The Analytic-Synthetic Dichotomy

[Daniel Barnes]

Ba'al:

>This is the same as Ayn Rand's instruction - check your premises. It was none other than modus tolens.

You may well be right, Ba'al, but it seems to me Rand meant something different by "check your premises." By this she usually means to make sure you are using the "true" definitions of terms, because these are Aristotle's basic premises.

Rand's instruction might relate to, say, experiencing some kind of emotional conflict (which she would say was some kind of internalised contradiction) when you act selfishly. She would say that this means you have got hold of the wrong "basic premise" (or definition) of the concept of selfishness - that you picked it up without realising it from the collectivist society around you. To her, the philosopher's mission was to purge such erroneous concepts and replace them with "true" ones, resolving such contradictions. As concepts are mental, and one cannot mind-read, the only way to approach this was by redefining the meanings of words. For Rand, this was philosophy's Job No.1.

This initially plausible argument unfortunately leads to a dead end. Firstly, by manipulating the meanings of words you can use logic to "prove" almost anything you like. Secondly, Aristotle realised that trying to prove all statements leads to an infinite regress, but seems to have overlooked that definitions themselves are merely statements. His doctrine, which he adapted from Plato, of the "intuition" of the meaning of basic terms i.e. the "essence" of them was one way out of this logical bind. Rand hoped to replace this "intuition" by "reality" as the "true" source of meaning for fundamental terms, but this cannot possibly work either, even using ostensive definitions. For if we were to argue over what a "true" democracy is, you might point to the USA and I might point to Saddam's Iraq, and there still would be no logical way of resolving such a dispute. Hence the two of us must decide to use a definition we mutually agree on in order to begin to discuss democratic politics; which of course makes such a definition a convention, a solution Rand utterly rejects.

This basic little-recognised problem with her theory explains IMHO a great deal of Objectivism's lack of progress. This is because it installs the philosopher as fundamental arbiter of the truth of terms - and thus the truth of statements - but equips him with no logical way of doing this. As a result, he can either waffle away in fundamentally unresolvable arguments over the meanings of words, or, on becoming disillusioned with such pointlessness, retreat to a dogmatic "here-I-stand" attitude. Either way, the principle of "checking your premises" in this sense is, it turns out, an unwitting engine for irrationalism.

Edited September 15, 2007 by Daniel Barnes

[Michael Stuart Kelly]

Here is the first time this phrase came up in Atlas Shrugged, (p. 188). Francisco is speaking.

Contradictions do not exist. Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong.

I see nothing wrong with this method, even when applying it to quantum physics. It is one hell of a prompt to keep looking.

Daniel, your analysis is wrong.

Michael

[Daniel Barnes]

Mike:

>Daniel, your analysis is wrong.

Assertin' won't make it so...;-) Plus the quote you supply doesn't contradict my theory in the least. In fact I could have used it myself.

[tjohnson]

Hence the two of us must decide to use a definition we mutually agree on in order to begin to discuss democratic politics; which of course makes such a definition a convention, a solution Rand utterly rejects.

I think you'll find that we need to state our undefined terms, not agree on definitions. Even if we agree on definitions there's no guarantee we are speaking about the same thing. By agreeing on undefined terms we bring mutual experience into the picture and so agreement may follow. Undefined terms are the building blocks of all language.

[Michael Stuart Kelly]

Assertin' won't make it so...;-)

Daniel,

Ditto for your entire post. There are simply too many unfounded assertions to argue over. I merely want to register disagreement.

Michael

[Daniel Barnes]

Mike:

>Ditto for your entire post. There are simply too many unfounded assertions to argue over. I merely want to register disagreement.

Actually my post is a rather thorough, if somewhat compact, argument. We already know you disagree.

[Robert Campbell]

~ 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.

I agree with Dragonfly on this one.

