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Deduction (at best) is the Handmaiden of Induction

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Deduction (at best) is the Handmaiden of Induction

Amse

Case against Deduction

Deduction is bogus. Why?

The reason (psycho-epistemologically speaking) why deduction continued to bother me is that It has no referent in reality! It is like a flashlight that has to be continuously recharged; without which is just a stick of plastic and glass. It is a pointless science. The reason why we say that P:T and C:T is only because we chose it to be. Like you said, one could set up a situation in which we say the falsity of certain premises carries through; and everything else would follow.

To illustrate this, take the following argument (I may have already used it, but it is a good one):

Argument I-

P1 - All dogs are fish.

P2 - All Fish live on land.

C- Therefore, all dogs live on land.

This argument is valid, in the same respect that this is valid:

Argument II -

P1 - All dogs are animals.

P2 - All animals need food.

C - All dogs need food.

There is NO difference in validity between the I and II. NONE! We only accept I because we know its P1 and 2 are true. Truth is simply another plaything in Deduction. It, at best, is the handmaiden of induction.

Case for Induction

The main charge against Induction is, “At best, Induction creates probabilities, or a likelihood”. This is completely and unequivocally false. Why?

We as humans can only base our conclusions on what we know. What does that mean? It means that we as humans operate on our context of knowledge – the sum total of all the knowledge that is possible to us. The word all is important – it means we cannot know of something, until we know of it.

To illustrate this, take the often used example of “the world is flat”. Suppose we created a time machine that could take us back to the Middle Ages (ie. when the theory of “world flatism” was in prominence). The catch is, however, that in doing so, we would lose all of the knowledge that mankind has accumulated from then up until now. We (reluctantly) agree to do so, and we enter the machine. A few seconds later we appear in the Middle Ages. We find ourselves in a church, where there are some people talking about the latest ideas of the day. The most popular idea, the idea that everyone agrees on (except a few radicals, but they are probably a bunch of hedonist atheists anyway) that the world is flat. What evidence are they resting on? In other words, what evidence are they using? Perhaps they say that ships who dare try sailing past “the edge of the world” have not be able to (have died trying); for the simple fact that no one has tried and/or tried and returned. “Okay”, you say, “that seems to make sense”. After all, you are tabula rasa, and until you hear evidence which contradicts that, that principle is true. (Assume you have never heard of the contrary arguments which did in fact exist at that time). The next day you wake up and go and try and explore some more. This time, however, you hear some arguments which seem to refute “world-flatism”. Perhaps you hear the argument about the moon’s cycles, or of ships disappearing, then reappearing on the horizon, etc. This all seems to make sense, but as you are trying to digest all of this a boy runs into the church screaming, “Magellan has just returned from his voyage across the world, and boy were we wrong!”. This, to you, seems like undeniable proof that the world is round. If the world was flat, then Magellan, in order to complete his voyage, would have to stop at “the edge”, turn around, and come back. Clearly that wasn’t the case. Now that your context of knowledge has expanded, your conclusions may or may not change. You don’t start with a theory (out of now where) and try to validate it. It was just the opposite.

What is the nature of the fallacy that opponents of induction claim? They say that because a conclusion may change, we must somehow account for it. How? We can never say, they reason, that we know 100% about anything. We can only say 99%, or even 99.99999999%. But never 100%. This is wrong, wrong , wrong. Let us follow this thinking.

Suppose we wanted to account for the chance we are wrong. Basic probability says that the total possible outcomes of an event and each of their likelihoods must equal the total, or 1. In other words:

Event of A - A%

Event of non-A – non-A%

Total possibility (or possibility of something happening) – A% + non-A% (ie. the probability of A + the probability of any non A event) which must equal 100% (something must happen).

The problem? There is no way of applying that law to knowledge. Why? There is no knowledge of non-A’s existence (until we know of it – at which point there can be no legitimate distinction between A and non A. A would = non A (which is A))! Ergo, there is no way of calculating the probability of non-A’s occurrence!

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The first paragraph should actually read like this:

"The reason (psycho-epistemologically speaking) why deduction continued to bother me is that it has no referent in reality! It is like a flashlight that has to be continuously recharged; without which is just a stick of plastic and glass. It is a pointless science. The reason why deduction says "is the premises are true, the conclusion MUST be true" is an aribitrary choice. The converse could have been chosen as the standard, and the rest of the rules would logically follow from that."

