The Analytic-Synthetic Dichotomy


Dragonfly

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Bill,

Your closing line:

Some of the most obvious things are not obvious until someone points them out.

is very appropriate for this discussion, as it involves a central (perhaps the central) issue on which those who believe in the dichotomies Peikoff attacks go wrong: they don't realize that some truths can be analytic, necessary and definitional, because deducible from a definitions, and consequently obvious because they follow by obviously valid inferences from obvious truths, and yet not be obvious at first because a lot of deductive work is needed to discover them. For example, the truths of trigonemetry may be derived from the definition of triangles (and perhaps a few general geometric truths), which definition is are obvious, and can be expressed as analytic and necessary truths, and so are trivial (and are wrongly called as "not factual" (not about the world) and "a priori"), but the truths deduced from them can be surprising and interesting (as even the Logical Positivist A. J. Ayer said), and therefore not obvious and not trivial.

I have much more to say on this, but it is better said as replies to other posts.

Greg

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Dragonfly,

Your discussion of the unusual kind of ice is significant:

Let us illustrate this with the ice example. Suppose you define ice as the solid form of water. A logical deduction from that definition would be "ice is a solid". But you can't logically deduce from that definition that ice floats on water. If that would be possible, one logically deduction would be that the statement "ice sinks in water" is wrong, right? Wrong! Ice can have 13 different types of crystal structure. One of them, very high density amorphous ice, in fact sinks in water. This shows the fallacy in Peikoff's reasoning: we can't deduce a synthetic truth logically from a definition while man isn't omniscient. In this example the synthetic truth is only known to a limited number of people, so most people would incorrectly deduce that the statement "ice sinks in water" is wrong. This shows that there is a sharp division between an analytic statement that logically follows from the definition like "ice is a solid", this can never be proved wrong, and a synthetic statement that can only be verified empirically, like "ice floats on water" (which is only strictly true when a necessary condition is added to the statement, like "ice with a hexagonal crystal structure").

"Ice floats on water" is not an example of a synthetic truth, or a contingent truth, because, as you go to acknowledge, it is not strictlytrue: assuming that it means "All ice floats on water", your counterexample shows that generalization to be a falsehood. Therefore, you cannot use it as example of synthetic truth or a contingent truth or any other kind of truth.

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Dragonfly,

You say:

"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. It is a logical truth that is independent of the real world, just as a mathematical statement is independent of the real world."

Peikoff would not concede that a mathematical statement is independent of the real world, and neither would I (and neither would most philosophers before Hume). So you need to argue for it.

And this points to a more general matter: in your critique of Peikoff, you often assume as true claims that he would dispute and which are therefore part of the debate, and which you therefore must argue for. Among them are various appeals to dichotomies that Peikoff rejects. This is common in philosophical debates: one side underestimates just how radically the other side disagrees with them.

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For example, the truths of trigonemetry may be derived from the definition of triangles (and perhaps a few general geometric truths), which definition is are obvious, and can be expressed as analytic and necessary truths, and so are trivial (and are wrongly called as "not factual" (not about the world) and "a priori")

There is a distinction between a purely mathematical theory, like Euclidean geometry, and the application of that theory in a model of the physical world. The theory, based on a set of axioms, is not factual, it is a purely abstract construction, the truth of which logically follows from the definitions (even if it originally may have been inspired by empirical observations). Whether the theory gives a good description of the physical world is an empirical question however, it may turn out that it doesn't (always) give a correct description of what we measure in reality. That doesn't falsify Euclidean geometry, the mathematical theory will always be correct, but it does falsify a model that uses this theory to describe the physical world.

, but the truths deduced from them can be surprising and interesting (as even the Logical Positivist A. J. Ayer said), and therefore not obvious and not trivial.

That's what I've said in previous posts, for example here.

I doubt that anyone of us thinks that analytic truths are meaningless or illogical and I'm amazed that anyone could think that I would defend such a viewpoint, I think my posts have been clear enough on that point. It's rather frustrating to be misunderstood so thoroughly! Analytic truths are logical par excellence. I gave an example of a mathematical statement as an analytic truth and I certainly don't think that mathematics is meaningless or illogical. However, analytic truths don't give us any information about the physical world that isn't already contained in the premises from which they are derived, so they are only interesting if they are not obvious, as in complex mathematical deductions. They are useless to prove the correctness of the premises themselves, that would be a case of circular reasoning, which is a bad thing.
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"Ice floats on water" is not an example of a synthetic truth, or a contingent truth, because, as you go to acknowledge, it is not strictlytrue: assuming that it means "All ice floats on water", your counterexample shows that generalization to be a falsehood. Therefore, you cannot use it as example of synthetic truth or a contingent truth or any other kind of truth.

"What is truth?" Pilate asked already many years ago. I chose the ice example, as it is an example brought up by Peikoff himself. He writes:

(a) Consider the following pairs of true propositions:

i) A man is a rational animal,

ii) A man has only two eyes.

i) Ice is a solid.

ii) Ice floats on water.

i) 2 plus 2 equals 4.

ii) 2 qts. of water mixed with 2 qts. of ethyl alcohol yield 3.86 qts. of liquid, at 15.56°C.

