The Analytic-Synthetic Dichotomy

[Dragonfly]

Here is a reproduction of the article I wrote for the NB list:

Peikoff's article about the analytic-synthetic dichotomy (ASD) has repeatedly been used on this list to refute Mike's arguments without any further explanation. Let's therefore have a look at what Peikoff really says in that article.

He starts with an exposé of the ASD with some examples of true statements in pairs, with the first statement of each pair being an example of an analytic truth and the second statement an example of a synthetic truth. I'll use one of his examples:

i) Ice is a solid

ii) Ice floats on water

His example is incomplete, as he doesn't give the definition of "ice", but I think we may assume that the implied definition is "ice is the solid form of water". With that definition the first statement is obviously true, as Mike said: you don't have to leave your armchair to know it's true, it's an analytical truth which follows logically from the definition of ice. The second statement doesn't follow from the definition of "ice" however, it is an empirical fact, which you can only discover by leaving your armchair. This is called a "synthetic truth", in Peikoff's words: "A 'synthetic' proposition is defined as one which cannot be validated merely by an analysis of the meanings or definitions of its constituent concepts.

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. But a definition isn't the same as the concept, it's only a label on a box, it doesn't tell us what is in that box. If you want to equate the definition with the concept, you'll have to state all the properties of that concept explicitly in your definition. In that case you could say that any characteristic follows logically from the definition. But it is of course impossible to give such a complete definition, therefore the characteristics don't follow logically from that definition. You have to determine empirically what those characteristics are (get out of your armchair!).

Even if we assume for the sake of argument that the definition of a concept does imply all the characteristics of that concept, Peikoff's argument fails. He emphatically states that not only all known characteristics belong to the concept, but also all the characteristics that still have to be discovered. This is indeed a crucial part of his argument, as there otherwise would be always room for doubt, which is incompatible with an analytic deduction. Now this is a good example of what you may call a giant floating abstraction bearing no relationship to reality, a kind of Platonic construction. We can't derive anything from this Platonic concept, as it is in principle unknowable, man isn't omniscient, there ain't no such thing as perfect complete knowledge. We can only derive conclusions from a concept that subsumes all the current knowledge about the subject. This may be largely correct, but we can't be sure and it's always possible that what is now accepted as a correct description of characteristics may ultimately turn out to be wrong or may even be wrong while we'll never know it's wrong. We can of course live very well with the fact that 100% certainty can't be attained in real life, but it's fatal to Peikoff's argument. All the statements derived from a certain definition are synthetic statements if they are not derived from the explicit definition but from the implied characteristics of the defined concept. We can't make deductions from a Platonic unrealizable concept, only from a concept that we use in real life, including all the errors and omissions.

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").

Now we could of course adapt our definition like this: ice is the solid form of water that floats on water. In this case the statement "ice floats on water" would follow logically from the definition. The kind of "ice" that sinks in water would according to that definition not be ice. How you exactly define "ice" is in fact arbitrary - with a minimal definition (solid form of water) the concept includes more than with a more specified definition (solid form of water that floats on water). There is no exact criterion for that, it is a matter of convenience and here is room for fuzziness (classification and separation of concepts). This is in itself no problem as long as people know what definition is exactly used.

Another example is of course Mike's question about the definition of self-esteem - is "reality-based" part of the definition, then the statement that self-esteem is reality-based is of course a trivial analytic truth. A disadvantage is that such a theory of self-esteem becomes unfalsifiable in this respect, it becomes a mere assertion. Without "reality-based" in the definition you may test the theory that self-esteem is reality-based, otherwise it becomes a mere tautology. In general it's better to make a definition as small as possible if you want to gain knowledge about your subject. 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.

[Michael Stuart Kelly]

Dragonfly,

That was a pretty clear exposition of what should be included in a concept. I happen to agree with you that a concept can be added to, fundamentally changed or overturned once we learn what we don't yet know, but to say that it automatically includes information that has not yet been discovered is silly.

On definitions, I agree with Rand (and you seem to also). From ITOE, Chapter 5:

All definitions are contextual, and a primitive definition does not contradict a more advanced one: the latter merely expands the former.

I dug up the original essay by Peikoff, but I don't have time to reread it with full concentration just yet. I will do so and get back to this thread.

You might be interested in one of the harshest criticisms so far of Peikoff's essay. It is from a post by one Gary Merrill on a newsgroup, sci.philosophy.tech,sci.philosophy.meta, dated Aug. 2, 1993. It is titled "Rand’s work: style and quality." He was discussing the poor standards of scholarship in Rand's references from literature, making special complaint against her broad all-inclusive statements about other philosophers and their ideas.