Sorry! (the post was actually an email to my philosophy prof!)

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P1 - All dogs are fish.

P2 - All Fish live on land.

C- Therefore, all dogs live on land.

This argument is valid

This argument is valid, in the sense of being internally consistent, but it is not sound, in the sense of its premises being true. The truth of its premises is verified through induction. But induction alone cannot accomplish everything -- Ayn Rand put it best: induction is concept formation, while deduction is concept application. As such, it is not bogus.

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[...] Ayn Rand put it best: induction is concept formation, while deduction is concept application. As such, it is not bogus.

Yes, and to drive the point home, I would say, based on introspection and observation of others, that most people in day-to-day living do a lot more applying than forming. Deduction is a far more common tool than induction.

Of course, induction versus deduction is a false dichotomy, just as analysis versus synthesis, and theoretical versus practical are false dichotomies when presented as if they were ultimately separable actions of the mind.

Further, I would say that induction -- as a continuing process -- is psycho-epistemologically impossible without deduction. One must, for example, apply rules and methodologies in guiding induction. That is what logic is, a body of ideas one applies as a guide to make sure that our identifications of reality are correct.

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An interesting question might be: which of the two, deduction or induction, is more useful in everyday life. I'm not talking about, let's say, a Sherlock Holmes who would prefer deduction, or a scientist who would prefer induction, but [i]all[/i] people in their every day living -- which of the two do they use, and need to use, the most?

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An interesting question might be: which of the two, deduction or induction, is more useful in everyday life. I'm not talking about, let's say, a Sherlock Holmes who would prefer deduction, or a scientist who would prefer induction, but all people in their every day living -- which of the two do they use, and need to use, the most?

Deduction. Think about the inductive effort required to create a new concept. The first person who discovered a particular concept had to perform a difficult cognitive task. Others following who grasp the concept, have an easier time because of that first discovery, but it still requires real effort to grasp concepts and their referents for the first time. But after that grasp is made, it can be used countless times, and become automatized and practically effortless.

To take a classic syllogism:

(Major premise) All men are mortal

(Minor premise) Socrates is a man

(Conclusion) Therefore Socrates is mortal.

The deduction takes some effort to grasp, but I would argue that it took significantly less effort than the inductive effort to form the major premise - lots of observation about many different men across many years.

Peripherally, I've noticed for some time that there seems to be an inherent asymmetry of cognitive difficulty between operations that are essentially inverses of each other. I haven't figured it out why this is, generally.

In other words, in some sense they are symmetrically related operations, but doing one tends to be easier than the other. Examples from mathematics, ordered from least to most asymmetrical difficulty, are (with the first operation compared being the easier): Addition vs. subtraction; Multiplication vs. Division; Differentiation vs. Integration (in calculus). You could also include Multiplication of factors vs. Factorization - it is extremely easy to multiply the prime factors of a number together to get the number, it is far more difficult to factorize that number into its prime factors (which is the basis for public key encryption.) No doubt there are many other examples.

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This argument is valid, in the sense of being internally consistent, but it is not sound, in the sense of its premises being true. The truth of its premises is verified through induction. But induction alone cannot accomplish everything -- Ayn Rand put it best: induction is concept formation, while deduction is concept application. As such, it is not bogus.

Or maybe, "Deduction...is the Handmaiden of Induction?"

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Yes, and to drive the point home, I would say, based on introspection and observation of others, that most people in day-to-day living do a lot more applying than forming. Deduction is a far more common tool than induction.

Of course, induction versus deduction is a false dichotomy, just as analysis versus synthesis, and theoretical versus practical are false dichotomies when presented as if they were ultimately separable actions of the mind.

Further, I would say that induction -- as a continuing process -- is psycho-epistemologically impossible without deduction. One must, for example, apply rules and methodologies in guiding induction. That is what logic is, a body of ideas one applies as a guide to make sure that our identifications of reality are correct.

Did anyone read the title? :) "Deduction (take out the "at best" - it was just a result of my frustration) is the handmaiden of Induction". In short, I say "Deduction is bogus" because it can never provide NEW knowledge; it can only describe new relationships.

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[...] I say "Deduction is bogus" because it can never provide NEW knowledge; it can only describe new relationships.