Now Peikoff may disagree with the classification of these statements into analytical (i) vs. synthetic (ii) truths, but it's obvious that he thinks they are all truths. Now if you define "truth" as the absolute definitive truth, the real state of the physical world, then you're right that "ice floats on water" is not strictly a truth. But Peikoff thought it was! The problem with this strict definition of "truth" is that, apart from analytical truths, which are not dependent on empirical evidence, truth would be unknowable, as we would have to be omniscient to be able to say whether a certain statement is true. (To avoid misunderstandings: we're talking here about general truths about the physical world, that which is generally described by science, and not about such "truths" like "there is no green elephant in my room now", which are not very interesting.) This wouldn't be very practical however, and therefore we say that some things are true, even if we know that this is only our opinion, which may be incorrect. "Real" truth may be inaccessible, but we can use the next best thing, that is what to the best of our knowledge is the real state of affairs, and call that "truth". As this applies to all our knowledge about the world, it isn't necessary to qualify our knowledge as tentative every time we state something that seems obviously true to us. And that is what we call synthetic truths (Peikoff calls them "contextual truths"). They may correspond to "real" truths, but we'll never know, as we're not omniscient. Therefore Peikoff's example was so interesting: he chose statements that were to him obviously true and yet one of them was disproved!

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Peikoff would not concede that a mathematical statement is independent of the real world, and neither would I (and neither would most philosophers before Hume). So you need to argue for it.

Well, it depends on what you mean exactly by "independent of the real world". If you mean that you only can make mathematical statements with physical means (human beings who can think, writing materials etc.) then in that sense it is of course not independent of the real world. But I think that is not an interesting viewpoint. If it is about the content then it is independent of the real world. As I've said many times before: one should not confuse mathematics with the application of mathematics, neither with physical structures that may have inspired mathematical ideas. Counting cows may have been the inspiration for creating natural numbers and the rules of addition, but the mathematical theory is an abstraction from what we observe empirically, and by that abstraction it becomes independent of physical reality. Instead of empirical statements a set of axioms is created from which the theory is deducted. In the case of the natural numbers the axioms are Peano's axioms. Once we have such an abstract strucure, we may extend this, for example from natural numbers to integers, rational numbers, real numbers, complex numbers etc. The notion of physical space may have been an inspiration for the mathematical notion of space, but once we have an abstract version of space, it can be extended in many ways: space of many dimensions, infinitely many dimensions, manifolds, topological spaces etc. These are all completely abstract structures, independent of physical reality (what is for example the physical reality of a 254306-dimensional sphere? Mathematically it is very well defined.) Now the interesting thing is of course that many of these abstractions sooner or later turn out to be very useful in physical theories, so that we can apply an abstract mathematical theory in theories about the real world. But the applicability of an abstract theory has nothing to do with its validity. Rand concluded that imaginary numbers are a valid concept while someone told her that they could be applied to physical problems (for example in electronic circuits). But that is of course not a valid criterion! It is very well possible that there is now some mathematical theory for which we don't know any physical application, but that will for example in 50 years turn out to have extremely practical applications. Should it only then become a valid theory and now only a 'floating abstraction'?

And this points to a more general matter: in your critique of Peikoff, you often assume as true claims that he would dispute and which are therefore part of the debate, and which you therefore must argue for. Among them are various appeals to dichotomies that Peikoff rejects. This is common in philosophical debates: one side underestimates just how radically the other side disagrees with them.

It's not clear to me what you're referring to. Could you be more specific and give an example?

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Greg,

A warm welcome to OL.

When I wrote those previous posts on this thread, I had not read much Objectivist epistemology for years. I read and reread and reread all this years ago, but I still did not have the understanding I now have, precisely because of the kind of questioning developed on OL added to a recent focused study.

Now I see a concept as what I call a mental folder to denote a class of entity (or attribute or action or relationship). In the case of Fool's Gold, there is a new "folder" that is opened, but there is something added to the genus of the definition that is not included in the genus of gold: the statement would be "a mineral that looks like gold" or something like that. So even though a new concept is formed, it is not a primary concept. A conceptual connection to gold is maintained.

The idea of commensurability is fundamental to concept formation in Objectivism, but one cannot forget that before measurement, there is a percept. I now see the case of sinking ice to be a need to revise the initial concept because of a different root percept that does not act like the other one. In this case, the original percept is not changed, though. Floating ice still exists. But for the concept of ice to be valid, it has to scoot over to make room for another percept and is no longer the sole root of the concept. Actually, two concepts now exist: the general one, which is incomplete, and the technical one, which includes sinking ice.

(btw - "Bill" is William Dwyer. He does not post here, but on RoR instead. We are friendly, but we have some strong differences.)

