Blame David Hume

[Darrell Hougen]

In fact the Law of Identity is about as relevant to the problem of induction as a fish is to a bicycle.

The law of identity is never relevant in philosophical arguments as no one denies that law, and claims that someone violates that law in an argument are mere Objectivist rhetoric and cannot be proved.

So says you. The Problem of Induction clearly violates the Law of Identity, as I have shown.

Darrell

[Darrell Hougen]

Really? The nature of an egg says nothing about what will happen if you throw it against a brick wall?

AOI says the egg shell is the egg shell. It does not say how brittle or strong it is (or isn't). That has to be established by observation. And even if every egg you have ever seen will break if dropped on a hard surface, that does not preclude the existence of an egg with a much tougher shell. It is not self evident that eggs break when dropped on or thrown against a a hard surface.

Ba'al Chatzaf

Strictly speaking, according to Hume --- the logical conclusion of the Problem of Induction --- it is not merely the case that a particular egg might not break, if dropped, but that it might be the case that no egg will ever break again --- because eggs have no particular nature. Mysteriously, however, they can still be identified as eggs. A manifest contradiction.

Darrell

[Michael Stuart Kelly]

I don't think a mathematical statement is knowledge. "2" per se refers to nothing. "2 + 2 = 4" per se refers to nothing. "2X + 2Y" tells us nothing about X or Y. X and Y tell us nothing about 2.

Brant,

Think along these lines using the law of identity:

2 mental units of the same kind + 2 mental units of the same kind = 4 mental units of the same kind.

These mental units have a specific nature that can be identified. (1) Each unit is an individual member of a wider category of existents (mental units), (2) They are countable, (3) They exist only in the mind, (4) Each unit has the same significance as any other unit on a primary level, (5) They can be added to both external and internal referents for identification, including themselves. I can probably think of some more characteristics. (I haven't mulled this over enough to get genus and differentia yet, but it is not difficult.)

Having an identifiable nature, they are referents. They exist.

Thus 2 + 2 = 4 actually does represent something.

EDIT: I guess the point of this is to say that the human mind exists as part of reality, not as something outside reality. If the mind exists, what it does exists also.

Michael

[Michael Stuart Kelly]

... in view of the tenor of certain posts I've seen on OL, I would like to make emphatically clear that I am not the slightest bit interested in ~attacking~ Ayn Rand, or Popper, or anybody else. What I ~am~ interested in doing is refining and improving my knowledge and understanding of ~philosophy~, a subject I have been interested in since I was sixteen years old.

Nick,

That is a breath of fresh air if I ever read one.

Michael

[merjet]

Here is a breath of nitrous oxide.

http://video.google.com/videoplay?docid=-4215496701990923822

[tjohnson]

Yes, in "pure" mathematics, a higher level of abstraction is assumed. Numbers, points, lines, functions, etc., are treated as if they were objects, not characteristics of objects. However, this is a convenience only. It is not a repudiation of the context required to make numbers, and thus arithmetic and mathematics, meaningful. It is just "permission" to leave out the extra language. When people take "science" and/or "mathematics" to be superior, purer, more certain, etc., than philosophy or reason at large, they are mistaking that convenience as lack of encumbrance, which it isn't. There isn't pure mathematics without applied mathematics, and there isn't either without pre-existing concepts.

Here is the difference between mathematics and all other languages. In mathematics our definitions contain all particulars and no others are allowed. This is possible because mathematical objects are not related to perception like ordinary objects. In other languages we define things by certain criteria but there are always characteristics we can observe not included in our definitions and things can change over time, etc. It is not a case of superiority it's just different. You might say that mathematics is a perfect language but in it we can only speak about limited things but in other languages we can speak about everything but imperfectly.

[tjohnson]

Thus 2 + 2 = 4 actually does represent something.

Very true, but I think what you will find is that they represent relations in general and they can be used to represent specific relations in a given example.

[Brant Gaede]

I don't think a mathematical statement is knowledge. "2" per se refers to nothing. "2 + 2 = 4" per se refers to nothing. "2X + 2Y" tells us nothing about X or Y. X and Y tell us nothing about 2.

Brant,

Think along these lines using the law of identity:

2 mental units of the same kind + 2 mental units of the same kind = 4 mental units of the same kind.

These mental units have a specific nature that can be identified. (1) Each unit is an individual member of a wider category of existents (mental units), (2) They are countable, (3) They exist only in the mind, (4) Each unit has the same significance as any other unit on a primary level, (5) They can be added to both external and internal referents for identification, including themselves. I can probably think of some more characteristics. (I haven't mulled this over enough to get genus and differentia yet, but it is not difficult.)