<{POST_SNAPBACK}>

Are you distinguishing between knowledge and descriptions of relationships? If so, would you explain what you mean by "knowledge"? Isn't a description of a relationship an instance of knowledge?

The definition of knowledge that I use is the one that Ayn Rand formulated: "'Knowledge' is ... a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation ..." (Ayn Rand, Introduction to Objectivist Epistemology, 2nd edition, p. 35).

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In short, I say "Deduction is bogus" because it can never provide NEW knowledge; it can only describe new relationships.

But deduction is a cognitive effort. Application of principles to specific situations, for example, is a process of deduction. And this is indeed new cognition. The result is new knowledge. And, even in your formulation, new relationships are new *knowledge.*

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But deduction is a cognitive effort.  Application of principles to specific situations, for example, is a process of deduction. And this is indeed new cognition. The result is new knowledge. And, even in your formulation, new relationships are new *knowledge.*

Here is what I said on OO.net. The same applies to all of you:

OH MY GOD!!! You are all missing the POINT!!! FORGET about the first part, if it really bothers you. I achieved something in my defense of Induction that you ALL are missing. I may have been wrong about deduction, but that is because you don't understand the frustration I was going through in learning how it works. What you are all doing is semantics!

Please, please, please just re-read the second part and understand what I have made.

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Here is what I said on OO.net. The same applies to all of you:
OH MY GOD!!! You are all missing the POINT!!! FORGET about the first part, if it really bothers you. I achieved something in my defense of Induction that you ALL are missing. I may have been wrong about deduction, but that is because you don't understand the frustration I was going through in learning how it works. What you are all doing is semantics!

Please, please, please just re-read the second part and understand what I have made.

<{POST_SNAPBACK}>

If you want to change the dual focus of your argument and have everyone forget about deduction (a vital cognitive tool), then you need to restate your argument and narrow the focus to that which you are now claiming is important.

In other words, do not get upset or frustrated because people are addressing the argument you actuallymade rather than the argument you should have made or thought you made.

Put simply, if you wish to retract as invalidyour comments about 'deduction', then do so. But, if you continue to argue their validity (see your last post - "deduction is bogus"), then do not blame others for disputing the argument you continue to make. That is not "semantics". That is addressing YOUR argument as YOU present it.

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It seems like you're trying to deduce that deduction isn't important. You make some clever arguments, but I'm not really sure what you're trying to prove.

Also, your "case for induction" relies upon deduction. Simply knowing that Magellan went around the world isn't enough to use induction to prove that the world is round. You use these premises (arrived at through induction):

1) All round things do not have edges

2) All flat things do have edges

3) Magellan went around the world without reaching an edge

to DEDUCE that the world is round.

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Firstly, I was not thinking clearly. You were right to attack my attacks on deduction. I apoligize.

Secondly, let us begin again. Here is a better summation of my thoughts (again expressed in an email to my prof):

"Lets see is I got this right. Induction produces [high -good/low-bad]

levels of certainty because of the nature of the logic itself. Deduction is

setup such that it is impossible for both the premises to be true and the

conclusion false (if a connection exists between them); thus includes an

inherent truth/falsity preserver. Induction, however, does not guarantee

such a property. It is conceivable, although perhaps very unlikely in some

cases (ie. gravity), for the premises to be true, and the conclusion false.

This doesn't apply in every case, but the possibility is there.

If that is true, then I would disagree and agree. I say that an inductive conclusion

only speaks to its premises, not the future. I grant you that the link you

are looking for [between inductive premises and it's conclusions] doesn't

exist qua existing, but in a sense it does. I see how one might think there

is an inherent uncertainty involved in induction, but I think that as long

as one says "I am 100% sure about THESE ravens being black ("these ravens"

being all the ravens I have observed), one should be fine. In other words,

as long as one sets one's frame of reference.

Amse"

I am going to try and keep my emotions out of my arguments from now on. (The same thing happened between HaloNoble6 and I on the "Batman Begins" thread on OO.net)

Thirdly, I don't have the time to read through all of your posts as there are now, so please try and keep your arguments as concise as possible ( I will try and do the same).

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Almost every sentence in that summary is incorrect. There is no terse answer to the problem's present in it so I would just offer you three recommendations that might help you to grasp the nature of induction. The first (and cheap one) is to read or reread "The Analytic-Synthetic Dichotomy" by Leonard Peikoff included in Introduction to Objectivist Epistemology. My second recommendation is the considerably more costly but much more relevant lecture series, Objectivism through Induction. Lastly, I guarantee that debating the topic of induction with a humanities professor (most especially a philosophy professor) will do nothing but hinder your understanding.