Michael

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this example in fact supports Peikoff's position that unknown attributes are part of the concept of gold, since iron pyrite's lack of various properties that gold has but which were once wholly unknown and still are unknown to lay people (or undetectable by them without scientific apparatus), such as gold's atomic number entails that it is not true gold.

But what gold is we know only by hindsight: "real" gold (metal with atomic number 79) has "won" the race for the concept, probably while it had the oldest rights and was considered to be the most valuable. Another example: "star" (or the Latin "aster"). There has been a time when a star was any starlike light point in the night sky, including what we now call planets (we still have the "morning star" and the "evening star"). Today we might say that the balls of plasma that emit their own light have won the race for the concept "star", but in a sense this is arbitrary. Under different circumstances, for example if we had earlier known the physical nature of "real" stars, we might for example have called them "suns" and what we now call planets might have become "stars". This shows that there is no such thing as a real, unchanging concept. What once was the concept "star" has split into two different concepts: "planet" and "star" (in the modern sense). What was the "real" concept that had to be adapted? We now say it was the ball of plasma, but that is just a historical contingency. The problem with Peikoff's definition is that he wants to equate the human construction "concept" with some physical fact or structure, or at least with our knowledge about that physical fact if we were omniscient. But whereas those physical facts in essence are unalterable (they may change with time, but that change is part of the essence), human mental constructs do change with time, including concepts. Without human beings, the physical facts and structures still would be there, but there would be no concepts, so it is not logical to equate them. I think it would therefore be much more natural to equate "concept" with our current knowledge about that which is indicated by that concept (which is really "that what we conceive"). Then concepts can evolve naturally with our increasing knowledge, they are knowable, but not infallible. Phlogiston was once a concept that was thought to be a valid representation of a physical phenomenon. Now the concept "phlogiston" denotes an erronious theory about heat.

To switch an example even closer to everyday life, consider Putnam on water. He asked us to imagine a planet, Twin Earth, very much like Earth, which had on it a material that appeared to be water: it was liquid, it quenched thirst, was tasteless, colorless and odorless, etc. (in the literature it is called "twater). We started to call it "water". But later we did chemical analysis and discovered that it was not H20. So was twater a kind of water? Putnam says "no", and so would Peikoff, Rand, Aristotle and I, whereas the position of Locke and the Logical Positivists (and I would add Hume and Descartes) entails that twater is a kind of water.

Is heavy water a kind of water?

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Is heavy water a kind of water?

Yes. It is either D20 (D for deuterium or double heavy hydrogen) or T20 (T for tritium, triple heavy hydrogen). They are all chemically similar, but have different nuclear makeup.

D has a nucleus consisting of a proton and a neutron. T has a nucleus consisting of a proton and two neutrons.

Ba'al Chatzaf

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"There is a distinction between a purely mathematical theory, like Euclidean geometry, and the application of that theory in a model of the physical world. The theory, based on a set of axioms, is not factual"

Here is one example of a claim that needs to be argued for. Neither Peikoff nor I would concede this, nor would most philosophers before Locke, and Quine seems to deny this too.

"it is a purely abstract construction,"

Again, this needs to be argued for. I maintain that it is discovered, not constructed, by means of derivation of self-evident axioms through analysis of mathemetical concepts which are abstracted from experience.

, but the truths deduced from them can be surprising and interesting (as even the Logical Positivist A. J. Ayer said), and therefore not obvious and not trivial.

That's what I've said in previous posts, for example here.

I doubt that anyone of us thinks that analytic truths are meaningless or illogical

I can't think of anyone who actually says that they are meaningless or illogical.

However, many say that they are "not factual" (i.e., not about the world) or "vacuous", including Hume, the Logical Positivists and some Ordinary Language philosophers, and I believe that you agree with that.

Also, some people seem to think that analytic truths are trivial, obvious or "trifling" (Locke's word)--and even I concede that some are, but not all. You indicate that you agree with me on that.

"However, analytic truths don't give us any information about the physical world that isn't already contained in the premises from which they are derived"

If you had simply said they don't give us any information about the physical world, as the above philosophers would, I would disagree with you , but you correctly add a qualification. However, I think you believe that those premises don't give us any information about the physical world, either, and so I believe you would agree to the unqualified version of the statement, with which I disagree.

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" "What is truth?" Pilate asked already many years ago. "

I would say that truth is correspondence to the facts: "S is P" is true if and only if it is a fact that S is P. But that's a topic for another thread.

"I chose the ice example, as it is an example brought up by Peikoff himself.

....Now if you define "truth" as the absolute definitive truth, the real state of the physical world, then you're right that "ice floats on water" is not strictly a truth. But Peikoff thought it was!"

It is doesn't matter: since it is not true, it cannot be a synthetic or a contingent truth and so cannot be used to prove the existence of such truths.

"The problem with this strict definition of "truth" is that, apart from analytical truths, which are not dependent on empirical evidence,"

Again, Peikoff and I would not concede this, even if we believed that only some truths are analytic. Even truths based on analysis of concepts can be known empirically, if the concepts are empirical, and, being an empiricist, I say that all concepts are.