Willard van Orman Quine was one of the biggest names in analytic philosophy when Leonard Peikoff published his article on the analytic-synthetic dichotomy. And Quine's views were obviously inconsistent with Dr. Peikoff's characterization of contemporary philosophy. Since Dr. Peikoff's dissertation (completed in 1964) never mentions Quine, I suspect he just didn't do his homework.

As for Dr. Peikoff's references to Karl Popper, he has made a few--always in passing, always without any indication that he has actually studied Popper's work.

Back in the days of The Objectivist Forum (June 1981), there was a brief article by Jim Lennox, a philosopher of science with a solid reputation who still teaches at the University of Pittsburgh.

Obviously Lennox (who wrote no other articles for that journal) was asked to confirm for readers that philosophy of science was going to hell in a handbasket (something it was definitely not doing in 1981, but you wouldn't want to cloud the minds of orthodox Objectivists with suggestions that good things were happening in Western culture without mass conversions to the philosophy of Ayn Rand). The title (wouldn't you know it?) was "The Anti-Philosophy of Science."

In the article Lennox refers to Karl Popper as a positivist, accuses Popper of arbitrariness, and insists that Popper is an anti-realist. (The first and third statements are false; the second is true only if the Peikovian doctrine of the arbitrary assertion is true.) He also blames Popper for unleashing Paul Feyerabend, a genuine subjectivist who was viewed by other philosophers of science as a wild man, on an unsuspecting world. (Feyerabend was a student of Popper's, but to say that Popper did not care for the direction of his later work would be an understatement.)

Even allowing for the fact that Dr. Lennox, whose specialty is various figures in the history of biology from Aristotle to Darwin, is somewhat outside his area of expertise writing about Karl Popper, Tom Kuhn, and other 20th century figures, the article is disgraceful. But it has pretty obviously set the pattern for what is taught about Popper at the Leonard Peikoff Institute.

Robert Campbell

[Robert Campbell]

Daniel,

Can you tell me where Karl Popper's piece on "Two Kinds of Definitions" originally appeared? And which of his later collections it ended up in?

It's not included in Conjectures and Refutations or Objective Knowledge.

Since it is dated 1945 in the online source I'm using, I'm on the lookout for differences with Popper's later philosophy, which IMHO somewhat tones down the anti-Aristotelianism.

When I'm done reading it, I'll make my comments on the Popper Talk thread.

Robert Campbell

[Michael Stuart Kelly]

Actually my post is a rather thorough, if somewhat compact, argument.

Assertin' won't make it so...;-)

:devil:

[Daniel Barnes]

Robert

>Can you tell where Karl Popper's piece on "Two Kinds of Definitions" originally appeared? And which of his later collections it ended up in?

It's actually an adaption and condensation of Chapter 11 of "The Open Society and Its Enemies" called "The Aristotelian Roots of Hegelianism." It first appears AFAIK in "Popper Selections". The plus with reading the original is the massive footnotes which expand Popper's basic arguments further. The minus is you get his rather clumsy term methodological nominalism, which Popper dropped for "Two Kinds" in favour of (from memory) scientific nominalism or just "nominalism".

TOSE is a great book, worth reading for its main arguments against Marx and Plato natch but also studded with offhand gems like his chapter on Aristotle.

>Since it is dated 1945 in the online source I'm using, I'm on the lookout for differences with Popper's later philosophy, which IMHO somewhat tones down the anti-Aristotelianism.

You'd be right. Popper actually warmed to Aristotle a bit later in life in areas other than the essentialist method.

[Robert Campbell]

Daniel,

Thank you.

I will definitely read the piece on definitions in its original context. In Popper's writings, the action is often in the footnotes, or in appendices--sometimes to a greater extent than in his main text.

