The Analytic-Synthetic Dichotomy

[Gregory Browne]

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.

I agree with DF, too (with your terminlogical amendment, GS)--and Peikoff agrees with DF, too: a definition, to be useful, can only list a few characteristics. Unfortunately, the fact that it lists only a few has led many to assume that it does not imply many more.

[Gregory Browne]

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.

How old do you think that the mathematician's use of the word "axiom" in such a way as to include mere postulates is? Is it older than about a century?

Dictionaries do list the modern mathematical definition of curves, because these definitions have come into common use among mathematicians, but they also list the definition that expresses the meaning that non-mathematicians use, and that is older. The mathematician's definition is an innovation, and that is unfortunate, because it involves changing the meaning of words, resulting confusion and ambiguity (see my reply to General Semanticist, 2 posts back).

[Gregory Browne]

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.

Yes, it is. But for a statement to be meaningful, whether it is true or false, it has to have some tie to reality. The concept of unicorns is based on concepts for real things such as the concept of horse and concept of horn.

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.

It is not extra to the concept of truth, but it is extra to convention. You say that the above statement about bachelors is true merely by convention, and nothing else. I have pointed out that it is due to both convention and the Law of Identity, and the Law of Identity is not due to convention.

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.

I never said that it was. What made think that I did?

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

You are talking about 3 of the 4 distinctions, right in this passage: the analytic/synthetic one, the factual/non-factual one (non-factual truths, if there were any, would be ones that don't tell us anything about the real world) and the empircal/a priori one. You are saying (1) all analytical truths are non-factual, and (2) all factual truths are empirical. You have been claiming these things since the beginning, but you have not yet proved (1). (2) I already agree with.

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.

Mind your language, Dragonfly: I don't call your posts "rubbish", so do not call mine "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.

I deny also that the axioms are arbitrary. The concepts in the axioms may be arbitrarily put together, but that does not make the truth of axioms arbitrary. This is exactly analogous to the case of minyaks and munyaks: I arbitrarily picked the numbers 28 and 29 and arbitrarily chose to combine the concepts of them with out concepts to make the new concepts of minyaks and munyaks, but the statement "A minyak has 28 sides" is not an arbitrary statement: we are free to use the term and concept of minyaks, or not use them, but if we do use them we are not free to deny the statement (that is, we cannot do so and still avoid falsehood).

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.

So you're saying that it is true because it is consistent? But that is not enough to make something true. At a minimum, the words have to mean something.

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.

No. It says something about what is possible and impossible for a world to be: Euclidean geometry is saying that a world cannot have straight space and yet fail to agree with the propositions of Euclidean geometry.

I'll illustrate my point this way: answer me this: is "Arsenic is poisonous" about the world?

You still have not proved

1. that all empirical truths are synthetic[/quote

That follows from the definition. An empirical truth cannot be analytical, as an analytical truth doesn't tell us anything about the real world,

That's another assumption you have not yet proven.

even if it may refer to things in the real world, which is not the same.

If it refers to things in the real world, and says something about them, then it is saying something about the real world.

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.

You still have not proven that assumption.

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.

So why do think that they are true. Just because they are consistent?

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.

If Peikoff only counted floating ice as ice, it is still beside the point: he was attacking a theory and using the kind of definition that defenders of the theory would use.

Edited August 15, 2008 by Greg Browne

[Brant Gaede]

"Verbiage" isn't quite the same as "rubbish." The way DF used "verbiage" is correct if it is true. It refers to unnecessary words. "Rubbish" is just rubbish. Your word, not DF's. It can't be reduced so it's just prejorative without objectifying any particular(s).

--Brant

[Gregory Browne]

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,

That's what you still have to prove.

as he's completely ignorant in science and mathematics.

Are you still under the impression that these issues are primarily issues of science and mathematics?

