The Analytic-Synthetic Dichotomy


Dragonfly

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Greg Browne:

>And changing the meanings of terms, using old terms to refer to new concepts or, in this case, to other old concepts, is a very bad habit of mathematicians and of non-mathematicians, as I have said before. It creates confusion and allows for unintentional and intentional deception. Mathematicians already had the terms 'postulate' and 'assumption', and so there was no need hijack 'axiom' from its existing meaning...

Ho, ho, yes mathematicians "hijacked" the term "axiom" so it "allows for unintentional and intentional deception."

There is nothing funny about that, but misuse of the meanings of the words can be comic (though sometimes tragicomic, when major practical decisions rest on it): for example, redefining ‘curve’ so that it applies to all lines, straight or curved, so that lines which aren’t curved come to be called “curves” .

In any case, why are people having so much trouble understanding what I am saying on this point, and seeing that it is true?. It is almost common sense: we should not change the meanings of terms in the middle of an investigation or debate—unless we announce explicity beforehand that that is what we are doing, and give an explicit definition expressing the new meaning—since otherwise we would be using terms ambiguously, which is a basic logical fallacy. And further we should not even change meanings then, since it creates confusion, and leaves the door open to ambiguity.

It is ironic that happens so much in discussing these topics, since the Logical Positivists, who are main defenders of the view that Peikoff’s criticizing, aimed for an improved language in which each term had only one meaning, and yet they themselves contributed to ambiguous use of terminology by creating new meanings and definitions of existing terms.

Of course they usually would say that they didn’t want to add their definitions and meanings to existing ones, but rather replace existing definitions and meanings—but why should they have been allowed to do this, to give existing terms with well-established meanings new meanings? By what right to they remake the English language and other natural languages?

Now some people would take a middle-of-the road position, and they that these was all right for technical language, but not for ordinary language: for example, if, say, physicists wanted a technical vocabulary, using existing terms but with special definitions for physicists, while lay people used the terms with the old meaning, that is OK. But it is not: why should physicists and lay people use the same term differently? If physicists want a new vocubalary to express new concepts, that is fine, but it should be made up of new terms (either new words or new sets of old words), not old terms with new meanings. Otherwise ambiguity will be present and the physicsts and lay people will just talk past each other, and there is too much lack of commication between scientists and lay people as it is. Better to follow Leibniz’s saying: “We should think with the wise but speak with the common people”.

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So this, if it is an accurate description of mathematical practice, shows that mathematicians, at least some of the time, use 'axiom' and 'postulate' and 'assumption' to mean the same thing. But this involves changing the meaning of 'axiom', which did not refer to any arbitrary assumption, but to a foundational truth. And changing the meanings of terms, using old terms to refer to new concepts or, in this case, to other old concepts, is a very bad habit of mathematicians and of non-mathematicians, as I have said before. It creates confusion and allows for unintentional and intentional deception. Mathematicians already had the terms 'postulate' and 'assumption', and so there was no need hijack 'axiom' from its existing meaning (which, by the way, is still more or less used outside of math).

Also, the above passage leaves out the possibility of self-evident truths.

If all you have is arbitrary postulates and theorems deduced from them, then you have no reason to think any of them are true. Then mathematics would be worthless.

The term axiom is used for traditional reasons. It is picked up from Euclid's presentation of geometry. In -Elements- by Euclid, there are axioms and postulates. ...

....

Perhaps it were better if you studied the history of mathematics before using slam terms such as hijack and intentional deception.

Ba'al Chatzaf

If we're going to approach things that way, I'll point out that it would be better if you extended your studies of intellectual history beyond the history of mathematics, where you will find that concepts such as the concept of axioms are not confined to mathematics nor invented by mathematicians.

Also, be wary of assuming that premodern mathematicians shared all of the methodological presuppositions of modern mathematicians.

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So this, if it is an accurate description of mathematical practice, shows that mathematicians, at least some of the time, use 'axiom' and 'postulate' and 'assumption' to mean the same thing. But this involves changing the meaning of 'axiom', which did not refer to any arbitrary assumption, but to a foundational truth. And changing the meanings of terms, using old terms to refer to new concepts or, in this case, to other old concepts, is a very bad habit of mathematicians and of non-mathematicians, as I have said before.

That you don't know the meaning of mathematical terms does not mean that these are somehow secondhand and less correct than the meaning you happen to be familiar with.

I did not say they were secondhand. Insofar as they are incorrect they are incorrect because they do not express the meaning of the term in ordinary language. Why is this bad? See my latest reply to Daniel.

As Bob told you, the notion of an axiom in mathematics is nothing new.

I never said it was new. Where did you get that idea?

If all you have is arbitrary postulates and theorems deduced from them, then you have no reason to think any of them are true. Then mathematics would be worthless.

You still don't get it. Arbitraty postulates and theorems deduced from them are by definition true.

No: we cannot make anything true by simply making a definition (except in special cases of self-referential truth, such "I am making a definition" which is true if you utter while making a definition). It sure would be nice if we could, but that's a magical view of the world.

Even if we make up new concepts by making new definitions, we don't make the truths that can be derived from them true. For example, consider the case of minyaks and munyaks, which I discussed earlier here. I supposed that for some reason I made up these new concepts, definining 'minyak' as 'a geometric figure with 28 equal straight sides of 1 inch in length" and 'munyak' as 'a geometric figure with 29 equal straight sides of 1 inch in length". The concepts are arbitrary products of my mind and the terms and their definitions are my arbitrary linguistic creations. Nonetheless, the truths that can be derived from these concepts and definitions are not arbitrary or produced by me. For example, the truth that the ratio of the area of a minyak to the area of a munyak is______(whatever quantity it is) is something that was not created by me (I don't even know what it is) but rather has to be discovered by careful reasoning, whose rules are not arbitrary creations.