You know, of course, that at least one major Rand scholar--Chris Sciabarra--would not find an alleged Aristotle-Hegel connection off-putting

Robert Campbell

[Guyau]

Sidebar: Sterile Neutrino Update

. . . . Beginning in 1968 experimental counts of neutrinos reaching the earth from the sun were found to be less than half the number expected according to our understanding of the nuclear-fusion process by which they are produced in the sun. There are three types of matter neutrinos (and three types of anti-matter neutrinos, and perhaps, a seventh neutrino, called “sterile” [which might constitute the negative-pressure sea we call “dark energy”]). These are the electron-, muon-, and tau-neutrinos.

Discussion of implications of new experimental results bearing on possible seventh neutrino:

http://resonaances.blogspot.com/2007/04/after-miniboone.html

Candidate for dark energy: sterile neutrino (above).

Candidate for dark matter: neutralino (below).

http://www.physorg.com/news134822510.html

http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.2968v2.pdf

Edited August 2, 2008 by Stephen Boydstun

[Gregory Browne]

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.

Ba'al Chatzaf

Much you say after this is good, but it shows you have misunderstood my point. I am saying that modern scientists do so well because they do not practice Logical Positivism, which apparently many scientists still preach (as indicated by Cal's remarks). Abduction is not a concept the Logical Positivism--at least in its classic form--uses.

And I do not share the view that all science is based on induction.

(By the way, Bacon did not have a high opinion of the mere induction by enumeration, which he said is

"puerile".)

[Gregory Browne]

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.

Some of them are incorrect, because they run contrary to ordinary usage. For example, the habit of modern mathematicians defining "curve" in such a way as to include straight lines it contrary to ordinary usage.

Now are you under the impression that I think that the meaning is determined by philosophers??? That is precisely the view I I have been rejecting: as I said, Leibniz was right to say that we should think with the wise but speak with the common people.

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.

That's just what I have been saying. The English word "curve" has excluded straight lines for centuries. The redefing "curve" so as to include straight lines probably goes back only to the Logical Positivists or their forerummer such as Russell, about a century ago. (If you tell me that Descartes or somebody of his time used "curve" that way I would still point out that these did not become the standard English usage.)

[Gregory Browne]

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.

No: it owes it truth partly to definition (which we made true by convention or stipulation) but also partly to the Law of Identity. The definition allows us to subsitute "bachelor" for "unmarried man" in

"A bachelor is an unmarried man"

to get

"An unmarried man is an unmarried man"

and that is an instance of the Law of Identity, and that law is not a product of convention. We did not make everything identical to itself.

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.

If you base your claim that analytic truths are non-factual (not about the world) on the claim that they are mere arbitrary human products (products of convention or stipulation), then it does contradict what you 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!

It may be that the answer to the correct question of whether the world is Euclidean or not is a contingent truth, whereas truths of geometry, including those about minyaks, are necessary truth, but you cannot assumet the contingent/necessary distinction is the same as the analytic/synthetic, empirical/apriori or factual/non-factual distinctions. I know you assume all of those things, but you still have not proven any of them. (See my earlier post on the things you still need to prove.)

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...

You need to read what I say more carefully, as I read what you say carefully. I did not say that they were not true. I said that they were not made true by mere arbitrary assertion, i.e., that they did not owe their truth to merely arbitrary assertion.

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.

Then what is your reason for saying that Euclid's geometry is true, and useful in physical models?

My reason for saying that Euclid's geometry is true, and useful in physical models, is that it describes a possible world, a way the world could be--with uncurved space. If space were uncurved, Euclid's proposition would be true. And this last sentence is a truth of mathematics (and so it is necessary and analytic) and yet it is about the world (and so it is factual)

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!

You still have not proved

1. that all empirical truths are synthetic

2. that geometry is non-empirical.

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.

Again: why do you think that they are true (and useful) if they do not apply to physical systems?

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.

No. D stands for deuterium, which is an isotope of hydrogen, and therefore a kind of hydrogen, and so D2O is a kind of H20.

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.

Not sloppy: he assumed it because it was what the people whose views he was critiquing would say--that "Ice floats on water" is not analytic but "Ice is solid" is analytic, because the former does not follow from the definition "Ice is solid water" while the later does.