As I pointed out last year, these issues concerning these dichotomies are philosophical issues, and the doctrines that their are such dichotomies are philosophical doctrines, invented by philosophers. Most were argued for by Hume (and some of these are older than him); Kant gave the name to the A/S distinction; the Logical Positivists developed the whole system explicitly. All of these were philosophers. Scientists did not invent these distinction (to their credit!). It was philosophers who persuaded many scientists of their validity. From their, of course, scientists passed the doctrine on to other scientists, but it is still a fact that philosophers invented these distinctions. Anybody who knows much about these issues knows this--whether they love the dichotomies or hate them. This is a pretty basic point.

I've heard of many people who discuss these issues, but I've never heard anyone else treat them as anything but philosophic issues.

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.

You are just making personal insults of Peikoff again, and those are just Ad Hominem arguments. Ad Hominem arguments are irrelevant and therefore fallacious, unless they are used to undermine a claim to authority. And, as I pointed out before, neither Peikoff nor I ever asked you to take anything on authority.

And even these insults were relevant, they are somewhat circular reasoning: you base your insults on the stands he takes in the ASD, and so to then use the insults as a basis for criticizing the ASD is arguing in a circle.

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 know a lot about economics

she got from people like von Mises and Hazlitt,

Probably not. Mises thought she had a first-rate mind, so she probably already understood a lot when she met him.

and while their theories might not have been popular at the time, they had a background in a tradition that already existed much longer.

Almost any economist or economic writer has some background in some economic tradition.

And are you saying that we shouldn't listen to anybody discuss economics unless they have a background in the economic tradition? And would you extend that to other fields? If so, then how are we ever going to get any external check on the people in any field of study? Indeed, how do you know that they are experts in the field, without some external test? Otherwise, you will simply say that certain people are experts on economics because other people in economics say they are, and you say that those people experts because still other people say that are, and so on.

Rather, the fact that Rand got so much right when economists who were supposed to be expert got them wrong is a credit to her and shame to them.

[tjohnson]

No. It says something about what is possible and impossible for a world to be: Euclidean geometry is saying that a world cannot have straight space and yet fail to agree with the propositions of Euclidean geometry.

Technically, mathematics is about fictitious things, even though many of the terms are used in everyday language. A good example is a mathematical circle. We may notice what we call 'circles' all around us but a mathematical circle only exists as an imaginary object. Geometry is not about "a world", propositions about the structure of space-time are in the province of physics. Mathematics grew out of everyday experience which is why many common terms are used which may be problematic but unfortunately we just have to deal with it. The important distinction in mathematics is that definitions contain ALL particulars and no other" future" characteristics are allowed. This is why deductions work absolutely in mathematics but only relatively well in ordinary language.

[Brant Gaede]

Rand did pretty good with economics, to say the least, even though she did not innovate save by making it make sense in the context of her philosophy by combining it with morality in the strongest yet way to date.

--Brant

[BaalChatzaf]

Greg Browne writes:

No. It says something about what is possible and impossible for a world to be: Euclidean geometry is saying that a world cannot have straight space and yet fail to agree with the propositions of Euclidean geometry.

Ba'al Chatzaf responds:

Not quite. Projective Geometry is derived from Euclidean Geometry by adding "a line at infinity" so that all pairs of distinct lines intersect. A pair of lines determines a point. A pair of points determine a line. There is a formal duality between points and lines in Projective Geometry.

Projective Geometry is the geometry of projections of three-space upon a plane. It is the geometry of perspective drawing. That is how it started out. It has been generalized to higher dimension spaces. Think of Projective Geometry as the geometry where parallel lines (like railroad tracks) converge to a point Far, Far Away.

Euclidean Geometry is the geometry of transformations that preserve distance and angles (isometries). Projective Geometry is the geometry of transformations that preserve intersections, colinearities and the four point cross ratio.

The geometries are related, but not identical. They are both about straight lines. This is a counter example to what you asserted.

Greg Brown writes:

I'll illustrate my point this way: answer me this: is "Arsenic is poisonous" about the world?