That implies that they don't tell us anything about the real world, in other words, these are analytic statements.

That's assuming that analytic truths don't tell us anything about the real world, which is one of the major points you need to argue for (I will send an updated version of the list in my next post).

And analytic truths, even in the narrow sense, cannot be made true simply by arbitrarily asserting that they are true.

That mathematical theories can be used in physical models is a completely different issue.

If they did not tell us anything about the real world it would be unlikely in the extreme that they were of value in physical models.

In those models we don't test the correctness of the mathematics, but the applicability of that particular mathematical theory.

The correctness of the math should already be established. But in a sense we did test Euclid's math and found that it does not wholly accurately describe the space of our world, which turned out to be curved.

You cannot prove or disprove a mathematical postulate (or axiom). Example: Euclid's 5th postulate.

You can prove something if you can show that it is self-evident or derive it by deduction from something self--evident.

You can disprove a postulate if you can deduce from it a conclusion that itself can be disproved.

No you cannot. Can you prove Euclid's 5th postulate? No, you can't. Can you disprove Euclid's 5th postulate? No, you can't. That is why it is called a postulate (or an axiom). You are confusing a postulate with a hypothesis.

Euclid thought that he was describing the properties of actual physical space. Relativity Theory says that he was not entirely correct, that space is curved, and their properties are described by the alternative geometries.

If you define ice as "Solid water that floats on water" then the definition will be inaccurate as an expression of the meaning of the word 'ice' in English, because it refers to any solid water, even those newly discovered forms that don't float.

Why would that be inaccurate? Bill Dwyer assured me that when Peikoff talked about "ice": "he's talking about normal ice, not very high density ice. Can't you see that??". So two Objectivists use a different definition of ice, one inclusive (also sinking ice is ice - implying that Peikoff's statement was incorrect), the other one exclusive (only floating ice is ice - implying Peikoff's statement was correct). This is of course just an illustration that definitions are arbitrary, not in the sense that any definition will do, but that there is not one single correct definition. Is heavy water a form of water?

The two different definitions of 'ice' express two different meanings of 'ice', because they determine two different reference classes, one of which includes sinking ice and the other does not, the latter being a subset of the former. Each of these definitions is correct as an expression of that meaning and reference, and each is incorrect as an expression of the other meaning and reference. I think that my definition expresses the meaning of the term 'ice' as expressed in ordinary language, because I think that ice is like a Shallow Kind, and therefore there is nothing more to it than being solid and water. However, Bill Dwyer seems to be taking ice as a Deep Kind, and if ice were a Deep Kind, the meaning of 'ice' would be in part determined by paradigm cases, and the ice samples we encounter in everyday life are paradigm cases of ice and so to be an ice sample it would have to share all of their common attributes, even the unknown ones, and so the unusual sinking ice would not be true ice, though similar in many qualities including many internal ones.

If some of the water of everyday life is Heavy Water (and my current understanding is that it is), then it is included in the meaning of the term 'water' and so Heavy Water is water, because water is a Deep Kind, and therefore its meaning is in part determined by paradigm cases, and the water samples we encounter in everyday life are paradigm cases of water, and if some of them are Heavy Water then Heavy Water is a subkind of water.

In any case, neither Peikoff nor I nor anyone else has defined 'water' in this way.

You'll mean "ice". Peikoff was so sloppy that he even didn't give any definition of ice.

That wasn't sloppiness: he assumed the definition "Ice is solid water", which almost everyone would have agreed to.

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Cal,

In late June we started to discuss the following claims, and then you got busy. Now if you have time we should resume discussion of them, since they are central to debate.

These are some of the claims which Peikoff and I deny and which Cal presumably affirms (where "definitional truth" means a truth expressing a Nominal Definition, which is a definition we learn when we first learn the meaning of a term, and includes all truths of logic and all truths of math):

1. that only definitional truths are such that their denial yields a contradiction (i.e., are analytic)

2. that only definitional truths are necessary (i.e., such that it is impossible for them to be false)

3. that only definitional truths are non-falsifiable (i.e., certain, provable with certainty)

4. that definitional truths are not knowable empirically (i.e. from experience)

5. that definitional truths are "non-factual"--i.e., they "say nothing about the world"

Now you need to argue for each of the claims on this list without using any of the others claims on this list as a premise. Otherwise you will not make your case.

Now as regards 1, you wanted to say that to say that say it was true by definition. And I said that if you want to define 'synthetic truth' this way, and define 'analytic truth' as definitional truth, I coull accept that, for the sake of the argument, but then you must be accept the consequences of doing so: now you can no longer say that the following are true by definition:

Truths whose denial is a self-contradiction = analytic truths

Truths whose predicate is contained in their subject = analytic truths

because those presuppose

Truths whose denial is a self-contradiction = definitional truths

Truths whose predicate is contained in their subject = definitional truths

which needs to be argued for.

(note: I do not deny that all of those the right of the = sign are included among those to the left of it, but I deny that all of those to the left of it are contained in those to the right of it).

So now you have 2 more to argue for.

Now regarding 2:

2. that only definitional truths are necessary (i.e., such that it is impossible for them to be false)

you say:

2. The necessity of a synthetic truth has no meaning to me. Such a statement may be true in this universe but not in another one. What does "necessity" mean in that regard?

No, a truth that is not true in some another universe is not a necessary truth: a necessary truth is a true that is true in all possible universes, by definition.