"truth would be unknowable, as we would have to be omniscient to be able to say whet,er a certain statement is true. (To avoid misunderstandings: we're talking here about general truths about the physical world, that which is generally described by science, and not about such "truths" like "there is no green elephant in my room now", which are not very interesting.)"

I disagree. I believe that we can have certain knowledge of general truths about kinds, if we can perceive a necessary connection between subject and predicate.

"....Real" truth may be inaccessible, but we can use the next best thing, that is what to the best of our knowledge is the real state of affairs, and call that "truth". As this applies to all our knowledge about the world,"

I disagree; see my last comment

"it isn't necessary to qualify our knowledge as tentative every time we state something that seems obviously true to us. And that is what we call synthetic truths"

Synthetic truths are not the same as truths which are not known with certainty (nor are contingent truths the same as truths which are not known with certainty). The classic definitions (the first two from Kant, the third from Logical Positivists) are:

(1) truths whose predicates are not contained in their subjects;

(2) truths which can be denied without contradiction;

and

(3) truths which are not true merely in virtue of the meaning of the words in them.

"(Peikoff calls them "contextual truths")."

He would not equate contextual truths with synthetic truths, since he does believe in the analytic-synthetic distinction.

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Peikoff would not concede that a mathematical statement is independent of the real world, and neither would I (and neither would most philosophers before Hume). So you need to argue for it.

Well, it depends on what you mean exactly by "independent of the real world".

Actually, the phrase comes from a passage you wrote and I quoted, to which the above comment is a reply:

"It is a logical truth that is independent of the real world, just as a mathematical statement is independent of the real world."

I assumed it meant what Hume and Logical Positivists meant by "not factual"--namely, saying nothing about the world"--more or less what you say below:

"If it is about the content then it is independent of the real world. As I've said many times before: one should not confuse mathematics with the application of mathematics, neither with physical structures that may have inspired mathematical ideas. Counting cows may have been the inspiration for creating natural numbers and the rules of addition, but the mathematical theory is an abstraction from what we observe empirically, and by that abstraction it becomes independent of physical reality."

No. Abstraction does not make it independent of physical reality. If it did, every general term, and ever sentence using that term as a subject, would be independent of physical reality, but it is not: the term 'dogs' is an abstraction from individual dogs, but "All dogs have a 4-chambered" heart is clearly a factual truth (assuming that it is really true).

"Instead of empirical statements a set of axioms is created"

Discovered rather than created---or at least only created in the sense of being manufactured from what is discovered

from which the theory is deducted. In the case of the natural numbers the axioms are Peano's axioms. Once we have such an abstract strucure, we may extend this, for example from natural numbers to integers, rational numbers, real numbers, complex numbers etc. The notion of physical space may have been an inspiration for the mathematical notion of space, but once we have an abstract version of space, it can be extended in many ways: space of many dimensions, infinitely many dimensions,

Mathematicians talk of space with more than 3 dimensions, but that is changing the meaning of the term "space". They should have come up with a new term.

"manifolds, topological spaces etc. These are all completely abstract structures, independent of physical reality (what is for example the physical reality of a 254306-dimensional sphere? Mathematically it is very well defined.)"

What is the definition?

"Now the interesting thing is of course that many of these abstractions sooner or later turn out to be very useful in physical theories, so that we can apply an abstract mathematical theory in theories about the real world. But the applicability of an abstract theory has nothing to do with its validity. Rand concluded that imaginary numbers are a valid concept while someone told her that they could be applied to physical problems (for example in electronic circuits). "

I lean toward a version of the view in philosophy of mathematics which I think is called "formalism" which says that mathematical entities do not exist in the real outside of mind or language, nor do they exist in the mind, but are rather a facon de parler or figure of speech. The version I would hold says that nonetheless they do express something in reality; it's just that there isn't really twoness or imaginary quantities in the world; rather, the mathematically expressions as whole say something about reality. For example, to say that 10 + 6 = 16 is to say that if you take a group of things of one kind, count them correctly, and stop counting at 10, and then do the same with another group but stop counting at 6, then if you put the two groups together and count them correctly you will stop at 16.

"But that is of course not a valid criterion! It is very well possible that there is now some mathematical theory for which we don't know any physical application, but that will for example in 50 years turn out to have extremely practical applications. Should it only then become a valid theory and now only a 'floating abstraction'?"

It may make a statement about what is possible in the world.

And this points to a more general matter: in your critique of Peikoff, you often assume as true claims that he would dispute and which are therefore part of the debate, and which you therefore must argue for. Among them are various appeals to dichotomies that Peikoff rejects. This is common in philosophical debates: one side underestimates just how radically the other side disagrees with them.

It's not clear to me what you're referring to. Could you be more specific and give an example?

/quote]

I will probably go back and select some passages from previous posts, but right now I can list some from memory:

1. That Peikoff assumes that attributes contained in concept are merely attributes contained in its definition, when in fact he denies this; in fact, his denial is one of the most important claims---and perhaps the most important claim, in his article.