Ba'al Chatzaf answers:

A question with a question. In what quantities? Arsenic (or lead) taken in small enough doses is not fatal. Water taken in large enough doses can kill. Too much water inhibits the transfer of potassium ions through the membrane of nerve fibers which can lead to death or severe neurological dysfunction.

Ba'al Chatzaf

[Gregory Browne]

"Verbiage" isn't quite the same as "rubbish." The way DF used "verbiage" is correct if it is true. It refers to unnecessary words. "Rubbish" is just rubbish. Your word, not DF's. It can't be reduced so it's just prejorative without objectifying any particular(s).

--Brant

Brant,

Calling something "verbiage" implies more than just that what was said could be expressed more economically, i.e., in fewer words. It implies that the words are worthless or of little value. It is connected to verbosity and the French word for chatter. In my experience is it always use pejoratively.

Greg

[BaalChatzaf]

Rand did pretty good with economics, to say the least, even though she did not innovate save by making it make sense in the context of her philosophy by combining it with morality in the strongest yet way to date.

--Brant

I think Francisco's speech on money is the best in -Atlas Shrugged-. Rand nailed it just right.

Ba'al Chatzaf

[Brant Gaede]

Rand did pretty good with economics, to say the least, even though she did not innovate save by making it make sense in the context of her philosophy by combining it with morality in the strongest yet way to date.

--Brant

I think Francisco's speech on money is the best in -Atlas Shrugged-. Rand nailed it just right.

Ba'al Chatzaf

A real gem.

--Brant

[Gregory Browne]

....

In the second part of the article Peikoff starts his attack on this distinction by elaborating on the concept of "a concept". His position is that a concept of a thing (for example "ice") contains all the characteristics of that thing, in the case of ice all the physical and chemical properties of ice, even those that are still unknown. Peikoff: "Thus, a concept subsumes and includes all the characteristics of its referents, known and not-yet-known." He emphasizes the latter: "It is crucially important to grasp the fact that a concept is an 'open-end' classification which includes the yet-to-be-discovered characteristics of a given group of existents."

Peikoffs conclusion is then that it isn't possible to distinguish between analytical and synthetic statements, as any characteristic that is deemed a synthetic truth (like: "ice floats on water"), is already part of the concept itself, so it follows logically from the definition of ice.

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. Peikoff silently assumes however that a limited definition of a concept automatically implies all the characteristics of that concept, even those that are still unknown.

No: he assumes the exact opposite: he denies that the definitional attributes are all there is to a concept. In fact, that is his key point in this section of the article. The unknown characteristics are part of the concept, but they are not (not always) part of the definitions.

[tjohnson]

No: he assumes the exact opposite: he denies that the definitional attributes are all there is to a concept. In fact, that is his key point in this section of the article. The unknown characteristics are part of the concept, but they are not (not always) part of the definitions.

I keep seeing this confusion between concepts and words. A concept is an imagination and we can not know what someone is imagining. Words, on the other hand, are things that exist outside our nervous system. Words cause imaginations in other people and, if all goes right, they may imagine the same thing we are.

[Dragonfly]

How old do you think that the mathematician's use of the word "axiom" in such a way as to include mere postulates is? Is it older than about a century?

They were definitely used that way in the 19th century.

Dictionaries do list the modern mathematical definition of curves, because these definitions have come into common use among mathematicians, but they also list the definition that expresses the meaning that non-mathematicians use, and that is older. The mathematician's definition is an innovation, and that is unfortunate, because it involves changing the meaning of words, resulting confusion and ambiguity (see my reply to General Semanticist, 2 posts back).

Which meaning is older is totally irrelevant. If a meaning is well-established it is by definition correct. There isn't any mathematician who is confused about the meaning, and that's the only thing that counts. Otherwise you could as well attack Rand for introducing new meanings of such words as "selfishness" or "altruism", that are confusing to people who use these terms in their traditional, well-established meaning. Sauce to the goose...

[Dragonfly]

Yes, it is. But for a statement to be meaningful, whether it is true or false, it has to have some tie to reality. The concept of unicorns is based on concepts for real things such as the concept of horse and concept of horn.