When you say that necessity of a synthetic truth has no meaning to you you are simply expressing your firm belief that necessary truths cannot be synthetic, but that is no justification for saying that you don’t understand my denial of this belief and does not prove that synthetic truths cannot be necessary..

I assume that you agree that I necessary truth is one that cannot be false (in any possible universe), and you are using synthetic to mean “non-definitional”. So a necessary synthetic truth, given your definitions, would be

a non-definitional truth that cannot be false in any possible universe.

You deny that there are such truths, because of your belief in 2:

2. that only definitional truths are necessary (i.e., such that it is impossible for them to be false).

But you still have not argued for 2. So that remains on the list.

Now for the next one:

3. that only definitional truths are non-falsifiable (i.e., certain, provable with certainty)

You say to this that statements may be non-falsifiable without being certain.

This implies then that 3 imaking at least 2 claims:

3a. that only definitional truths are non-falsifiable

3. that only definitional truths are certain (i.e., certain, provable with certainty)

So this will replace 3 on the revised list.

Now for 4:

4. that definitional truths are not knowable empirically (i.e. from experience)

You say:

This formulation is vague. The definitional truth may refer to something that is known empirically, but its truth cannot be derived empirically,

I would say that ‘derived’ is vaguer than ‘known’, but if you prefer this terminology you can have it. So 4 becomes:

4. that definitional truths are not derivable empirically (i.e. from experience)

Your argument is for this is that definitional truths cannot be falsified by empirical observation. This leaves one premise unstated.

4a. Definitional truths cannot be falsified by empirical observation.

(4b. What cannot be falsified by empirical observation cannot be derivable empirically.)

4. Definitional truths are not derivable empirically.

But now 4b needs to be argued for.

Now for 5:

5. that definitional truths are "non-factual"--i.e., they "say nothing about the world"

You say:

This formulation is also vague. A definitional truth may refer to things in the world, but it doesn't give any new information about the world, as its truth is independent of any empirical evidence.

Yes, they don't tell you anything about the world that is not already contained in them. On this we agree

But now the question is: do definitional truths give ANY information about the world. And I think you believe that the correct answer is “No”, and in that case we still have a disagreement, over this claim:

5’ that definitional truths do not give any information about the world.

So now the revised list of claims to be proven is this:

1'a. that only definitional truths are truths whose denial is a self-contradiction

1'b. that only definitional truths are truths whose predicate is contained in their subject

2. that only definitional truths are necessary (i.e., such that it is impossible for them to be false)

3a. that only definitional truths are non-falsifiable

3b. that only definitional truths are certain (i.e., certain, provable with certainty)

4b. what cannot be falsified by empirical observation cannot be derivable empirically.

and perhaps

5’ that definitional truths do not give any information about the world.

2 and 3b are the most important for you to prove.

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....modern physics. You know, the physics that has given us the A-bomb and the GPS system, as well as transistors and lasers. That latter is based on quantum physics which is held by Orthodox Objectivists to be patently absurd. Why is it that philosophically absurd theories predict reality correctly to twelve decimal places?

Ba'al Chatzaf

Philosophically absurd philosophies of science do not do these things; science does.

So why does modern scientists do so well? Because modern scientists do not practice the philosophy of scientific methodology that they preach--thank goodness. What most of them apparently still preach is a version of the philosophy of Logical Positivism, as do you and Cal. According to Logical Positivism, science can only be based on induction. But Logical Positivists have never been able to justify induction. Why? Because their philosophy is based on the premises of David Hume, who claimed that induction cannot be justified--and if you accept his premises you cannot justify induction (this is the famous "problem of induction"--which is only a problem if you accept his premises, which I of course do not). Some Logical Positivists tried to justify it, but their work did not satisfy other Logical Positivists. Two of the most prominent, one by Rudolf Carnap and one by Hans Reichenbach, were critiqued by Wesley Salmon, another Logical Positivist. Carnap argued that induction could be justifed by the laws of probability. However, Salmon pointed out that the laws of probability are mathematical truths, and so are necessary truths, whereas when you claim that induction from some past or present truth(s) to (alleged) future truths is true, you are make a factual claim. But Logical Positivists (folllowing Hume) say that there a no necessary factual truths. So if they are right (which they aren't) Carnap's attempt at justifying induction fails. A similar objection was made by Salmon against Reichenbach's attempt. In short, both of the attempts at justifying induction made by these two Logical Positivists violated their own Logical Positivist assumptions.

Fortunately most scientists, though they preach Logical Positivism, go right ahead and do their inductions, with the great successes you mentioned.

Now since I believe in necessary factual truths I can use Carnap's strategy and say that induction can be justified by mathematical laws of probability.

But since you believe that there are no necessary factual truths, Ba'al, how would you try to justify induction? (And I ask the same question of Cal.)

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Greg,

You haven't covered one point that I do want to talk about. (I am talking about these recent posts. If you covered it above, I missed it.) Our knowledge consists of both induction and deduction as processes of identification and reasoning. For some darn reason, I keep seeing an all-or-nothing approach in discussions about science. On a Popperian end, the existence of induction is flat-out denied. On the Objectivist end, I heard Peikoff say in one of the DIM Hypothesis lectures he provided online that all scientific truths are inductive (implying that they were not deductive).

All this is a false dichotomy. Both processes are needed. I recently wrote about this all-or-nothing approach in philosophy in discussing another subject.

When we get to discussions of this nature, I can't help but think that on being born, we are dealt a hand in a game we didn't choose. We have no control over the rules of the game, but we do over how we play.