Nor is this brand of scholarship restricted to Rand herself. Her closest followers embrace it as well. Consider Peikoff’s article, “The Analytic-Synthetic Dichotomy”. This article, said to have been published first in 1967, contains the sweeping claim (p. 89) that “It [the analytic-synthetic dichotomy] is accepted, in some form, by virtually every influential contemporary philosopher – pragmatist, logical positivist, analyst, and extentialist alike.” Well, consider please the following:  

But, for all its a priori reasonableness, a boundary between analytic and synthetic statements simply has not been drawn. That there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith. (W. V. Quine, “Two Dogmas of Empiricism”).

My copy of From a Logical Point of View has an initial copyright date of 1953. The original paper appeared in The Philosophical Review in 1951. Look folks, it simply is not possible for anyone who was aware of what was happening in Anglo-American philosophy in the 50’s and early 60’s to claim with any honesty what Peikoff does in the quote above. So was Peikoff dishonest or ignorant? Take your pick. He had to be one or the other. If one were forced to select a single paper of Quine’s that had the most impact on contemporary philosophy it would have to be “Two Dogmas”. But Peikoff appears ignorant of both it and its impact on the field. Further, it appears that Peikoff’s article appears only in the second edition of IOE, published in 1990. Certainly by this time someone should have noticed “Two Dogmas” and at least conceded in a footnote that Peikoff’s claim was unsupportable both now and when it originally was made. Peikoff, like Rand, goes to great lengths to claim (I would say “make a case”, but no genuine evidence is ever introduced) that he is proposing a novel approach where all other philosophers have failed. In the case of the analytic/ synthetic dichotomy I’ve got news for Peikoff: It was done 15 years earlier, and it was done better.

Michael

[Roger Bissell]

Wow, Michael, thanks for providing those quotes -- and thanks, Dragonfly, for posting your own article on Peikoff's ASD article.

You know, I'm wondering if this isn't why Peikoff never tried to publish his Ph.D. dissertation. Its theme was the Law of Contradiction in Classical Logical Ontologism (well, actually, that's the title, or close to it), but he devoted a significant portion of it to the views on logic of modern philosophers. I wonder if Quine wasn't included in the mix. If so, it is all the more curious that Peikoff wouldn't have known about his "Two Dogmas."

Of course, Objectivists seeking to defend Peikoff on this can always resort to the "nonequivalence" gambit and claim that anyone whose views aren't properly founded aren't really holding those views. Libertarians argue for non-initiation of force, but they eschew a unified metaphysical base for their argument, so their view is floating, and they aren't really holding the same view as Objectivists. Similarly, Quine may argue against the ASD, but he does so from a non-Aristotelian, non-Objectivist metaphysical base, so his argument is basically floating.

We've seen a lot of this lately. It is used as a two-edged sword. If an Objectivist disapproves of someone's views, they write them off as not being grounded. If they approve of someone's views (like von Mises), they say he has a valid "implicit" metaphysics. (Peter Schwartz actually engages in this kind of do-si-do.) I've always wondered what metaphysics has to do with it, if a person has arrived at his views inductively, from the ground up. He might hold wrong metaphysical premises, but they would only lend a fishy appearance to what are basically valid generalizations.

Anyone else have any thoughts about this issue?

REB

[Ellen Stuttle]

REB:

You know, I'm wondering if this isn't why Peikoff never tried to publish his Ph.D. dissertation. Its theme was the Law of Contradiction in Classical Logical Ontologism (well, actually, that's the title, or close to it), but he devoted a significant portion of it to the views on logic of modern philosophers. I wonder if Quine wasn't included in the mix. If so, it is all the more curious that Peikoff wouldn't have known about his "Two Dogmas."

Roger, I believe you mentioned that J. Roger Lee was present at that event you attended where Nathaniel, Barbara, and John Hospers were reminiscing. You might want to ask J. Roger for some thoughts on this. He's been known to wax loquaciously on the subject of Leonard's lack of knowledge of modern philosophy. (J. Roger is an old-time friend of Larry's and mine.) You could get in touch with him through John. I'm not sure what J. Roger's current email address is, but I think that he and John are in fairly frequent contact.

Ellen

___

[Bill]

In his criticism of Piekoff's essay on the analytic-synthetic dichotomy, Cal writes:

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.

Peikoff's position is not that any characteristic of ice "follows logically from the definition of ice." It's that any characteristic of ice is part of the concept of ice, which I think is correct. Ice is whatever it is, and therefore includes whatever characteristics it has, even if we're not aware of them.

