation?”

Peikoff: “No. That’s a great question. Induction is not used in the forming of a concept. The forming of a concept just…for instance, here’s one table and another table and another, and I’m going to set these aside as against “chair,” and I’m going to use this as a category from now on, and call it “table.” There’s no generalization in that. There’s simply the setting aside of some concretes and opening a file. But now, the first time you start studying tables and you find, for instance, they’re made of wood, assuming that was true, and you do that by studying ten of them and then you say, ‘okay, that goes into the file now, all tables are wooden.’ That is an induction.”

Edit: I’m uncertain as to what’s proper, with respect to copyrights, when quoting such material. If posting such a quote is inappropriate, please let me know and delete this post. I could simply post a statement, in my own words, of the gist of Dr. Peikoff’s response, but I thought the quote, if appropriate, given that it’s brief, would be clear and helpful.

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Thank you Trebor. I found the quotes to be very helpful!

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I’ve recently listened to Dr. Peikoff’s course, “Objectivism Through Induction,” and took some notes with respect to what he said concerning concept formation and induction.

Disc 10, Track 4, 01:00

Question: “I don’t understand the difference between concept formation and induction.”

Peikoff: "Well now those are radically different. I mean, not opposites, but a concept, think of as a single word, like “table,” “chair,” “man,” “star,“run,” “hit,” “red,” “green,” etc. Concept is like a file-folder which you designate a certain category, all the things which have this shape, for instance, table, or this structure, man, and then you put in that file-folder every piece of information you gather by studying a few men, and you say, ‘since it belongs to this category, what I have learned about the few men, that they are mortal, for instance, applies to all the rest in this category.’ So induction is, let’s say, is the cash value of concept formation. Concept formation, you form the single word which is the file-folder. Induction, you formulate a proposition, a sentence, a statement, all so-n-so is so-n-so, which consists of applying to every member in the category the things that you learned by studying some of them.”

And: ‘“Man” is a concept. “All men are mortal” is four concepts united into a proposition which is reached by induction.’

Question: “Is induction used in concept formation?”

Peikoff: “No. That’s a great question. Induction is not used in the forming of a concept. The forming of a concept just…for instance, here’s one table and another table and another, and I’m going to set these aside as against “chair,” and I’m going to use this as a category from now on, and call it “table.” There’s no generalization in that. There’s simply the setting aside of some concretes and opening a file. But now, the first time you start studying tables and you find, for instance, they’re made of wood, assuming that was true, and you do that by studying ten of them and then you say, ‘okay, that goes into the file now, all tables are wooden.’ That is an induction.”

Edit: I’m uncertain as to what’s proper, with respect to copyrights, when quoting such material. If posting such a quote is inappropriate, please let me know and delete this post. I could simply post a statement, in my own words, of the gist of Dr. Peikoff’s response, but I thought the quote, if appropriate, given that it’s brief, would be clear and helpful.

From The Logical Leap" Harriman states:

Deduction takes for granted the process of conceptualization. Induction is the conceptualization process itself in action.

Pg 35

???

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Induction is not used in the forming of a concept.

Induction is the conceptualization process itself in action.

Concepts are prior to induction, that is the hierarchy. In induction, simply using concepts by naming what is perceived to be happening creates an induction. Deduction additionally requires forming propositions into valid forms.

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Induction is not used in the forming of a concept.

Induction is the conceptualization process itself in action.

Concepts are prior to induction, that is the hierarchy. In induction, simply using concepts by naming what is perceived to be happening creates an induction. Deduction additionally requires forming propositions into valid forms.

I prefer Mrs Rands take on this…

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I prefer Mrs Rands take on this…

Which differs in what way?

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Which differs in what way?

Was trying to wait till I had more time but wrestling season is upon me and Ill just have to settle for brevity. The answer is in the OP of this thread:

"The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction.

Maybe its because Ive spent countless hours debating Popperian/kantian epistemologist about essential characteristics being “arbitrary tautologies” and irrelevant. Or maybe its from reading Prof. Mccaskeys works:

http://ndpr.nd.edu/review.cfm?id=19387

Aristotle says that induction (epagōgē) is a progression from particulars to a universal. But there is an ambiguity here. Does he mean proceeding from particular things (or groups of things) to a universal concept or term? Or does he mean proceeding from particular statements to a universal statement? The first is – or is somehow related to – abstraction and concept-formation. The second is a process of propositional inference…

Groarke identifies different kinds or “levels” of induction (Chapter 4, “Five Levels of Induction”). The two most important are “induction proper” and “the inductive syllogism.” The first is the process of intuitive discernment by which we produce “abstraction of necessary concepts, definitions, essences, necessary attributes, first principles, natural facts, and moral principles” (158). The other is a rigorous process of inference, the process of turning empirical observations into a syllogism and using the syllogism to produce a universal conclusion…