Now you introduce a new criterion, meaningful. The truth of a statement doesn't depend on the fact whether it's "meaningful" (in the sense that it refers to real objects), however. Mathematical statements can be true while they don't refer to anything in reality.

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.

It is not extra to the concept of truth, but it is extra to convention. You say that the above statement about bachelors is true merely by convention, and nothing else. I have pointed out that it is due to both convention and the Law of Identity, and the Law of Identity is not due to convention.

I don't use the phrase "true by convention" as it is misleading, it suggests that you determine the truth of a statement by convention. This isn't what happens, however. You start with a certain definition (for example that of a bachelor) and then you logically deduce a statement from that definition. As I said before, any logical argument already implies the law of identity, so it's superfluous to mention it as something extra.

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.

I never said that it was. What made think that I did?

You conveniently omit the rest of my comments, I'll therefore repeat them here:

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.

That's my reply to your claim

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 don't give any argument why this would contradict what I said. I therefore concluded that you thought that I claimed that you can determine the truth of a statement merely by convention. But I never said that, see also above. It's up to you to prove that there is a contradiction in my statement.

You are talking about 3 of the 4 distinctions, right in this passage: the analytic/synthetic one, the factual/non-factual one (non-factual truths, if there were any, would be ones that don't tell us anything about the real world) and the empircal/a priori one. You are saying (1) all analytical truths are non-factual, and (2) all factual truths are empirical. You have been claiming these things since the beginning, but you have not yet proved (1). (2) I already agree with.

I think the problem is that you're confused about the term "non-factual". That a non-factual truth doesn't tell us anything about the real world does not mean that it necessarily doesn't refer to things in the real world. It means that the truth of the statement can be ascertained from the definitions alone, just while sitting in your armchair, so it cannot be falsified, it's empirically empty.

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.

I deny also that the axioms are arbitrary. The concepts in the axioms may be arbitrarily put together, but that does not make the truth of axioms arbitrary. This is exactly analogous to the case of minyaks and munyaks: I arbitrarily picked the numbers 28 and 29 and arbitrarily chose to combine the concepts of them with out concepts to make the new concepts of minyaks and munyaks, but the statement "A minyak has 28 sides" is not an arbitrary statement: we are free to use the term and concept of minyaks, or not use them, but if we do use them we are not free to deny the statement (that is, we cannot do so and still avoid falsehood).

Well, don't you see that that is exactly what I'm saying? You give an arbitrary definition of minyaks and munyaks, and then the statement "a minyak has 28 sides" can be deduced trivially from its definition, and is therefore an analytical truth.

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.

So you're saying that it is true because it is consistent? But that is not enough to make something true. At a minimum, the words have to mean something.

If you mean by "to mean something": "to refer to something in the real world", than you're wrong. A mathematical truth does not refer to something in the real world. That is the point that Objectivists and some other philosophers still don't get.

No. It says something about what is possible and impossible for a world to be: Euclidean geometry is saying that a world cannot have straight space and yet fail to agree with the propositions of Euclidean geometry.

Which doesn't tell us anything about the world, as I illustrated with another example in the same style: 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.

I'll illustrate my point this way: answer me this: is "Arsenic is poisonous" about the world?

Yup, as it can only be determined empirically. Now you may turn it artificially into an analytic statement by defining arsenic as a poisonous substance, but then its truth would no longer depend on empirical observation, and even if it turned out that we'd been wrong all the time, that arsenic isn't really poisonous, the statement within the framework of the definition would be automatically true. Only the definition would then no longer correspond to our observations. This is the floating ice example all over again.

That's another assumption you have not yet proven.

It follows directly from the definition, see above.

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.

You still have not proven that assumption.

What is there to prove? Are you really that ignorant about mathematics that you don't know that geometry as a mathematical system is derived from abstract axioms?

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.

So why do think that they are true. Just because they are consistent?

Yup, you got it!

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.

If Peikoff only counted floating ice as ice, it is still beside the point: he was attacking a theory and using the kind of definition that defenders of the theory would use.