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. But a definition isn't the same as the concept, it's only a label on a box, it doesn't tell us what is in that box. If you want to equate the definition with the concept, you'll have to state all the properties of that concept explicitly in your definition. In that case you could say that any characteristic follows logically from the definition. But it is of course impossible to give such a complete definition, therefore the characteristics don't follow logically from that definition. You have to determine empirically what those characteristics are (get out of your armchair!)....

This misrepresents Peikoff's view (See below). He would agree that a definition does not state all of the concept's characteristics, only the essential ones.

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.

Who's talking about deducing from ice is a solid form of water that ice floats. Certainly not Peikoff! He writes,

In one sense, no truths are "analytic." No proposition can be validated merely by "conceptual analysis"; the content of the concept--i.e., the characteristics of the existents it integrates--must be discovered and validated by observation, before any "analysis" is possible. In another sense, all truths are "analytic." When some characteristic of an entity has been discovered, the proposition ascribing it to the entity will be seen to be "logically true" (its opposite would contradict the meaning of the concept designating the entity). (IOE, 101)

...If that would be possible, one logical 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...

Are you serious? Ice is simply an example, and he's talking about normal ice, not very high density ice. Can't you see that??

If you want to refute Peikoff's article on the ASD, you're going to go do a lot better than this!

- Bill

[Dragonfly]

Who's talking about deducing from ice is a solid form of water that ice floats. Certainly not Peikoff! He writes,

In one sense, no truths are "analytic." No proposition can be validated merely by "conceptual analysis"; the content of the concept--i.e., the characteristics of the existents it integrates--must be discovered and validated by observation, before any "analysis" is possible.

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

In another sense, all truths are "analytic." When some characteristic of an entity has been discovered, the proposition ascribing it to the entity will be seen to be "logically true" (its opposite would contradict the meaning of the concept designating the entity). (IOE, 101)

And there Peikoff is dead wrong, he just doesn't understand what logic means and he confuses a definition of the concept with the concept itself. In logic you have to define the elements of a proposition, before you can conclude whether the proposition is true or false. Now, if you include that characteristic in the definition of the concept, it will follow logically from that definition that the proposition "[that concept] does have that characteristic" is true. Peikoff tries to circumvent this by saying that the concept subsumes and includes all its characteristics, known and not-yet-known. But in that case the concept is unknowable as we never can be 100% certain that a certain characteristic will be part of that concept. So one of the elements of that proposition is unknown, which means that you can't conclude logically that the proposition is true. It may be highly likely as far as we know, but the logic of propositions is not about likely or unlikely, but about true or false. And that is the essential difference between an analytical statement (which is a tautology) and a synthetic statement (which represents tentative knowledge).

Are you serious? Ice is simply an example, and he's talking about normal ice, not very high density ice. Can't you see that??

No, I can't see that. Where does he say that he's only talking about "normal" ice? He's so sloppy in his argument that he even doesn't give a definition of ice. I assume that (at least at the time he wrote that article) would have agreed with the definition "ice is the solid form of water". Well, that definition includes all forms of solid water. There appear to be 13 different possible crystal structures for solid water. Some of them will be common, others rare, but as long as you don't explicitly state in your definition of "ice" which of these you'll call ice and which not, we can't assume that one of them is not ice. In discussing logical propositions you have to be exact in your definitions! What you're trying to do here is to smuggle an extra characteristic into the definition: "ice is a solid form of water that does not sink in water". As long as Peikoff hadn't known that some solid form of water would sink in water, he'd no doubt have had no objections against the general definition of ice as the solid form of water, as he would have thought that "not sinking in water" was an analytical truth about ice in general. But here you see clearly the difference between an analytical truth and a synthetic "truth". The latter represents tentative knowledge. We may once have thought that all forms of solid water, which we call "ice", will float on water, but is has turned out not to be the case. Now you may try to repair this "anomaly" by changing the definition of ice, but that's what I've been saying all along. You can't replace an exact definition by an unknowable concept to conclude if a proposition is true or false.

[Ellen Stuttle]

Bill,

If you're going to be posting here, must you post in the assault-on-the-eyes large and bolded type? The type of itself is physically painful to me to be confronted by.

Ellen

___

[Ellen Stuttle]

Actually, Bill, it doesn't matter about the type font unless others complain about that too, since I can't go on with active elist participation in any case. I posted fairly extensively (for me) here last weekend, and as a result have spent much of the last four days hibernating in a dark room waiting for the light-triggered muscle twitches to subside. Trying to engage in the conversation on elists has become just not worth the resultant ordeal, though I'll continue to try at least for awhile to read the posts here every few days.

Ellen

PS to all: Sorry to desert. This is a fun list, and I wish I could play an active role.