[Gregory Browne]

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).

Robert,

You bring up a number of interesting points. I won't have time to address them all tonight but I may get back to them later.

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).

I'm not sure he would--but how does Peikoff define the term "conventionalist"?

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.)

I am not sure, but I suspect that he probably thought that Quine was something of a voice in the wilderness and that Quine's views wouldn't catch: his "Two Dogmas of Empiricism" came out in 1953, which is 11 years before the dissertation , which is a relatively short time, philosophically speaking, and in the following 3 years Peikoff probably figured little had changed.

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.)

The Port Royal school is important for this debate, as they used a version of the intension/extension distinction which was a forerunner of Frege's sense/reference distinction, which was used to bolster the dichotomies of truth we are discuss ing here.

There is much relevant to this debate in medieval scholasticism. Does Peikoff mention that?

GReg

[Gregory Browne]

Cal,

I think that much of our disagreement may come from the following.

It seems that perhaps your basic objection to Peikoff and the ASD could be phrased as follows:

"Peikoff is so ill-informed on these topics: he goes against everything my teachers taught me about scientific methodology"

If this is what you are saying, then I say: Peikoff knows this; his point is that the thinks that what your teachers taught you is wrong. He is challenging their basic premises.

To criticize Peikoff for going against the mainstream views would be like saying:

"Rand is so ill-informed on economics: she goes against everything my economics teachers taught me".

Yes, she did. She challenged their basic premises.

And neither Rand nor Peikoff merely asserted that the premises of the mainstream thinkers were wrong: they gives arguments in an attempt to prove that they are wrong.

And by coming to this discussion I had hoped, and still hope, to hear and participate in a debate on these basic premises.

Greg

[tjohnson]

For example, the habit of modern mathematicians defining "curve" in such a way as to include straight lines it contrary to ordinary usage.

Mathematicians often take common terms and give them technical meanings that only apply in mathematics. For example, 'function' has a very specific meaning in mathematics which has little to do with ordinary usage.

[Gregory Browne]

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

Michael,

I agree that both deduction and induction are justified, which is good, because we need both: we need to induction to help us in areas where we don't have enough information to use deduction: sometimes we must settle for probability rather than certainty. I believe in the model of demonstrative science (i.e., deduction from necessary and certain premises), used by philosophers as different as Aristotle and Descartes, supplemented by induction. I believe that the arguments of Hume and others against these forms of reasoning are invalid.

However, I don't think we can say that your claim:

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

is always true, since perhaps those two existents are the only ones of their kind.

However, since kinds are, as I put it, "wide" (that is, they can include other members besides the ones they actually include)--which corresponds to Rand's claim that their concepts are "open-ended" (specifically, I would say that they are "open-sided", but may or may not be "open-bottomed"), we could say

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

I have more to say on this later.

Greg

[Gregory Browne]

Greg wrote:

>...these beings do not exist in the physical world we should say that they don't exist at all, but we have thoughts of them...

I wrote:

>...it might be better to say these "beings" - such as perfect triangles - exist, but abstractly, and not physically.

Greg replied:

>No, this is just the sort of thing I want to avoid. I am a Conceptualist, not a Realist, on the subject of universals (and any other kind of absraction): there are no really existing abstractions outside the mind; the only abstract beings that exist are abstract thoughts in the mind.

Hi Greg

Just to get clarity on the above - by "abstract" I mean as distinct from physical i.e. non-physical. That is what you mean too, yes? So we can summarise your view as:

Non-physical things exist, but only in individual consciousnesses.

Presumably you consider that consciousness, where these non-physical entities existl, is also non-physical i.e. distinct from the physical brain (though of course this does not mean it can exist without the physical brain; any more than, say, a human being can exist without surrounding air pressure)

The reason I ask is because I sometimes encounter some confusion in this (abstract vs physical) area that's better cleared up before moving on to other issues.