In this game, there is chaos (chance) and causality, infinity and finiteness, consciousness and matter, logic and emotions, volition and prewiring, and so on. Death is the whistle indicating that the game is over. All this is "the given" to use Objectivist jargon.

Then some of the players set up their table at this game as "philosophers" and go about trying to change the rules by denying one or more elements and holding up a specific one as all there is. There are variations such as claiming that this or that element controls its counterpart, which actually exists but in an inferior state, etc., but the real idea is to pile on the complications to make it all sound good.

Voila! A school of philosophy is born.

I see this is true for the induction/deduction issue. It is like a tug of war and, at root, both sides are right when they say their type of reasoning is essential and both are wrong when they say (or imply) that the other type is not essential or somehow inferior.

The validity of deduction has been discussed so much that I have nothing to add. But I do about induction. A great deal of confusion about induction exists because of an axiom I arrived at that is never mentioned (or, at least, I have not seen it yet). I haven't formulated a definitive form but it goes something like this:

When two or more similar existents are perceived, more similar ones exist.

This is the root of induction and has nothing to do with mathematical probabilities. It is a fact of nature and, from what I see, it is a corollary of the Law of Identity. Not only is a thing what it is, it exists with similarities and differences to other things, thus all things can be categorized with other things when they are similar (if such are found). This is so strong that even when there is only one unique thing (like an individual person), it is possible to imagine another. In this last case, the idea of cloning has been around a long time.

This almost goes back to Aristotle's forms. Categories exist. Epistemologically they are components in a manner of mental organization. Metaphysically, they reflect something that actually can be perceived, so they exist. They are essentially differences and similarities. I don't see how one can deny that.

Michael

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x

Philosophically absurd philosophies of science do not do these things; science does.

So why does modern scientists do so well? Because modern scientists do not practice the philosophy of scientific methodology that they preach--thank goodness. What most of them apparently still preach is a version of the philosophy of Logical Positivism, as do you and Cal. According to Logical Positivism, science can only be based on induction.

Not so. Science develops along the lines of abduction which is hypothesizing the likeliest cause or maintaining the symmetry of the laws underlying the observed effects. See C. S. Peirce who first formulated abduction and Mario Bunge who elaborated on abduction. The way Einstein got to General Relativity was almost pure abduction. He presumed that one could not distinguish acceleration from the effects of a uniform gravitational field. How many spaceships and falling elevators did Einstein ride on? Another example was Maxwell who postulated the Displacement Current to account for a lack of symmetry in the laws of electromagnetic induction (not to be confused with Baconian induction). He introduced a term which accounted for a current that otherwise did not have a source. Maxwell insisted that currents have sources even when there are no wires to carry them. His -assumption- of the Displacement Current was driven by mathematical considerations alone, not empirical laboratory findings. The observables supporting the hypothesized displacement current were not seen until Hertz' experiments in the 1880's. The addition of the Displacement Current term to the equation for the curl of the magnetic field ultimately lead to the conclusion that electromagnetic waves must be produced by moving charges. Hello radio and T.V.! So much for induction of the the Baconian sort. When you look at what -scientists- do, as opposed to what the philosophers say they do, you get another story entirely.

Logical Positivism ala Carnap died back in the fifties and sixties. It was insufficient to describe what scientists really do. The non-deductive portion of theory formation is based on abducting to the likeliest cause. What scientists (the people who bring in the results) DO NOT DO MUCH OF is to take philosophers seriously. See some of Feynman's tart remarks on philosophy in his famous three volume lecture set. Feynman had nearly zero use for philosophers and philosophy, but he seemed to do alright without them. What lesson do I learn from this. If you want to understand science and what the scientists are doing, forget philosophy.

Ba'al Chatzaf

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Greg,

I'm arriving very late to this particular discussion, which has now grown beyond book length (a printout of the entire thread would run well over 300 pages of rather small print).

Still, I see that very little of the discussion has mentioned Willard van Orman Quine's rejection of the analytic-synthetic dichotomy, as presented in his 1951 essay "Two Dogmas of Empiricism."

Even if the criticism of Peikoff's account of other philosophers which was made in the [Gary] Merrill article were wholly justified, it largely misses the point, as regards ASD and most of Rand and Peikoff's work, because the account of other philosopher's views is history of philosophy, while it is clear that ASD is primarily a work of philosophy and only secondarily a work in the history of philosophy. (History of philosophy is taught in philosophy departments, and rightly so, but when you are doing history of philosophy you are not doing philosophy, but rather are studying how other people did philosophy).

It would only be a worry if no one at all advocated those views. But the views Peikoff attacks have certainly been advocated by many important philosophers. The position which combines all of these views is that of the Logical Positivists, the most important philosophers of the English-speaking world from the 1920s to the late 1940s (and, in philosophy of science, until the 1960s; it was still known as "the received view" of scientific theories in 1980s); it was not immediately criticized by their intellectual heirs, the Ordinary Language philosophers, who dominated philosophy in the English-speaking world from the 1940s to the 1960s, and before them it was defended by Hume in the mid-1700s.

Even today, prominent critics of the position, such as Hilary Putnam and Saul Kripke, still hold on to most of the dichotomies; they simply no longer align them all as Logical Positivists used to.

And a relatively pure form still is apparently strong among scientists, as Cal's [Dragonfly's] post indicates, which I expected.