Irrelevant. The fact that you and Dwyer come to different conclusions about Peikoff's statement means that he has been sloppy: even Objectivists themselves can't agree about what he really 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,

That's what you still have to prove.

I've shown lots of evidence for that in other threads on this forum.

as he's completely ignorant in science and mathematics.

Are you still under the impression that these issues are primarily issues of science and mathematics?

Someone who cannot understand the essential difference between mathematical statements and scientific statements disqualifies himself for this kind of discussion.

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.

You are just making personal insults of Peikoff again, and those are just Ad Hominem arguments. Ad Hominem arguments are irrelevant and therefore fallacious, unless they are used to undermine a claim to authority. And, as I pointed out before, neither Peikoff nor I ever asked you to take anything on authority.

And even these insults were relevant, they are somewhat circular reasoning: you base your insults on the stands he takes in the ASD, and so to then use the insults as a basis for criticizing the ASD is arguing in a circle.

Not at all. I've shown lots of evidence in other threads on this forum that Peikoff is a bumbling amateur in these fields, and that is still a mild qualification. Nowhere I used this as an argument in my article about Peikoff's errors, at most it was a conclusion.

[Roger Bissell]

"Verbiage" isn't quite the same as "rubbish." The way DF used "verbiage" is correct if it is true. It refers to unnecessary words. "Rubbish" is just rubbish. Your word, not DF's. It can't be reduced so it's just prejorative without objectifying any particular(s).

--Brant

Actually, "verbiage" ~does~ have at least a ~connotation~ that is pejorative. (I'm not sure if this is related to "prejorative." Perhaps the pejorative ~emerges~ from the prejorative?)

"Verbiage" is derived from the French verb (heh), "verbeier," which means "to chatter." This verb was in use 300 years ago, but it seems to be obsolete now. So, I guess that means we can refer to people's chattering -- use of unnecessary or unnecessarily technical words -- without intending to be pejorative? Cool!

However, it ought to be recognized that the phrase "unnecessary verbiage" is redundant: unnecessary unnecessary words. It's like saying "PC computer" (personal computer computer). In other words, "unnecessary verbiage" is a perfect example of verbiage. Heh.

REB

[Dragonfly]

....

In the second part of the article Peikoff starts his attack on this distinction by elaborating on the concept of "a concept". His position is that a concept of a thing (for example "ice") contains all the characteristics of that thing, in the case of ice all the physical and chemical properties of ice, even those that are still unknown. Peikoff: "Thus, a concept subsumes and includes all the characteristics of its referents, known and not-yet-known." He emphasizes the latter: "It is crucially important to grasp the fact that a concept is an 'open-end' classification which includes the yet-to-be-discovered characteristics of a given group of existents."

Peikoffs conclusion is then that it isn't possible to distinguish between analytical and synthetic statements, as any characteristic that is deemed a synthetic truth (like: "ice floats on water"), is already part of the concept itself, so it follows logically from the definition of ice.

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. Peikoff silently assumes however that a limited definition of a concept automatically implies all the characteristics of that concept, even those that are still unknown.

No: he assumes the exact opposite: he denies that the definitional attributes are all there is to a concept. In fact, that is his key point in this section of the article. The unknown characteristics are part of the concept, but they are not (not always) part of the definitions.

And that is where Peikoff makes his crucial error: you cannot derive a truth analytically from characteristics that are not part of the definitions.

[tjohnson]

If I say the word 'tree' to someone they can imagine a tree in their brain, but what will it look like? Will they imagine a fir tree, a beech tree, a spruce tree, etc.? What they imagine will depend a lot on their experiences and how they relate to the word 'tree'. If I say the word 'spruce tree' to someone they might imagine a spruce tree but again this is a private affair not available to anyone else. What we imagine are our concepts which are different than our language. Our concepts shape our language and our language shapes our concepts, it's a two way street.