Actually, I am a Substance Dualist: I think that the mind is a thing distinct from the brain.

Since it is a thing, an individual thing, it is not abstract; it is concrete.

And 'concrete' is the opposite of 'abstract', not 'physical'.

And you can see this without agree with my Substance Dualism: there are physical concretes and physical abstractions---or rather physical abstractable. For example, an apple is a physical concrete and its attribute of being red is a physical abstractable--i.e, a physical attribute which can be abstracted by the mind to produce the idea of its redness (and the idea of redness in general)>

[tjohnson]

This conclusion is fallacious, however. You may define concept to imply all the characteristics, known and yet-to-be-discovered, but a definition necessarily gives only a few essential characteristics.

I agree with your conclusion DF, but I would suggest that it makes no sense to speak about defining concepts whatsoever. Concepts must be considered as some sort of neural process and as such are not subject to definitions. Definitions only apply to words.

[Dragonfly]

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.

That's just what I have been saying. The English word "curve" has excluded straight lines for centuries. The redefing "curve" so as to include straight lines probably goes back only to the Logical Positivists or their forerummer such as Russell, about a century ago. (If you tell me that Descartes or somebody of his time used "curve" that way I would still point out that these did not become the standard English usage.)

Now wait a moment... we were discussing the word axiom, of which you claimed that mathematics hijacked it to give it a new meaning. Now it turned out that the mathematical axiom has a quite respectable age, you surreptitiously switch to the word "curve". But the fact that the word curve in may have been used for centuries in daily language to exclude straight lines does not imply that the meaning of "curve" in a mathematical sense isn't old as well. In every dictionary you'll find the mathematical definition of a curve as one of the possible meanings. Words do have different meanings and there is no single "correct" meaning, and neither does the etymology of a word necessarily define its current meaning.

[Dragonfly]

No: it owes it truth partly to definition (which we made true by convention or stipulation) but also partly to the Law of Identity. The definition allows us to subsitute "bachelor" for "unmarried man" in

"A bachelor is an unmarried man"

to get

"An unmarried man is an unmarried man"

and that is an instance of the Law of Identity, and that law is not a product of convention. We did not make everything identical to itself.

A statement can also be true if it doesn't refer to anything that exists in reality. With the conventional definition of a unicorn the statement "a unicorn has a horn" is an analytical truth. The law of identity is implicit in the concept "truth" and in any logical argument, so it's useless to invoke it in an argument as some extra factor.

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.

If you base your claim that analytic truths are non-factual (not about the world) on the claim that they are mere arbitrary human products (products of convention or stipulation), then it does contradict what you said.

No, not every statement that is a product of convention of stipulation is a truth. For example the statement "a triangle has 4 sides" is not an analytical truth, as the statement contradicts the definitions. Claiming that the ratio of the area of a minyak to the area of a minyak is something that differs from what you calculate using the theorems of geometry leads to a contradiction, in the same way as the statement "a triange has 4 sides" leads to a contradiction. The correct value follows analytically from the definitions.

It may be that the answer to the correct question of whether the world is Euclidean or not is a contingent truth, whereas truths of geometry, including those about minyaks, are necessary truth, but you cannot assumet the contingent/necessary distinction is the same as the analytic/synthetic, empirical/apriori or factual/non-factual distinctions. I know you assume all of those things, but you still have not proven any of them. (See my earlier post on the things you still need to prove.)

I'm not talking about all those distinctions, the only thing I say is that analytical truths, such as mathematical theorems or a particular geometry in themselves don't tell us anything about the real world, but that we'll have to determine empirically whether a particular mathematical model, like a geometry gives a good description of the physical world. That is the essential point, the rest is unnecessary verbiage.

You need to read what I say more carefully, as I read what you say carefully. I did not say that they were not true. I said that they were not made true by mere arbitrary assertion, i.e., that they did not owe their truth to merely arbitrary assertion.