2. That genuine scientific claims must be falsifiable, which he denies

3. That truths of math are not factual or not about the world.

3. That truths of math and logic are not empirical.

He, and I, deny all of these.

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a logical statement can be true without any reference to the real world. For example the proposition NOT (p AND NOT p) is true, regardless of whether p is true or false. This statement is completely independent of the real world (of course it can be applied to real-world problems).

That proposition is a factual truth, about the real world; indeed, it is true about all possible worlds. The fact that you don't need to know which possible world you are in doesn't change the fact that it gives information about each and every one of those possible worlds.

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Is there such a thing as an "analytic truth"? It seems to me that all truths are "empirical" in that they are true of entities, not definitions.

I think that all truths are analytic. This claim is shocking to most philosophers (but not Leibniz), but the fact is that they are wrong. I say this because in all truths the predicate is contained in the subject, is part of its meaning, and therefore to deny that the subject has that predicate is to utter a self-contradiction.

So I think that even contingent truths are analytic. Again, most philosophers will be shocked, but they are wrong. If a subject has a predicate contingently, it is still contained in that subject, still contained in its meaning. For example, it is presumably only contingently true that G. W. Bush is president, but so long as it is true then that predicate belongs to him as much as any necessary predicate.

(Peikoff says that, in one sense, all truths are analytic, but in another sense all are synthetic. However, if we stick to the standard definitions of those terms, our views imply that all truths are analytic).

I agree with you that all truths are empirical (and so does Peikoff), because, being any empiricist, I say that all concepts are empirical, and it seems absurd to me to say that a truth derived from analysis of an empirical concept (such as "All bachelors are unmarried") is to be classed as non-empirical simply because it is true by conceptual analysis.

I live in Sweden, and there is plenty of what I call "ice" (Swedes would say "is") outside my home. When I point to that white powdery stuff and seek to distinguish it with a definition from salt, sugar, and other perceptually similar, but chemically different, entities, the fact that the stuff I'm pointing to is the solid form of water is an empirical truth. The statement "ice is solid" could be false if I were to learn that ice isn't actually a true solid at all, but some other phase of matter. It would make little sense to say that the stuff I was pointing to really is a solid because it is "definitionally true", when it isn't "empirically true".

This relates to the distinction I made last night, in reply to Michael's post on Fool's Gold, between Shallow Kinds and Deep Kinds. When I first read your post, I assumed that ice is a Shallow Kind. If so, the term 'ice' refers simply to all and only that which is both water and solid. So there would be nothing more to discover about ice, and we could not discover non-solid ice: that non-solid stuff, whatever it was, was not ice.

But then I thought that ice may be a Deep Kind. We did not know from the beginning that ice was water (though we have known it from time immemorial, and so it did not require modern science to discover). So maybe the term contained what Hilary Putnam (see the Fool's Gold and Twin Earth examples) calls an "indexical component"---that is, a pointing components: part of the meaning is based on "paradigms" or examples, which we incorporate into the defition ostensively. To use his example of water, we point to water and say "By 'water' I mean that stuff (pointing at some water) (and everything like it in the appropriate way, which he has to further specify). So perhaps it is part of the meaning of 'ice' that it means ti]that stuff (pointing to some ice).

Then again, if it was not solid, why would we think it was ice?

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Is there such a thing as an "analytic truth"? It seems to me that all truths are "empirical" in that they are true of entities, not definitions.

I live in Sweden, and there is plenty of what I call "ice" (Swedes would say "is") outside my home. When I point to that white powdery stuff and seek to distinguish it with a definition from salt, sugar, and other perceptually similar, but chemically different, entities, the fact that the stuff I'm pointing to is the solid form of water is an empirical truth. The statement "ice is solid" could be false if I were to learn that ice isn't actually a true solid at all, but some other phase of matter. It would make little sense to say that the stuff I was pointing to really is a solid because it is "definitionally true", when it isn't "empirically true".

This relates to the distinction I made last night, in reply to Michael's post on Fool's Gold, between Shallow Kinds and Deep Kinds. When I first read your post, I assumed that ice is a Shallow Kind. If so, the term 'ice' refers simply to all and only that which is both water and solid. So there would be nothing more to discover about ice, and we could not discover non-solid ice: that non-solid stuff, whatever it was, was not ice.

But then I thought that ice may be a Deep Kind. We did not know from the beginning that ice was water (though we have known it from time immemorial, and so it did not require modern science to discover). So maybe the term contained what Hilary Putnam (see the Fool's Gold and Twin Earth examples) calls an "indexical component"---that is, a pointing components: part of the meaning is based on "paradigms" or examples, which we incorporate into the defition ostensively. To use his example of water, we point to water and say "By 'water' I mean that stuff (pointing at some water) (and everything like it in the appropriate way, which he has to further specify). So perhaps it is part of the meaning of 'ice' that it means ti]that stuff (pointing to some ice).