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Almost every sentence in that summary is incorrect.

Could you try and address some of my "problems"?

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Scare quotes aside, there most certainly is a problem—just as one example—with the statement, "an inductive conclusion only speaks to its premises, not the future." In fact, this idea is exactly one of the ways that induction has been attacked by its enemies; it is an expression of the analytic-synthetic dichotomy which is why I recommended that you read that essay.

If you hold that inductive conclusions do not apply to the future, then you have implicitly accepted this dichotomy. It divides knowledge into two kinds: the kind that's time-stamped and the kind that isn't. The former kind, it follows, is less certain than the latter because we do not know whether or not our conclusion will apply in the next instance until that instance has been observed. The latter kind is better because it is universal, it applies equally always. This is one of the ways that philosophers have divided knowledge into synthetic and analytic kinds.

The key to overcoming this confusion is to better understand the nature of concept-formation. There is a very important passage from Introduction to Objectivist Epistemology that identifies the crucial point here: "A concept is not formed by observing every concrete subsumed under it, and does not specify the number of such concretes. A concept is like an arithmetical sequence of specifically defined units, going off in both directions, open at both ends and including all units of that particular kind. For instance, the concept 'man' includes all men who live at present, who have ever lived or will ever live." (pp. 16-17) This is, in essentials, an answer to the "problem" of induction and it is why inductive conclusions do not carry time stamps.

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Scare quotes aside, there most certainly is a problem...

Oh, that's not what I meant. I was not being sarcastic. I really wanted you to address my "problems". I appreciate your help.

Let me think about all of this.

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Oh, that's not what I meant. I was not being sarcastic. I really wanted you to address my "problems". I appreciate your help.

<{POST_SNAPBACK}>

Ahh, thanks for the clarification. It's hard to convey subtleties like this through text so I appreciate the clarification.

Ray, are you speaking of "measurement ommision"?

<{POST_SNAPBACK}>

Well, yes. Measurement-omission is the means by which we attain "timeless" knowledge. The passage that I quoted is one of "two links between the conceptual and the mathematical fields." (ITOE, p. 16) The other link is measurement-omission so your subconscious is right to trigger this connection.

If you are finding this lead helpful, perhaps the following analogy will help. Miss Rand compares the relationship between concepts and their referents as the same relationship that exists between algebraic symbols and particular numbers. Now, you wouldn't say that 2a = a + a is true when a = 1 and we know this because we plugged 1 into the equation and derived 2 for both sides but we cannot say for certain that 2a = a + a is true when a = 100 because we have not yet done that math would you?

I think the statement that I argue against in my previous post is in essence saying this very thing. But it's wrongheaded because inductive knowledge stands in exactly the same relationship to the concretes that it subsumes as do algebraic equations to particular numbers. 2a = a + a is not just true now, it will always be true. The objection that every concrete subsumed by a generalization must be observed in order for that generalization to be universal is the same pattern, namely that you cannot be certain that your inductive conclusions apply tomorrow because a new concrete may come along that blasts the conclusion apart. But 2a = a + a will always be true and we don't need to plug every concrete number through the equation to know this.

The point here is that validly formed concepts serve the same role in cognition as algebraic symbols do in equations like 2a = a + a. And we know this thanks to those two revolutionary identifications by Miss Rand concerning the nature of concept-formation: open-endedness and measurement-omission.

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Here is an email I sent to my prof. "Point 1" is my answer to how we know what the fundamental characteristics of an existent is, and "Point 2" further elaborates on the nature of concepts; I think completing my theory.

Two points -

1) The way we determine the "essential characteristics" of an existent is sort of a backwards question. "Characteristics" is really a negative concept - it describes what an object IS NOT. It describes the differences between all the finite numbers of object of which we are aware AND their relation to a existent. The more objects/existents we are aware of, the more specific our language is. The Thus, a concept is NECESSARILY defined by its context - context in this respect meaning the sum total of our knowledge [of existents]. A concept is not the existent itself, but our way of representing it.