That's true(!), but the point is not that you assert arbitrarily that such a statement is true, but that a statement that is logically deduced from arbitrary (non-contradictory) axioms is analytically true.

Then what is your reason for saying that Euclid's geometry is true, and useful in physical models?

It's true while it is a consistent system based on Euclids axioms. That is it useful in physical models is an empirical fact.

My reason for saying that Euclid's geometry is true, and useful in physical models, is that it describes a possible world, a way the world could be--with uncurved space. If space were uncurved, Euclid's proposition would be true. And this last sentence is a truth of mathematics (and so it is necessary and analytic) and yet it is about the world (and so it is factual)

No, it's not about the world (more accurately: it doesn't tell us anything about the world), as you'll first have to prove empirically that space is uncurved. The statement "if mice are bigger than elephants, then mice are bigger than elephants" may be an analytical truth, but it doesn't tell us anything about mice or elephants.

You still have not proved

1. that all empirical truths are synthetic

That follows from the definition. An empirical truth cannot be analytical, as an analytical truth doesn't tell us anything about the real world, even if it may refer to things in the real world, which is not the same. Therefore an empirical truth is synthetic. Anyway, I've seen definitions where these terms are used as synonyms.

2. that geometry is non-empirical.

That statement is a bit ambiguous. A geometry as a mathematical system is non-empirical, as it is derived from purely abstract axioms. To determine which geometry describes the world best is an empirical question.

Again: why do you think that they are true (and useful) if they do not apply to physical systems?

Geometries and mathematical theories are analytically true, whether they can be applied to physical systems or not. Whether they are useful for science is an empirical question. Some abstract theories may remain completely useless for a long time, and yet turn out to be applicable to some physical system much later.

Not sloppy: he assumed it because it was what the people whose views he was critiquing would say--that "Ice floats on water" is not analytic but "Ice is solid" is analytic, because the former does not follow from the definition "Ice is solid water" while the later does.

It is sloppy, as evidenced by the fact that you and Bill Dwyer (both Objectivists, or Objectivist-leaning) make different assumptions about what Peikoff meant.

[Dragonfly]

I think that much of our disagreement may come from the following.

It seems that perhaps your basic objection to Peikoff and the ASD could be phrased as follows:

"Peikoff is so ill-informed on these topics: he goes against everything my teachers taught me about scientific methodology"

If this is what you are saying, then I say: Peikoff knows this; his point is that the thinks that what your teachers taught you is wrong. He is challenging their basic premises.

The problem is that he doesn't understand those basic premises, as he's completely ignorant in science and mathematics. That cobbler should stick to his last. Leave science to the scientists or at least to those philosphers who have a solid scientific background and not to bumbling amateurs.

To criticize Peikoff for going against the mainstream views would be like saying:

"Rand is so ill-informed on economics: she goes against everything my economics teachers taught me".

Yes, she did. She challenged their basic premises.

I think you're giving her too much credit. She wasn't an innovator in economics. The little she knew about economics she got from people like von Mises and Hazlitt, and while their theories might not have been popular at the time, they had a background in a tradition that already existed much longer.

[Gregory Browne]

For example, the habit of modern mathematicians defining "curve" in such a way as to include straight lines it contrary to ordinary usage.

Mathematicians often take common terms and give them technical meanings that only apply in mathematics. For example, 'function' has a very specific meaning in mathematics which has little to do with ordinary usage.

Yes.

And this is something that I have been criticizing them for--and criticizing philosophers, scientists and most people for. It multiplies meanings and thereby creates ambiguities, which can lead to misunderstandings and faulty reasoning--the Fallacy of Ambiguity. It's a bad habit.

When somebody comes up with a new concept, they should invent a new term--either a new word (as in the case of 'quark') or a new combination of existing works that describe--accurately describe--the things included under the concept.

(Specialists such as mathematicians may plead that they are only using the term with a new meaning in their field, but that merely quarantines the problem rather than curing it. Specialists need their own concepts, but that should not use existing terms to express them.)