Then again, if it was not solid, why would we think it was ice?

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Is there such a thing as an "analytic truth"? It seems to me that all truths are "empirical" in that they are true of entities, not definitions.

I think that all truths are analytic. This claim is shocking to most philosophers (but not Leibniz), but the fact is that they are wrong. I say this because in all truths the predicate is contained in the subject, is part of its meaning, and therefore to deny that the subject has that predicate is to utter a self-contradiction.

So I think that even contingent truths are analytic. Again, most philosophers will be shocked, but they are wrong. If a subject has a predicate contingently, it is still contained in that subject, still contained in its meaning. For example, it is presumably only contingently true that G. W. Bush is president, but so long as it is true then that predicate belongs to him as much as any necessary predicate.

(Peikoff says that, in one sense, all truths are analytic, but in another sense all are synthetic. However, if we stick to the standard definitions of those terms, our views imply that all truths are analytic).

I agree with you that all truths are empirical (and so does Peikoff), because, being any empiricist, I say that all concepts are empirical, and it seems absurd to me to say that a truth derived from analysis of an empirical concept (such as "All bachelors are unmarried") is to be classed as non-empirical simply because it is true by conceptual analysis.

I live in Sweden, and there is plenty of what I call "ice" (Swedes would say "is") outside my home. When I point to that white powdery stuff and seek to distinguish it with a definition from salt, sugar, and other perceptually similar, but chemically different, entities, the fact that the stuff I'm pointing to is the solid form of water is an empirical truth. The statement "ice is solid" could be false if I were to learn that ice isn't actually a true solid at all, but some other phase of matter. It would make little sense to say that the stuff I was pointing to really is a solid because it is "definitionally true", when it isn't "empirically true".

This relates to the distinction I made last night, in reply to Michael's post on Fool's Gold, between Shallow Kinds and Deep Kinds. When I first read your post, I assumed that ice is a Shallow Kind. If so, the term 'ice' refers simply to all and only that which is both water and solid. So there would be nothing more to discover about ice, and we could not discover non-solid ice: that non-solid stuff, whatever it was, was not ice.

But then I thought that ice may be a Deep Kind. We did not know from the beginning that ice was water (though we have known it from time immemorial, and so it did not require modern science to discover). So maybe the term contained what Hilary Putnam (see the Fool's Gold and Twin Earth examples) calls an "indexical component"---that is, a pointing components: part of the meaning is based on "paradigms" or examples, which we incorporate into the defition ostensively. To use his example of water, we point to water and say "By 'water' I mean that stuff (pointing at some water) (and everything like it in the appropriate way, which he has to further specify). So perhaps it is part of the meaning of 'ice' that it means ti]that stuff (pointing to some ice).

Then again, if it was not solid, why would we think it was ice?

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Is there such a thing as an "analytic truth"? It seems to me that all truths are "empirical" in that they are true of entities, not definitions.

Well, that's a matter of definition of course. If you define truth as something that can only be based on an empirical observation of entities in the real world, then by definition only a "synthetic truth" would be a truth,

No. You are assuming that empirical truths are synthetic, which I deny (and so does Peikoff). Rather, I say that empirical truths are analytic, shocking as that might sound (see my last reply to Eudaimonist).

Also, even those the Logical Positivists, who are the classical example of believers in the dichotomies Peikoff attacks, and who think that all of them line up, nonetheless deny that "empirical truth" and "synthetic truth" mean the same thing or have the same definitions, though the say that they refer to the same truths (this is because they think that the meaning is not the same as the reference, which I deny).

It would make little sense to say that the stuff I was pointing to really is a solid because it is "definitionally true", when it isn't "empirically true".

That's true(!) but not relevant to the discussion. As I said in my original article:

The more you include in your definition, the more analytical statements you may derive from it, but the higher the risk that your definition no longer adequately describes a subject in the real world.

Yes. Being analytic and even being necessary does not guarantee certainty. If I, and Peikoff, Putnam and Saul Kripke are right, "Water is H20" is a necessary truth, but it was not always certain, or even known at all: it was unknown before the 19th century and took much investigation to discover. (Most philosophers before Kripke wrote Naming and Necessity in the 1970s confused necessity and certainty.

It is even possible that it turns out that the smallest possible definition doesn't describe a subject in the real world. To take the ice example: it could be that: (a) what we generally call ice is not the solid form of water, ..... In (a) the definition is still consistent with reality, but highly impractical as it no longer corresponds to the general consensus about what "ice" means ("ice" is no longer what everybody calls "ice");.....

If (a) were true, what we should do would depend on whether ice is a Shallow Kind or a Deep Kind, as I discussed in my reply to Eudaimonist. If ice is a Shallow Kind that is necessarily identical to solid water, then we would have been mistaken in calling "ice" that which we have been calling "ice." If ice is a Deep Kind based on paradigm cases, then what we called "ice" must be ice, but we would have been mistaken in thinking that all ice was solid water.