Having an identifiable nature, they are referents. They exist.

Thus 2 + 2 = 4 actually does represent something.

EDIT: I guess the point of this is to say that the human mind exists as part of reality, not as something outside reality. If the mind exists, what it does exists also.

Michael, the point is qua mathematics, if I have this right, the units don't have to be identified. If they aren't you just have math. Mathematical statements (correctly formulated?) are always true. When you ID the units the question is whether the ID is correct: static or manipulated (with math).

I'm now going to shut up until DF comments, at least, for I'm in over my head here.

--Brant

[Darrell Hougen]

Hi Nick

I am puzzled. Do you disagree with the purely logical situation as outlined by Hume? For Hume's problem doesn't mean that things don't have identity; merely that our knowledge of that identity cannot be certain.

Thus there is an obvious distinction to be made between:

1) The identity of a thing

and

2) Our knowledge of that identity

This is the point at which Hume's logical problem begins AFAICS.

For as most here seem to agree, it is simply illogical to conclude that all eggs break on impact with concrete from the fact that you have seen X number of them do so. Same with sunrises. Thus, our theories as to what an egg is, its identity (for example, our expectations of how it will behave in certain situations such as in collision with concrete) are illogical if we hold them with certainty.

The issue is not simply certainty. If it were, we would be pretty close to agreement. According to Hume and Popper, not only is it illogical to hold a theory with certainty, it is illogical to place any weight whatsoever on the probable truth of a theory. Here is another quote from Popper, The Problem of Induction (http://dieoff.org/page126.htm):

The logical problem: Are we rationally justified in reasoning from repeated instances of which we have had experience to instances of which we have had no experience?

Hume's unrelenting answer was: No, we are not justified, however great the number of repetitions may be. And he added that it did not make the slightest difference if, in this problem, we ask for the justification not of certain belief, but of probable belief. Instances of which we have had experience do not allow us to reason or argue about the probability of instances of which we have had no experience, any more than to the certainty of such instances.

So, are you defending Popper's view or not? If so, then you cannot assign any probability other than 0.5 to the event of the Sun rising tomorrow or to an egg breaking when dropped on concrete. You must assume complete ignorance because past experience has "no bearing" on expectations about the future.

If it is knowledge, rather than the Law of Identity that is in question, then it is Popper's view (and Hume's view) that it is impossible to have any knowledge at all of a predictive nature about anything. Is that your view?

Darrell

[Darrell Hougen]

Induction most certainly is a valid form of reasoning. Since when is establishing categories not validly rational?

The observation that some things belong to the same category is not a process of induction. If it were, how could you determine that two objects were of the same kind? How could you determine that two birds were swans (or were even birds)?

The whole notion of induction depends upon the assumption of a rather funny scenario in which a teacher repeatedly points and tells a learner, "that is a swan and that is a swan and that is a swan, etc.," until the dumb pupil finally catches on. Seeing enough swans allows the student to bound the variation in the concept of swan and catch on to the parameters delimiting the category of swan. Unfortunately, the unthinking student doesn't understand anything about swans, and so, seeing only white swans, retains that characteristic as important, only to be embarrassed later.

I know exactly how this scenario works because I learned it when I studied Artificial Intelligence in college. However, instead of a human student, the "student" was a computer program. The program was fed a number of examples labeled "swan" or "not-swan" (or "cow" or "horse", etc.). It was then the job of the program to form a statistical model of the "concept" swan on the basis of the labeled training examples. The hope was to emulate human learning. Some success was achieved. See my Master's Thesis, Fast Texture Recognition Using Information Trees.

The problem is, what do you do with unlabeled examples? What if there is no teacher around to tell you what is a swan and what is not a swan? The AI community has had very little success (the last time I checked) with "unguided learning." There are some clustering algorithms, but none of them come close to the performance of a human. Why? Because the category formation process is not fundamentally probabilistic in nature. It is a process of isolating essential distinguishing characteristics. Yes, it is necessary to know about inter and intra-class variation, but, generally, there is no overlap of essential distinguishing characteristics between reasonably formed classes of objects.

Darrell

[Daniel Barnes]

So, are you defending Popper's view or not? If so, then you cannot assign any probability other than 0.5 to the event of the Sun rising tomorrow or to an egg breaking when dropped on concrete. You must assume complete ignorance because past experience has "no bearing" on expectations about the future.