[Lukon]

While I've only read 2 or 3 posts in this topic from the 35 pages, I really want offer a comment about Peikoff versus Quine on this.

I do think many philosophers prior to Peikoff have also rejected the ASD. Peikoff would probably claim, at least implicitly, that these prior rejections were the wrong kind of rejection. And I myself would have a label for these wrong kinds of rejections: "asymmetrical." An asymmetrical rejection of the ASD is the kind that rejects the dichotomy by rejecting only one side of it. So one can reject the dichotomy by rejecting just the analytic side, claiming by default that all knowledge is synthetic. Or you can do an asymmetrical rejection vise versa.

I suspect Quine did an asymmetrical rejection. The exact nature of it escapes me at the moment. I'd have to put on that audio lecture about Quine again to remember it.

But anyway, Peikoff, by contrast, appears to do a completely "symmetrical" rejection. He refuses to let either category of knowledge take over the other. They are both fundamentally flawed and both need to be rejected.

This distinction I make between "asymmetrical" and "symmetrical" rejection of the ASD is something I obviously haven't explored in depth. It is just a hypothesis I'm slowly exploring. But I thought you folk might enjoy my current thoughts on it.

-Luke-

[Mindy Newton]

While I've only read 2 or 3 posts in this topic from the 35 pages, I really want offer a comment about Peikoff versus Quine on this.

I do think many philosophers prior to Peikoff have also rejected the ASD. Peikoff would probably claim, at least implicitly, that these prior rejections were the wrong kind of rejection. And I myself would have a label for these wrong kinds of rejections: "asymmetrical." An asymmetrical rejection of the ASD is the kind that rejects the dichotomy by rejecting only one side of it. So one can reject the dichotomy by rejecting just the analytic side, claiming by default that all knowledge is synthetic. Or you can do an asymmetrical rejection vise versa.

I suspect Quine did an asymmetrical rejection. The exact nature of it escapes me at the moment. I'd have to put on that audio lecture about Quine again to remember it.

But anyway, Peikoff, by contrast, appears to do a completely "symmetrical" rejection. He refuses to let either category of knowledge take over the other. They are both fundamentally flawed and both need to be rejected.

This distinction I make between "asymmetrical" and "symmetrical" rejection of the ASD is something I obviously haven't explored in depth. It is just a hypothesis I'm slowly exploring. But I thought you folk might enjoy my current thoughts on it.

-Luke-

Following your terms, I think Peikoff's rejection is also asymmetrical. He says that a concept's meaning is exhaustive, or determinate, it includes everything about all possible referents, including the unknown. Thus, the predicate, if true, is, in fact, contained in the subject, and all statements are equally "analytic." All dilemmas are canceled by removing any one "horn," so that tactic destroys the A/S dichotomy, for him.

= Mindy

[BaalChatzaf]

.

I define myself as Creator of the universe. Did I create the universe?

It depends what you mean by "create".

Ba'al Chatzaf

[Starbuckle]

Dragonfly wrote: "That's just wrong. If you define ice as the solid form of water, it follows logically that ice is a solid, even if ice wouldn't exist at all in the real world"

So, by the same reasoning, if I define ice as the chocolate form of water, it follows logically that ice is a chocolate, even if a chocolate phase of water doesn't and can't exist at all in the real world, never has, never could?

So...if I stipulate a definition for a concept that has no relationship to or basis in reality, it follows "logically" that my claim of a non-existent entity or attribute of an entity is "true," i.e., says something about reality, even though there is nothing in reality that the concept could be based on?

[jth42]

Hi Dragonfly,

I'm a mathematician and came across Objectivism about a year ago.

This issue is indeed one I'm with you firmly and I'm excited to have found somebody who got this issue right.

Maths isn't about reality.

[perspicaciouscogitator]

Dragonfly and all,

 

I didn't take the time to read this entire post but has anyone brought up the fact that "high density ice" wasn't discovered until 1996, so Peikoff, nor anyone else even knew of its existence when he gave his example. ...Kind of brings this whole discussion back to Peikoff's original point. LOL