As to whether Peikoff's quoted statement [that the analytic-synthetic dichotomy is accepted by "virtually every influential contemporary philosopher"] is an accurate summary of the situation, I calculate his college career must have run from the late 1950s to early or middle 1960s, and then Ordinary Language philosophy was still dominant (except in philosohy of science, where Logical Positivism remained the received view). Sartre's Existentialism was prominent, and he accepted at least the analytic-synthetic distinction. I know less about the Pragmatists, but their fallibilism, I believe, stopped at logic and math, and so most of them probably accepted it, too. That left Quine as the only real big name opposing it.

Leonard Peikoff's dissertation, completed in 1964, was titled "The Status of the Law of Contradiction in Classical Logical Ontologism." Now that Clemson University has a subscription to ProQuest digital dissertations, I've been able to download the entire thing in PDF.

So far I've only read only the two sections on Kantianism and conventionalism (pp. 165-188). But I can tell you that the dissertation is primarily an investigation of the history of philosophy. The focus of the dissertation is on accounts that ground the laws of logic in the nature of things, i.e., on variants of Platonism and Aristotelianism. The views that supplanted them--first Kantianism, then what Dr. Peikoff calls "conventionalism"--get a lot less attention, though there is enough material about conventionalism to give the reader a reasonable idea of which contemporary philosophers Dr. Peikoff had in mind.

Willard van Orman Quine is not mentioned in the dissertation. Among the logical empiricists (as Dr. Peikoff calls them) are A. J. Ayer, Carl Hempel, Hans Reichenbach, C. I. Lewis, and Ernst Nagel. Ayer, Lewis, and Nagel are quoted at some length on logic having no grounding in ontology.

There is scarcely a lick about Ordinary Language Analysis in the dissertation.

The sole pragmatist to be cited and quoted is John Dewey, who was a major influence on Dr. Peikoff's dissertation advisor, Sidney Hook. Although the revisability of logical truths doesn't come up explicitly in his response to Dewey, I recall that in his early 1970s lectures on modern philosophy, Dr. Peikoff devoted a lot of attention to Jamesian and Deweyan pragmatism, including some colorful stories that were almost certainly about exchanges with Hook (he spent little time on Charles Peirce, commenting that Peirce was a "mixed case" who held back from the subjectivism that Dr. Peikoff considered typical of pragmatism). Dr. Peikoff attributed to Dewey the view that, everything inevitably being in flux, the laws of logic had worked for so long that they were bound to need replacing in the near future.

Because Dr. Peikoff wanted to argue that Kantian views on logic were an unstable intermediary between old-fashioned ontologism and 20th century conventionalism, he also quoted two figures from the mid-1800s: Sir William Hamilton and Henry Mansel (the latter's interpretation of Kant was an obvious favorite with him; it's pretty clear where Ayn Rand got the Mansel quote that she used in one of her essays).

As to Peikoff's rejection of the analytic-synthetic dichotomy having been done earlier and better by Quine, it is true that there are many similarities in their positions but also many differences, and, as Roger says, they came at it from different premises, and they also came at in from different directions and reached some opposite conclusions: Peikoff thinks that all truths are such that their denial is self-contradictory, whereas Quine thinks that all truths are revisable. The former is true and I have been giving my reasons in other posts, whereas is the latter claim is hard even for great admirers of Quine to swallow. So, no, Quine did not do it earlier or better.

Clearly, Leonard Peikoff would have considered Quine a "conventionalist" (in the loose sense in which he uses that word in the dissertation).

But why he didn't refer to Quine in the dissertation, as an influential philosopher strongly opposed to logical ontologism, or in "The Analytic-Synthetic Dichotomy," for arguing against the dichotomy in what Dr. Peikoff would have considered precisely the wrong way, I have no idea. (If you read some of Doug Rasmussen's defenses of logical ontologism, you will find that Quine is a target, and for good reason.)

Ellen Stuttle mentioned J. Roger Lee back in the earliest stages of the discussion. The one time I met Roger Lee, he told me that Dr. Peikoff didn't know a whole lot about contemporary academic philosophy. I suspect there is something to this complaint...

Robert Campbell

PS. A surprising feature of this dissertation, at least to me, is Leonard Peikoff's strong interest in some fairly obscure figures from the 17th century, such as the "Cambridge Platonists" (Lord Herbert of Cherbury is on the reference list and Ralph Cudworth is quoted with great frequency) as well as the Port Royal school. He gives far more attention to Locke vs. Leibniz than to any issue or controversy in 20th century philosophy. Dr. Peikoff should have been in a strong position, had he wanted to, to mix it up with Noam Chomsky on innate language capabilities. (On account of his commitment to innate ideas, Chomsky is one of the few non-specialists you will find citing the Cambridge Platonists and the Port Royal school.)

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I did not say they were secondhand. Insofar as they are incorrect they are incorrect because they do not express the meaning of the term in ordinary language. Why is this bad? See my latest reply to Daniel.

They are not incorrect. This meaning can be found in any dictionary, and is not determined by pretentious philosophers who think that they have the monopoly of language.

As Bob told you, the notion of an axiom in mathematics is nothing new.

I never said it was new. Where did you get that idea?

If it is not new, it is correct. Language is determined by usage, not by ivory tower theoreticians who think that they know better. If a term is used for centuries, it is by definition correct.

If all you have is arbitrary postulates and theorems deduced from them, then you have no reason to think any of them are true. Then mathematics would be worthless.

You still don't get it. Arbitraty postulates and theorems deduced from them are by definition true.

No: we cannot make anything true by simply making a definition (except in special cases of self-referential truth, such "I am making a definition" which is true if you utter while making a definition). It sure would be nice if we could, but that's a magical view of the world.

Of course we can. If we define a bachelor as an unmarried man, then the statement "a bachelor is an unmarried man" is true by definition. This is what we call an analytic truth.