2) I can anticipate the question already - "That is all fine and good, but that still cannot possibly predict the future. Even if we understand the nature of concepts, and of the "essential characteristics of the sun", what's not the say that tomorrow the sun WOULDN'T rise?" The answer to this question is that we DON'T know that the sun will certainly rise tomorrow. There is a possibility that it won't rise, but one cannot predict the events that may or may not take place tomorrow. What was the point of all that then? Have I conceded my case? No. The key thing here is that a concept is NECESSARILY defined by its context. Our sum body of knowledge that conditions a given context [of a concept] may or may not change, but that doesn't mean that our statement is false.

Let me explain. Suppose the sun didn't rise tomorrow. This is the EFFECT we observe. By it's nature in reality, a cause must exist. Once we figure out this cause, we revise our statement by adding a qualifier. This does not mean we were wrong in saying that "the sun will rise tomorrow"/ or "the sun will always rise"; because implicit in that statement is a reference to context; the body of knowledge that we based that conclusion on. If we learn that the sun didn't rise because (let's say) an alien used a really big oven mitt to hold the sun down, we have added knowledge to our context and our conclusion changes, but NOT our initial conclusions about the nature of the sun.

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The way we determine the "essential characteristics" of an existent is sort of a backwards question.

Actually, this is a very good question worth asking. Why do you think it is backwards?

"Characteristics" is really a negative concept - it describes what an object IS NOT. It describes the differences between all the finite numbers of object of which we are aware AND their relation to a existent.

A characteristic of an object is most certainly not what the object is not. Knowledge is knowledge of what things are.

I can anticipate the question already - "That is all fine and good, but that still cannot possibly predict the future. Even if we understand the nature of concepts, and of the "essential characteristics of the sun", what's not the say that tomorrow the sun WOULDN'T rise?" The answer to this question is that we DON'T know that the sun will certainly rise tomorrow.

<snip>

This does not mean we were wrong in saying that "the sun will rise tomorrow"/ or "the sun will always rise"; because implicit in that statement is a reference to context; the body of knowledge that we based that conclusion on. If we learn that the sun didn't rise because (let's say) an alien used a really big oven mitt to hold the sun down, we have added knowledge to our context and our conclusion changes, but NOT our initial conclusions about the nature of the sun.

<{POST_SNAPBACK}>

I would recommend against approaching induction as primarily a means of predicting the future. It is not, and your example shows this. The purpose of induction is to discover underlying principles of nature, which requires identifying their causal mechanisms. This knowledge lets us predict what will happen when only those same causes are at work in the future, but it does not let us say which causes will necessarily be in effect in any given situation.

Thus, there is no qualification needed to our knowledge about the sun or the earth if a "big alien" stops the earth from rotating (and thus the sun from "rising"). That big alien is not invalidating our knowledge, since it is presumably just exerting enough counteracting force on the earth to stop the rotation, with its giant oven mitt. :) Our knowledge about terrestrial motion would only require qualification if we discovered there was a way to stop the earth's rotation without, say, exerting any force on the earth.

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I would recommend against approaching induction as primarily a means of predicting the future....

I thought of an example that might make my distinction more clear than the issue of the sun rising. Consider Dr. Peikoff's excellent blood-type example. A medical principle was discovered that, for instance, "All blood with type A is compatible for transfusions." The principle was not "A man with blood type A will live when you give him type-A blood," although on first glance this seems the same. (This compares to "the sun will rise tomorrow.") That would be a lousy principle--there are all kinds of ways a man can die, and having matching blood types is not some magic talisman that wards off death. Thus if you give type-A blood to such a man, and he dies of infection from the operation or gets a disease from the transfused blood, that does not reflect on the blood-type knowledge in the least. No qualifier is needed--the principle was that the man would not die from blood-type incompatibility, and he didn't (he died from some other cause).

Now contrast this with the discovery of the Rh-factor. Now there were cases in which a man with type-A blood died as a result of being given other type-A blood. This effect was not accounted for in the original knowledge, and thus this new cause had to be studied so that the principle could be qualified to include it.

Does that illustrate why it is very misleading to expect principles derived by an inductive process to "predict the future"?

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I would recommend against approaching induction as primarily a means of predicting the future....

I thought of an example that might make my distinction more clear than the issue of the sun rising.

[....]

Does that illustrate why it is very misleading to expect principles derived by an inductive process to "predict the future"?

Yes, it does. Does the rest of my logic follow though? I am rather fond of the "identifying the fundamental characteristics of an existent " :) .

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