There is even a discipline where analytical truths are far from trivial: mathematics. Here the fact that some complicated proof boils down in fact to a tautology doesn't mean that such a proof is useless - it may be a tautology, but it is a hidden tautology. We may derive that A → B, by showing that B is logically implied by A, but before we had the proof we didn't know that (though we may have suspected it of course).

Right. A non-trivial truth can be deduced from a trivial one. However, a factual truth cannot be deduced from a non-factual truth. So if admit that the non-trivial conclusion of the proof is factual you would have to concede that the trivial premise is also factuality.

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There are still a lot of posts I want to reply to, but it will be best to make some comments that apply to several at once.

1. Rand and Peikoff do use "concept" in a way that I found unusual and so would most people, but it seems to be one, or similar to one, that is common in current philosophy: most people assume that a concept is something mental, an idea, but Rand, Peikoff and many modern philosophers seem to treat as a sort of abstract entity. This allows them to say concept includes attributes that are not yet known.

2. There are 2 kinds of definition that of especial importance to our debate, distinguished by Aristotle or at least by the Scholastics: what the latter called "nominal definitions" and "real definitions". Nonminal definitions are the kind of definition which express what we learn when we learn the meaning of the word. For example, a nominal definition of water would be one that merely mentioned its apparent, observable attributes--it quenches thirst, it is a liquid at normal temperatures and pressure, it is tasteless, colorless and odorless (when pure). A real definition expresses the fundamental necessary attributes (which Rand and others call "the essential attributes", though others use that term to apply to all necessary attributes), from which others are derived causally and from which the others can be deduced. In the case of water, that would be having the atomic structure of being H20. This requires a lot of investigation to discover.

Now in Deep Kinds, such as water, the real and nominal definitions are normally different, while in Shallow Kinds they are the same (for example, the nominal and real definition of 'bachelor' is 'unmarried male human of marriageable age').

Now real definitions are not made by arbitrary linguistic convention or stipulation, nor are they derived from these; they are either correct or incorrect.

Nominal definition are expressions of arbitrary linguistic convention or stipulation, but even here a definition may fail to accurately express the convention or stipulation (though its rare in the latter case, because when one person stipulates a meaning they usually do so be given the definition).

I will add that those who want to define a new concept by stipulation ought to come up with a new term (a term word or combination of existing words) and not give definitions to existing words, which simply creates confusion.

3. When Peikoff says that the new definitions we come up with as science advances do not contradict each other, I think he means that they need not contradict each other. This allows different theories to refer to the same thing. Without this, there might not be communication across what Kuhn referred to as "paradigms"--and Kuhn and others do thin that this is impossible, at least sometimes. But if Peikoff, and Hilary Putnam and other "realists" about science are right, all of the different theories can be referring to the same thing. So today when we theorize about gold we can, as Putnam argued, be talking about the same thing the ancient Greeks called "gold" (or rather "chrysos").

Edited by Greg Browne
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Greg,

I thought of correcting your quote code errors like I did once, but since the problem has reappeared over several posts, I suggest you take a look at the following tutorial (it is short and sweet and should take no more than 5 minutes or so):

Inserting quotes from other posts

You will probably find where the error is and it should make posting for you and others reading your posts easier. If you have any doubts, please ask (online or off).

Michael

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Hello and Welcome, Greg Browne!

From Amazon, we learn of:

Necessary Factual Truth

Gregory M. Browne

"In this book Gregory Browne rejects the views of David Hume and the Logical Positivists, and argues that there are necessary factual truths, which include a wide range of truths from many fields of knowledge. Browne argues for the necessity of Newton's Laws and truths about natural kinds, and for the factuality of definitional truths and truths of logic and mathematics. Browne synthesizes the work of Kripke, Putnam, Quine and others, but goes beyond the usual discussions of the meanings and definitions of terms to discuss the references of various kinds of terms, and specifically to develop a theory of kinds, distinguishing "Deep Kinds" (roughly, natural kinds) and "Shallow Kinds" (e.g., triangles, bachelors). His theory of Deep Kinds does not accept all of the assumptions commonly associated with a theory of natural kinds."

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"In this book Gregory Browne rejects the views of David Hume and the Logical Positivists, and argues that there are necessary factual truths, which include a wide range of truths from many fields of knowledge. Browne argues for the necessity of Newton's Laws and truths about natural kinds, and for the factuality of definitional truths and truths of logic and mathematics. Browne synthesizes the work of Kripke, Putnam, Quine and others, but goes beyond the usual discussions of the meanings and definitions of terms to discuss the references of various kinds of terms, and specifically to develop a theory of kinds, distinguishing "Deep Kinds" (roughly, natural kinds) and "Shallow Kinds" (e.g., triangles, bachelors). His theory of Deep Kinds does not accept all of the assumptions commonly associated with a theory of natural kinds."

Some of this is similar to a topic in my Appendix B of Understanding Imaginaries, which begins: "Appendix B: Taxonomy of Concept Types / Concepts may be categorized by type of referent, such that the category of any given concept suggests whether its definition is open to change and under what conditions. The types I have noticed so far are:" Etc.