Even if we make up new concepts by making new definitions, we don't make the truths that can be derived from them true. For example, consider the case of minyaks and munyaks, which I discussed earlier here. I supposed that for some reason I made up these new concepts, definining 'minyak' as 'a geometric figure with 28 equal straight sides of 1 inch in length" and 'munyak' as 'a geometric figure with 29 equal straight sides of 1 inch in length". The concepts are arbitrary products of my mind and the terms and their definitions are my arbitrary linguistic creations. Nonetheless, the truths that can be derived from these concepts and definitions are not arbitrary or produced by me. For example, the truth that the ratio of the area of a minyak to the area of a munyak is______(whatever quantity it is) is something that was not created by me (I don't even know what it is) but rather has to be discovered by careful reasoning, whose rules are not arbitrary creations.

This doesn't contradict anything I've said. You define your minyaks and munyaks and the geometry you use, with its axioms. From those axioms and definitions follows your ratio analytically. Whether you can apply this result to certain physical objects depends on the question whether the geometry you've used applies to those physical objects, and that is an empirical question, the answer to that question is a synthetic statement. The difference is obvious!

That's assuming that analytic truths don't tell us anything about the real world, which is one of the major points you need to argue for (I will send an updated version of the list in my next post).

And analytic truths, even in the narrow sense, cannot be made true simply by arbitrarily asserting that they are true.

An analytic truth is not true? That's interesting: truths that are not true...

That mathematical theories can be used in physical models is a completely different issue.

If they did not tell us anything about the real world it would be unlikely in the extreme that they were of value in physical models.

Not at all. We can for example construct different geometries; if one of these can be applied to a certain physical system, the other ones cannot, as they would give different results. In other words, all those other geometries don't tell us anything about that system. Nevertheless they are all equally valid, the truth of the mathematical statements does not depend on their applicability in physics.

In those models we don't test the correctness of the mathematics, but the applicability of that particular mathematical theory.

The correctness of the math should already be established. But in a sense we did test Euclid's math and found that it does not wholly accurately describe the space of our world, which turned out to be curved.

That doesn't in any way invalidate Euclidean geometry; its theorems are always true. Whether we can apply them to physical systems is a different question. Again, this is the essential distinction between analytical truths (like the theorems of Euclidean geometry) and synthetic truths (empirical statements about the geometry of physical objects). The distinction is crystal clear!

Euclid thought that he was describing the properties of actual physical space. Relativity Theory says that he was not entirely correct, that space is curved, and their properties are described by the alternative geometries.

These are empirical questions, which have no bearing at all on the correctness of Euclidean geometry. This is the essential point you keep evading: a mathematical theory like Euclidean geometry can be completely consistent and correct in its own right. Its statements are analytic truths. Whether you can apply them to physical systems is a different question - that is the domain of synthetic truths.

If some of the water of everyday life is Heavy Water (and my current understanding is that it is), then it is included in the meaning of the term 'water' and so Heavy Water is water, because water is a Deep Kind, and therefore its meaning is in part determined by paradigm cases, and the water samples we encounter in everyday life are paradigm cases of water, and if some of them are Heavy Water then Heavy Water is a subkind of water.

This is in contradiction with what you wrote in an earlier post: 'I say, for example, that "All water is H20" (that is, all water has the atomic structure expressed by that formula) is true and we know it to be true, because we know that being H20 is a necessary fact about water, not just a contingent one.' Heavy water is D20, so your statement was wrong.

In any case, neither Peikoff nor I nor anyone else has defined 'water' in this way.

You'll mean "ice". Peikoff was so sloppy that he even didn't give any definition of ice.

That wasn't sloppiness: he assumed the definition "Ice is solid water", which almost everyone would have agreed to.

In that context it was very sloppy, as the exact definition is important for determining whether the statement "ice floats on water" is an analytic or a synthetic truth.

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What scientists (the people who bring in the results) DO NOT DO MUCH OF is to take philosophers seriously. See some of Feynman's tart remarks on philosophy in his famous three volume lecture set. Feynman had nearly zero use for philosophers and philosophy, but he seemed to do alright without them. What lesson do I learn from this. If you want to understand science and what the scientists are doing, forget philosophy.

I'll say amen to that.

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What scientists (the people who bring in the results) DO NOT DO MUCH OF is to take philosophers seriously. See some of Feynman's tart remarks on philosophy in his famous three volume lecture set. Feynman had nearly zero use for philosophers and philosophy, but he seemed to do alright without them. What lesson do I learn from this. If you want to understand science and what the scientists are doing, forget philosophy.

I'll say amen to that.

If you want to understand what the bus driver is doing, forget philosophy.

--Brant

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  • 4 weeks later...

DRAGON:

~ I've pinned down the prob with why others (such as moi) have a prob with your analysis of Piekoff's analysis of the ASD. You disagree with Rand's/Piekoff's view of concepts, definitions, 'truth', the use/purpose/source of logic, and even the meaning itself of logic...BUT...you only start making varied parts of these disagreements clear whilst debating subjects (such as the ASD) whose views thereupon are derivative from such disagreements. Ie, the subjects you debate are trivial to the source of the disagreements.

~ Why not just start with the nub itself in all these discussions? For instance, your 1st critique of LP's ASD critique is that he didn't 'define' ice. Like, if he did, that takes care of things? I think not; not whilst you and he disagree on the whole meaning, purpose, and use of 'definitions.' Given the latter, much of what you argue is too easy to get lost within in seeing the 'logic' of.