Well firstly Darrell, to be honest, from your comments here it doesn't sound like you fully understand the argument you're attempting to criticise. (For example, Popper would not assign a 0.5 probability to the sun rising tomorrow based on X no. of previous observations. He would say that no such probability is assignable. And so does Hume.)

If it is knowledge, rather than the Law of Identity that is in question, then it is Popper's view (and Hume's view) that it is impossible to have any knowledge at all of a predictive nature about anything. Is that your view?

No, and it's not Popper's view either. In fact probability was one of Popper's favourite fields of study. Probability is, however, deductive, not inductive. Are you sure you are familiar enough with Popper's theories to criticise them?

[Daniel Barnes]

Induction most certainly is a valid form of reasoning.

Stolen Concept Alert!

[Daniel Barnes]

[Popper]:"The logical problem: Are we rationally justified in reasoning from repeated instances of which we have had experience to instances of which we have had no experience?"

Actually, here seems to be the problem. You need to focus on the first three words of this quote.

Edited August 23, 2008 by Daniel Barnes

[Daniel Barnes]

Strictly speaking, according to Hume --- the logical conclusion of the Problem of Induction --- it is not merely the case that a particular egg might not break, if dropped, but that it might be the case that no egg will ever break again --- because eggs have no particular nature. Mysteriously, however, they can still be identified as eggs. A manifest contradiction.

As I wrote in another post, the basic problem with this whole line of argument is that it conflates two different things:

1) Reality

2) Our knowledge of reality

Hume's critique applies to 2), not 1). It doesn't entail that things "have no particular nature." You are quite mistaken. All it says is that from X previous experiences we are not entitled to draw a logically valid future prediction. This is a knowledge problem, not a reality problem. Thus there is no "manifest contradiction", and no conflict with the LOI.

[tjohnson]

So, are you defending Popper's view or not? If so, then you cannot assign any probability other than 0.5 to the event of the Sun rising tomorrow or to an egg breaking when dropped on concrete. You must assume complete ignorance because past experience has "no bearing" on expectations about the future.

No, and it's not Popper's view either. In fact probability was one of Popper's favourite fields of study. Probability is, however, deductive, not inductive. Are you sure you are familiar enough with Popper's theories to criticise them?

Interesting, from http://en.wikipedia.org/wiki/Bayesian_probability

In Bayesian theory, the assessment of probability can be approached in several ways. One is based on betting: the degree of belief in a proposition is reflected in the odds that the assessor is willing to bet on the success of a trial of its truth. Richard T. Cox showed that Bayesian inference is the only inductive inference that is logically consistent.

...Subjective Bayesian probability interprets 'probability' as 'the degree of belief (or strength of belief) an individual has in the truth of a proposition', and is in that respect subjective. Some people who call themselves Bayesians do not accept this subjectivity, whereby they would regard this article's definition of Bayesian probability as mistaken. The chief exponents of this objectivist school were Edwin Thompson Jaynes and Harold Jeffreys. Perhaps the main objectivist Bayesian now living is James Berger of Duke University. José-Miguel Bernardo and others accept some degree of subjectivity but believe a need exists for "reference priors" in many practical situations.

[tjohnson]

Strictly speaking, according to Hume --- the logical conclusion of the Problem of Induction --- it is not merely the case that a particular egg might not break, if dropped, but that it might be the case that no egg will ever break again --- because eggs have no particular nature. Mysteriously, however, they can still be identified as eggs. A manifest contradiction.

As I wrote in another post, the basic problem with this whole line of argument is that it conflates two different things:

1) Reality

2) Our knowledge of reality

Hume's critique applies to 2), not 1). It doesn't entail that things "have no particular nature." You are quite mistaken. All it says is that from X previous experiences we are not entitled to draw a logically valid future prediction. This is a knowledge problem, not a reality problem. Thus there is no "manifest contradiction", and no conflict with the LOI.

Yes, it's very important to distinguish the two. Korzybski used the term 'event' or 'scientific object' to mean what most people do by 'reality', I think.

[tjohnson]

You need to understand what someone is saying and actually verify what they need before telling them what they need.

Did you do this with me?

Edited August 23, 2008 by general semanticist

[Michael Stuart Kelly]

The observation that some things belong to the same category is not a process of induction. If it were, how could you determine that two objects were of the same kind? How could you determine that two birds were swans (or were even birds)?