The combination is central to Aristotelian science, for it provides the major premises of scientific demonstrations. Consider thunder (184, 192-3). Scientific demonstration begins with a definition, e.g., all extinguishing of lightning is thunder. This definition forms the major premise. A minor premise is added, e.g., all storm clouds extinguish lightning, or, these noises are the extinguishing of lightning. A scientific conclusion follows: all storm clouds thunder, or, these noises are thunder. But where does the major premise, the definition, come from? From an inductive syllogism which itself relies on the insight of induction proper: These noises are thunder; these noises are also an extinguishing of lightning; by an intuitive, non-discursive “flash of bare intelligence” (203) we see that the extinguishing of lightning is the very cause and essence of these noises; therefore, all extinguishing of lightning is thunder. Thus we get the major premise needed for the scientific demonstrations.

Or this opening paragraph of prof. Mccaskey’s, which when I first read it made me think he was far too humble with regard to his qualifications:

Induction and Concept-Formation in Francis Bacon and William Whewell John P. McCaskey PhD Candidate Department of History, Stanford University May, 2004

In Objectivist epistemology, induction and concept-formation are closely related. In Introduction to Objectivist Epistemology, Ayn Rand writes, ―The process of forming . . . concepts contains the essential pattern of . . . induction. . . . The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction.‖1 Unfortunately, she does not elaborate extensively on this relationship—and, in this essay, neither will I. Others, including some at this Workshop and of course Leonard Peikoff in his recent lectures on induction, have been examining this relationship more in-depth than I am qualified to do. My goal instead is simply to introduce you to a line of British philosophers from Francis Bacon (1561–1626) to William Whewell (1794–1866) who, like Rand, held induction to be closely associated with concept-formation. By exploring the thought of Bacon, Whewell and others, we may learn more about this association on which Rand left frustratingly little.

http://www.johnmccaskey.com/Induction%20and%20Concepts%20in%20Bacon%20and%20Whewell.pdf

But its all too obvious and I cant imagine how a Oist could not do a double take at the idea induction is not involved in concept formation.

Even the opponents of this idea understood this:

Moreover, Aristotle and all other essentialist held that definitions

are ‘principals’ ,that is to say, they yield primitive propositions

(example. All bodies are extended )which cannot be derived from other

propositions in which form the basis or are part of the basis of

every demonstration

Karl Popper, Conjectures and Refutations

This Is why peikoff wrote:

It follows that there are no grounds on which to distinguish “analytic” from “synthetic” propositions. Whether one states that “A man is a rational animal,” or that “A man has only two eyes”—in both cases, the predicated characteristics are true of man and are, therefore, included in the concept “man.” The meaning of the first statement is: “A certain type of entity, including all its characteristics (among which are rationality and animality) is: a rational animal.” The meaning of the second is: “A certain type of entity, including all its characteristics (among which is the possession of only two eyes) has: only two eyes.” Each of these statements is an instance of the Law of Identity; each is a “tautology”; to deny either is to contradict the meaning of the concept “man,” and thus to endorse a self-contradiction.

A similar type of analysis is applicable to every true statement. Every truth about a given existent(s) reduces, in basic pattern, to: “X is: one or more of the things which it is.” The predicate in such a case states some characteristic(s) of the subject; but since it is a characteristic of the subject, the concept(s) designating the subject in fact includes the predicate from the outset. If one wishes to use the term “tautology” in this context, then all truths are “tautological.” (And, by the same reasoning, all falsehoods are self-contradictions.)

When making a statement about an existent, one has, ultimately, only two alternatives: “X (which means X, the existent, including all its characteristics) is what it is”—or: <ioe2_101> “X is not what it is.” The choice between truth and falsehood is the choice between “tautology” (in the sense explained) and self-contradiction

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But its all too obvious and I cant imagine how a Oist could not do a double take at the idea induction is not involved in concept formation.

Even the opponents of this idea understood this:

I find it all too obviously wrong that concept formation relies on induction in any way, you have simply accepted your opponents’ definitions and premises either knowingly or unknowingly.

All essentialists to date have gotten it wrong, which is why the opponents keep attacking them with justification and success. Knowledge is not based on definitions, it is based on perceptions which are not propositions. Demonstration must be ultimately perceptual not words on a page. The middle stage between wordless perception and forming and manipulating sentences is concept formation. Induction is based on generalizing and so is propositional and necessarily is after concepts in the hierarchy of methods of thought.

“Forming a new integration” is similarity uniting induction, deduction and concept formation, but what unites induction and concept formation against deduction is non-propositional justification by means of perception from first level concepts and first level generalizations. There are no first level syllogisms. Concept formation and induction do have something in common but concept formation is prior because generalizing is propositional.