LLAP

J:D

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DRAGON:

~ Most of what Dan Edge said is true. I'd rephrase and say that you and Piekoff just aren't even starting from the same page whatsoever.

~ LP's views of concepts (and all derivatives: propositions/statements/logic-use) and what-is-truth are skewerable by your 'analytic' arguments only for those already accepting of the ASD; but, not by those not.

~ In short, your arguments presume the validity of the 'analytic' way of dividing propositions, and, arguing about them, be they propositions about empirical occurrences or propositions about proper definitions. Your arguments cannot reach those who see logic as (sorry Brant) the 'art' of non-contradictory identification.

~ Given such, I must ask: Why do you 'argue' this way, with those who DON'T accept your...premises (or, if you wish, 'framework-of-thinking')?

LLAP

J:D

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~ I think the subject of Peikoff and Quine may be a tad over-stressed. Assume Quine was even mentioned in LP's 'ASD'; thence, all discussion about LP's ASD essay would really center around 'Peikoff's Differences With Quine,' rather than the essay's contents per se, no?

~ Other than referencing 'ancient' philosophers (Kant, etc), correct me if I'm wrong here, but all Peikoff's arguments about varied subjects A, B, C, etc really don't touch much on specific philosophers (especially relatively contemporary) per se; why expect Quine to be singled out merely because there's a common (and rarified) subject here? I mean: has Peikoff discussed Popper?

LLAP

J:D

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DRAGON:

~ You conclude, in your post #634 arguing with Greg Browne's last statement "That wasn't sloppiness: he [LP] assumed the definition 'Ice is solid water", which almost everyone would have agreed to," with...

In that context it was very sloppy, as the exact definition is important for determining whether the statement "ice floats on water" is an analytic or a synthetic truth.

~ Uh-h...'that context'? What 'context' was that? As Greg described it, your assertion doesn't really, er, hold water. --- 1st off: there is no 'the exact definition' for anything, dictionaries nwst. Clearly you do not accept (can we say 'personal', or 'common'?) contextuality itself as relevent to any term use. 2nd: the 'important' aspect you're concerned with, LP made clear he WASN'T concerned with, in his whole ASD essay. Or, did you miss that? Further, he made clear 'why.' (Well, clear to some.)

~ Methinks you're missing 'the forest' for the trees in this whole ASD thingee.

LLAP

J:D

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DRAGON:

~ Ok; here's my last say re this 'refutation', as you call it, re LP's ASD essay.

~ You really don't have a 'fundamental' beef with this, you know.

~ As Dan Edge implied, your real beef is with Rand's ITOE, which this is, as he spelled out, derivative from.

~ I think it'd be best that you start a clarification of your *real* argument...with that.

LLAP

J:D

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~ Why not just start with the nub itself in all these discussions? For instance, your 1st critique of LP's ASD critique is that he didn't 'define' ice. Like, if he did, that takes care of things?

That was just a minor point, I supplemented the definition that Peikoff probably had in mind. But it was sloppy to omit it, as the definition is important for the distinction between analytic and synthetic statements.

~ LP's views of concepts (and all derivatives: propositions/statements/logic-use) and what-is-truth are skewerable by your 'analytic' arguments only for those already accepting of the ASD; but, not by those not.

If that is true, then neither can LP's views ever convince those who accept the ASD. What he in fact tries to do is to define the distinction away. What I have shown is that his argument is meaningless, as it presupposes omniscience.

~ In short, your arguments presume the validity of the 'analytic' way of dividing propositions, and, arguing about them, be they propositions about empirical occurrences or propositions about proper definitions. Your arguments cannot reach those who see logic as (sorry Brant) the 'art' of non-contradictory identification

Only Randians use that definition of logic. Not people who really work with logic.

~ I think the subject of Peikoff and Quine may be a tad over-stressed. Assume Quine was even mentioned in LP's 'ASD'; thence, all discussion about LP's ASD essay would really center around 'Peikoff's Differences With Quine,' rather than the essay's contents per se, no?

~ Other than referencing 'ancient' philosophers (Kant, etc), correct me if I'm wrong here, but all Peikoff's arguments about varied subjects A, B, C, etc really don't touch much on specific philosophers (especially relatively contemporary) per se; why expect Quine to be singled out merely because there's a common (and rarified) subject here? I mean: has Peikoff discussed Popper?

You're missing the point of the criticism. That is that Peikoff wrote: "It [the ASD]is accepted, in some form, by virtually every influential contemporary philosopher—pragmatist, logical positivist, analyst and existentialist alike."

That is simply not true, as Quine wasn't exactly a nobody in philosophy. The conclusion can only be that either Peikoff didn't know about Quine's argument or he deliberately ignored it. Whatever it is, it makes Peikoff look bad. Either he didn't do his homework or he is disingenuous.

~ Uh-h...'that context'? What 'context' was that? As Greg described it, your assertion doesn't really, er, hold water. --- 1st off: there is no 'the exact definition' for anything, dictionaries nwst.

Where did I say that? If you read my article, you'll see that I in fact say that there is no single correct definition. The point is that you have to give an exact definition if you want to draw conclusions whether a statement is analytic or not, just for the reason that different definitions are possible. I have demonstrated that with examples as well.

~ Ok; here's my last say re this 'refutation', as you call it, re LP's ASD essay.

~ You really don't have a 'fundamental' beef with this, you know.

~ As Dan Edge implied, your real beef is with Rand's ITOE, which this is, as he spelled out, derivative from.

~ I think it'd be best that you start a clarification of your *real* argument...with that.

Such vague statements are no use to me. I have spelled out my argument in detail. If you have anything to criticize, you should give specific statements and arguments, not meaningless generalities.