Darrell,

This is covered in the beginning of ITOE. What we are concerned about with induction is not assigning things into a pre-existing category so much as identifying a category, and creating a category (i.e., a concept). You identify by noticing differences and similarities, then by differentiation and integration.

You don't need a teacher for this, either, as looking at any baby can prove. (But you can have a teacher like in your example. It's just not a requirement for noticing differences and similarities.)

That's the Objectivist version, at least.

Michael

[Michael Stuart Kelly]

Induction most certainly is a valid form of reasoning.

Stolen Concept Alert!

Semantics Alert!

[Michael Stuart Kelly]

You need to understand what someone is saying and actually verify what they need before telling them what they need.

Did you do this with me?

GS,

Yep.

On purpose.

Rhetorical emphasis by presenting an example and not talking about it. (There must be a technical name for this, but I don't know it. Artists use this method all the time.)

Michael

[Michael Stuart Kelly]

Michael, the point is qua mathematics, if I have this right, the units don't have to be identified.

Brant,

If the mental units cannot be correctly identified as themselves, then 2 does not have to follow 1, or 2+2 could equal 5 because they would not have an identity. You can't have the concept math without the referents of the basic units (albeit the concept entails method also).

This mental unit qua mental unit is something like an axiomatic concept like existence. You can observe it (internally) and identity it as something in itself, with a specific identity, but it is applicable to all things.

Michael

[Brant Gaede]

Michael, the point is qua mathematics, if I have this right, the units don't have to be identified.

Brant,

If the mental units cannot be correctly identified as themselves, then 2 does not have to follow 1, or 2+2 could equal 5 because they would not have an identity. You can't have the concept math without the referents of the basic units (albeit the concept entails method also).

This mental unit qua mental unit is something like an axiomatic concept like existence. You can observe it (internally) and identity it as something in itself, with a specific identity, but it is applicable to all things.

Michael

All 2 denotes is more than 1 and less than 3. 2 can be 2 of anything or different things or NOTHING at all except empty units. I now have to give up. I feel like a child trying to drive a car blocked by a truck I keep running into.

--Brant

[Michael Stuart Kelly]

All 2 denotes is more than 1 and less than 3. 2 can be 2 of anything or different things or NOTHING at all except empty units. I now have to give up. I feel like a child trying to drive a car blocked by a truck I keep running into.

Brant,

Don't these units have to be equal for that statement to be true?

If they are, isn't that already identity? How can something be equal to something else, be measurable, if it doesn't exist?

Units exist in our minds, but they still exist. An empty unit is still a unit. In other words a mental unit is an existent. And any existent can be a referent for a concept.

You appear to be blaming the existent (the unit) for not having the kind of identity you wish it to have. But that is no justification for the hypothesis that mental units don't exist. They do. In reality.

At least I know my mind is part of reality. (I am now biting my tongue on thinking about yours... )

Michael

[Brant Gaede]

All 2 denotes is more than 1 and less than 3. 2 can be 2 of anything or different things or NOTHING at all except empty units. I now have to give up. I feel like a child trying to drive a car blocked by a truck I keep running into.

Brant,

Don't these units have to be equal for that statement to be true?

They don't have to be anything. Why they wouldn't be anything is another matter. We are trying to get to the bottom of Dragonfly's statement that "All mathematical statements are true." I'd guess you'd do that by examining the structure of the statement, not the out-there reality. Hence, empty, contentless units. Anyway, I'm going over the Ananlytic-Synthetic thread when I have some time. I am curious why you aren't curious about whether a simple statement about mathematics made by a mathematician might be true.

--Brant

Edited August 23, 2008 by Brant Gaede

[BaalChatzaf]

Math isn't the holy grail you think. Did you know that two and two don't always make four? Take two bananas and add two quarts of swamp gas. What do you get? You don't get four of anything!! You don't get four objects, or four "measures." Would you like to say that what we can't do is "add" these two particular "twos?" But we can. We can add them to a tank, for example.

The point is that numbers are adjectives. "Two" is always two of some kind. We are so accustomed to leaving out the grammatical niceties, we lose sight of their existence. Math is nothing until you get its conceptual context straight.

--Mindy

Without mathematics there can be no quantittive science (in particular, physics). Without physics technology would be rather sparse and unsophisticated. So if you like really neat gadgets like computers and GPS you have to have mathematics.

It turns out that every non-primitive civilization has developed mathematics in one form or another. The Greeks developed axiomatic mathematics, which is the basis of the mathematics we have.

It may not be a holy grail but without it we are little more than grunting savages.

Ba'al Chatzaf