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Greg, you are posting so much that I can't keep up with it. Answering all your points would take me hours, and I just don't have that time. I'll address the points that in my opinion are the most relevant. If you think I've missed something essential, bring it up by all means, but please one at a time. Moreover, your posts are hard to read as your quotes don't work. Probably there is a mismatch between the number of "quote" and "/quote" codes. You should preview your posts to check this, if the quotes are not rendered correctly there are probably one or more unmatched quote codes left.

I would say that truth is correspondence to the facts: "S is P" is true if and only if it is a fact that S is P. But that's a topic for another thread.

But it is important in this thread.

"I chose the ice example, as it is an example brought up by Peikoff himself.

....Now if you define "truth" as the absolute definitive truth, the real state of the physical world, then you're right that "ice floats on water" is not strictly a truth. But Peikoff thought it was!"

It is doesn't matter: since it is not true, it cannot be a synthetic or a contingent truth and so cannot be used to prove the existence of such truths.

That is if you use your definition of truth. But with that definition you'll never know if a statement is really true (except analytical truths and the trivial cases I mentioned in my previous post), as we are not omniscient. That is exactly the reason I gave this example, as Peikoff no doubt was absolutely convinced of the truth of his statement and yet he was wrong! With your definition of truth you can never know whether a synthetic or a contextual "truth" is really a truth.

"The problem with this strict definition of "truth" is that, apart from analytical truths, which are not dependent on empirical evidence,"

Again, Peikoff and I would not concede this, even if we believed that only some truths are analytic. Even truths based on analysis of concepts can be known empirically, if the concepts are empirical, and, being an empiricist, I say that all concepts are.

Which is definitely wrong, mathematical concepts are not empirical, even if some of them are derived from an analysis of empirical evidence.

"truth would be unknowable, as we would have to be omniscient to be able to say whet,er a certain statement is true. (To avoid misunderstandings: we're talking here about general truths about the physical world, that which is generally described by science, and not about such "truths" like "there is no green elephant in my room now", which are not very interesting.)"

I disagree. I believe that we can have certain knowledge of general truths about kinds, if we can perceive a necessary connection between subject and predicate.

That is a bit vague. It is necessary to make a distinction here between analytical truths and synthetic truths. The first is logically true, that is, it follows logically from the definitions. But the definitions do not necessarily correspond to physical reality. If iI'd define a bachelor as an unmarried man that is at least 3 meters tall, then the statement that a bachelor is larger than 2,5 meters is an analytical truth, which doesn't correspond to a truth in the physical world. This is a deliberately absurd example, but the same principle applies to situations where the error is far from obvious. You may deduce logically a "truth" from some empirical premises, but you can never be certain that it is a truth in your definition, as you never can be 100% certain of the correctness of your premises.

Synthetic truths are not the same as truths which are not known with certainty (nor are contingent truths the same as truths which are not known with certainty). The classic definitions (the first two from Kant, the third from Logical Positivists) are:

(1) truths whose predicates are not contained in their subjects;

(2) truths which can be denied without contradiction;

and

(3) truths which are not true merely in virtue of the meaning of the words in them.

If such truths don't follow from the definitions, they can only be verified empirically, which automatically means that you never can be certain that they correspond to a truth in your definition (which I'll call for convenience a "real truth").

"(Peikoff calls them "contextual truths")."

He would not equate contextual truths with synthetic truths, since he does believe in the analytic-synthetic distinction.

Of course he doesn't do that, but that's his problem. The point is that he may use a different term, but in fact it boils down to the same thing.

Edited by Dragonfly
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"Instead of empirical statements a set of axioms is created"

Discovered rather than created---or at least only created in the sense of being manufactured from what is discovered

Certainly not. Take for example Euclid's fifth axiom. There are geometries with a different axiom, which are equally consistent and logical as Euclidean geometry. It is a matter of empirical research to find out what geometry can best used to describe the physical world.

Mathematicians talk of space with more than 3 dimensions, but that is changing the meaning of the term "space". They should have come up with a new term.

Why? It's the power of mathematics that enables us to see that our 3-dimensional space is only one particular example of a much wider class.

"(what is for example the physical reality of a 254306-dimensional sphere? Mathematically it is very well defined.)"

What is the definition?

The set of points x(1), x(2),...x(254307) in a 254307-dimensional vectorspace that is defined by R^2 = sumx(i)^2, where R is the radius of the sphere.
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a logical statement can be true without any reference to the real world. For example the proposition NOT (p AND NOT p) is true, regardless of whether p is true or false. This statement is completely independent of the real world (of course it can be applied to real-world problems).

That proposition is a factual truth, about the real world; indeed, it is true about all possible worlds. The fact that you don't need to know which possible world you are in doesn't change the fact that it gives information about each and every one of those possible worlds.

A possible world is not a real world. So the statement is indeed independent of the real world.

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