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DRAGON:

~ Ok. We know where we stand on this. 'East is east...' etc. You'll hear no more from me on this, but, expect elsewhere why I probably will disagree on whatever (not necessarily everything) with you.

~ At least we've made clear that your refutation of LP's analysis of ASD depends upon your views of the logical necessity of considering propositions as inherently divisible into two types, and, that O-ists (however 'self-styled') see such as arbitrarily superficial and near narcissistically incestuous linguistically, causing unnecessary semantic puzzles, and irrelevent to using logic and propositions applicable to empirical 'truths' about life and living.

~ Take care in your thinking.

LLAP

J:D

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Regardless of the validity of Rand's definition of logic--"The art of non-contradictory identification"--what dis-utility does it have? What conflicts arise between different logics and why? Are different logics different because they have different, non-overlapping field-specific utilities? Do we have subordinate logics verified by reference to facts and a master logic? And what are the actual utilities anyway?

--Brant

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Regardless of the validity of Rand's definition of logic--"The art of non-contradictory identification"--what dis-utility does it have? What conflicts arise between different logics and why? Are different logics different because they have different, non-overlapping field-specific utilities? Do we have subordinate logics verified by reference to facts and a master logic? And what are the actual utilities anyway?

--Brant

Conflicts? I think not. Differences maybe. There are logics which deal with propositions whose truth value is not completely determined. This is useful in dealing with statistical or probablistic situations. Then there are statements which express degrees of some property. Then there are the modal logics which deal with possible, necessary, believable. The deontic logics which deal with required, forbidden, optional, permissible impermissible etc.. The differences arise out of the intended use or application..

Is there a Mother of All Logic. So far none has emerged in the field of formal or mathematical logic, just as there is not a Mother of All Geometry or a Mother of All Algebras in mathematics.

Ba'al Chatzaf.

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Regardless of the validity of Rand's definition of logic--"The art of non-contradictory identification"--what dis-utility does it have? What conflicts arise between different logics and why? Are different logics different because they have different, non-overlapping field-specific utilities? Do we have subordinate logics verified by reference to facts and a master logic? And what are the actual utilities anyway?

--Brant

I see no utility of formal logic - one doesn't need to take a course in logic to be logical. For all intensive purposes you may as well say 'reasonable' and 'logical' are synonymous, IMO.

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Brant:

~ Good questions.

~ The responses since your question seem to indicate that many have a view of 'logic' as being, inherently, multiply divided, as though there were more than '1-type' (like, there were more than 1 type of math, rather than different sub-types of it.)

~ Unfortunately, informatively-wise, such a view has no over-all comprehensive meaning to their use of the term 'logic.' It's like saying "there are different types of cars"...without ever defining (aka: clarifying) what their meaning of 'car' is. This is where Rand set herself up as an easy target: she gave a definitional 'meaning'...and everyone else nitpicks it without attempting to give an improved replacement which the rest of us can work from, rather than chronically against.

LLAP

J:D

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Brant:

~ I see 'logic' as Rand (in?)famously 'defined' it; primarily, 1st and foremost, it is an 'art' which each person dealing with the 'medium' they personally experience in reality, learn to apply (however primitively, at first), and identify the connections relevent to their continued living, as well as to improving such...including identifying what the nature is of that process called 'logic' right up to linguistically formalizing its nature. --- Here, Aristotle's clarifications become relevent for some, and are considered mere symbol-manipulations for others.

~ Those who see 'Predicate/Mathematical/Symbolic [i call 'conjunction'] Logic' or 'Modal Logic' or 'Tertiary Logic' as different types clearly have no ONE meaning of 'logic.' Personally, I see all as derivative from Aristotle's clarifications. But, this subject is really a whole 'nother thread.

LLAP

J:D

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Brant:

~ I see 'logic' as Rand (in?)famously 'defined' it; primarily, 1st and foremost, it is an 'art' which each person dealing with the 'medium' they personally experience in reality, learn to apply (however primitively, at first), and identify the connections relevent to their continued living, as well as to improving such...including identifying what the nature is of that process called 'logic' right up to linguistically formalizing its nature. --- Here, Aristotle's clarifications become relevent for some, and are considered mere symbol-manipulations for others.

~ Those who see 'Predicate/Mathematical/Symbolic [i call 'conjunction'] Logic' or 'Modal Logic' or 'Tertiary Logic' as different types clearly have no ONE meaning of 'logic.' Personally, I see all as derivative from Aristotle's clarifications. But, this subject is really a whole 'nother thread.

LLAP

J:D

The underlying category into which all these formal logics fall is --- the art or discipline of valid inference ---.

In short logic is about inferring conclusions (correctly) from premises. It is not the discovery of what is true. Logic will tell you, that you either have a ten dollar bill in or wallet or you don't. It will not tell you IF you have a ten dollar bill in your wallet. To find that out, you have to look in your wallet. Logic will tell you that you don't both have and have not a ten dollar bill in your wallet. Any premise that leads to that conclusion must be false. In a sense, tautologies are trip wires that can be used to detect errors in reasoning. Any premise that leads to the contradiction of a tautology is false, because tautologies (be definition) are always true.

Rand's definition of logic has an element of correctness to it but is not the definition used by people who do logic for a living. Logic can be used, under certain circumstances, to detect falsehood. Popper invokes the principle - modus tolens - as the mechanism for falsification of scientific theories. Any set of premises that logically imply a factually false assertion must contain at least one factually false assertion. This is the same as Ayn Rand's instruction - check your premises. It was none other than modus tolens.

Ba'al Chatzaf

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