PPS to Dragonfly: Sorry to "hijack" your subject with this announcement. I considered posting it as a new thread in "Living Room," but decided that it followed "logically" (though whether "analytically" or "synthetically" so, I leave you to ponder) from my complaint to Bill about what I experience as his painful type style.

___

[Michael Stuart Kelly]

Ellen,

While I certainly do not wish to cause you pain, I cannot accept your resignation. Your ideas and stories are too valuable and, frankly, you are too loved around here. (Seriously.)

I adjusted Bill's font size, so see of that helps (that is, if you wish to read his post). I get the impression that he uses larger font size for being able to see better. If that is not suitable for him, maybe a size in between will hit the mean in what would be good for you both.

But by all means, be good to yourself. Don't overdo it and suffer - but don't go away.

(I ain't finished pestering you about that book, either, but I'll save that for off line...)

Michael

[Bill]

In replying to Dragonfly, I quoted Peikoff as follows:

In one sense, no truths are "analytic." No proposition can be validated merely by "conceptual analysis"; the content of the concept--i.e., the characteristics of the existents it integrates--must be discovered and validated by observation, before any "analysis" is possible.

In a post of February 1st, Dragonfly replied, 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. It is a logical truth that is independent of the real world, just as a mathematical statement is independent of the real world."

A proposition is true if it corresponds to reality. This applies to mathematical statements as well. The proposition "2 + 2 = 4" is true, because it corresponds to the fact that any two units of a specific kind added to any other two units of that kind equal four units of that kind. In other words, it refers to the fact that || + || = ||||. A statement that says nothing about the world is neither true nor false; it is meaningless.

Supposing, to take your example, that ice couldn't exist in the real world -- that water were incapable of freezing -- but that you had decided to call an imaginary form of solid water by the term "ice," then if you said, "Ice is a solid form of water," you'd be referring simply to the fact that the term "ice" is a name that you are using to symbolize an imaginary form of solid water. Your statement would then be true, only insofar as it is a fact that you have chosen the term "ice" to refer to such an imaginary entity. But you would have to have validated that by experience, for if you had not chosen the term "ice" to symbolize it -- if, instead, you had chosen the term "fire" -- your statement would be false. So you still have to refer to the real world -- to the fact that you have actually, in reality, chosen to use the term "ice" to symbolize that imaginary referent, because your choice of terminology is really what your statement refers to in this case.

Continuing with Peikoff's quoted statement:

In another sense, all truths are "analytic." When some characteristic of an entity has been discovered, the proposition ascribing it to the entity will be seen to be "logically true" (its opposite would contradict the meaning of the concept designating the entity). (IOE, 101)

To which you replied: And there Peikoff is dead wrong, he just doesn't understand what logic means and he confuses a definition of the concept with the concept itself.

On the contrary, it is your objection that fails to distinguish the definition of the concept from the concept itself. Peikoff does make that distinction, since according to Objectivism, a definition incorporates only an entity’s essential characteristics, whereas the concept itself incorporates all of the entity’s characteristics.

In logic you have to define the elements of a proposition, before you can conclude whether the proposition is true or false. Now, if you include that characteristic in the definition of the concept, it will follow logically from that definition that the proposition "[that concept] does have that characteristic" is true.

But you don't have to include it in the definition of the concept in order for it to be a logically necessary part of the concept. Once again, a definition of a concept names only the essential characteristics of the entity, not every characteristic. If something is a characteristic of the entity, then a proposition ascribing that characteristic to the entity will be logically true, because its opposite would contradict the meaning of the concept designating the entity.

Peikoff tries to circumvent this by saying that the concept subsumes and includes all its characteristics, known and not-yet-known. But in that case the concept is unknowable as we never can be 100% certain that a certain characteristic will be part of that concept.

To say that the concept includes all of its characteristics known and not-yet-known is not to say that the concept is unknowable. I don't have to know everything about the units of a concept in order to understand it. For example, I know what the concept "strawberry" means and refers to, namely, a certain red berry. The concept "strawberry" refers to that particular fruit, including all of its characteristics, even the ones I'm not familiar with. It won't do to say that the term "strawberry" refers only to those characteristics of the strawberry that I'm familiar with and not those that I'm unfamiliar with, for it refers to the fruit, and the fruit is all of its characteristics, even the ones I'm not aware of (like the ability, say, to reduce vascular inflammation).

So one of the elements of that proposition is unknown, which means that you can't conclude logically that the proposition is true.

I don't follow you. I can conclude that the proposition "Strawberries are red" is true, because I've seen what they look like. The fact that strawberries have properties that I'm not yet aware of does not alter the truth of that statement.

I wrote, Are you serious? Ice is simply an example, and he's talking about normal ice, not very high density ice. Can't you see that??

You replied, No, I can't see that. Where does he say that he's only talking about "normal" ice?

Do you really think that he was talking about high density ice that sinks in water? Seriously! :-)

He's so sloppy in his argument that he even doesn't give a definition of ice.

Does he have to? Do you really think that anyone besides yourself thought that he might be referring to high density ice? Do you think that Peikoff or the average reader is even aware of such a thing?

I assume that (at least at the time he wrote that article) he would have agreed with the definition "ice is the solid form of water". Well, that definition includes all forms of solid water. There appear to be 13 different possible crystal structures for solid water. Some of them will be common, others rare, but as long as you don't explicitly state in your definition of "ice" which of these you'll call ice and which not, we can't assume that one of them is not ice. In discussing logical propositions you have to be exact in your definitions! What you're trying to do here is to smuggle an extra characteristic into the definition: "ice is a solid form of water that does not sink in water". As long as Peikoff hadn't known that some solid form of water would sink in water, he'd no doubt have had no objections against the general definition of ice as the solid form of water, as he would have thought that "not sinking in water" was an analytical truth about ice in general. But here you see clearly the difference between an analytical truth and a synthetic "truth". The latter represents tentative knowledge.

What do you mean -- "tentative knowledge”? The knowledge that normal ice, which is what Peikoff is referring to, floats on water is not tentative; it's an observable fact. Peikoff may define this kind of ice as "solid water," because he's unfamiliar with high-density ice. But as soon as he becomes familliar with it, he will have to revise his definition of normal ice to "solid water that floats." But that doesn't alter the fact that his knowledge that normal ice floats on water is logically true insofar as its denial is self-contradictory.

A child who sees flying birds might define them as "things that move through the air," in order to distinguish them from things that he is aware of on the ground. But once he discovers kites, he will have to revise his definition to "things that fly under their own power" in order to distinguish flying birds from kites. Does that mean that his knowledge that these creatures fly through the air is "tentative"? No, it is still logically true, because its denial is self-contradictory. And, of course, once he discovers airplanes, he will have to revise his definition even further to "a living entity that has wings and can fly" in order to distinguish birds from airplanes. But his knowledge that birds fly will still be logically true, because its denial is, again, self-contradictory. And once he discovers moths and other flying insects...well, you get the idea. The fact that there is no logical stopping point at which our definitions of a concept will no longer require revision does not mean that our knowledge of the concept is not logically true. Nor does it mean that in each of these succeeding stages of revision, our definition is not valid or appropriate for the state of our knowledge at the time.

We may once have thought that all forms of solid water, which we call "ice", will float on water, but it has turned out not to be the case. Now you may try to repair this "anomaly" by changing the definition of ice, but that's what I've been saying all along. You can't replace an exact definition by an unknowable concept to conclude if a proposition is true or false.

As we have seen, the child's definition of ‘flying bird' was exact at every stage, because it was sufficient to distinguish these creatures from the rest of his knowledge. The same can be said for our definition of normal ice, as it is revised from "solid water" to "solid water that floats." Both definitions are exact for their respective times and contexts of knowledge. We were entirely correct in thinking that normal ice floats on water. We did not think that all forms of ice (including high-density ice) float on water, because we were not aware of all forms of ice. We were aware only of normal ice, and were correct in thinking that all ice of that kind floats on water.

- Bill

[Dragonfly]

A proposition is true if it corresponds to reality. This applies to mathematical statements as well. The proposition "2 + 2 = 4" is true, because it corresponds to the fact that any two units of a specific kind added to any other two units of that kind equal four units of that kind. In other words, it refers to the fact that || + || = ||||. A statement that says nothing about the world is neither true nor false; it is meaningless.

No. Mathematics does not correspond to reality, it may be applied to reality, but that is something quite different. The proposition 2 + 2 = 4 can be derived from Peano's axioms in a purely formal system that does not refer to reality, mathematics is not the same as kindergarten arithmetic. The same for formal logic: 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).

Supposing, to take your example, that ice couldn't exist in the real world -- that water were incapable of freezing -- but that you had decided to call an imaginary form of solid water by the term "ice," then if you said, "Ice is a solid form of water," you'd be referring simply to the fact that the term "ice" is a name that you are using to symbolize an imaginary form of solid water. Your statement would then be true, only insofar as it is a fact that you have chosen the term "ice" to refer to such an imaginary entity. But you would have to have validated that by experience, for if you had not chosen the term "ice" to symbolize it -- if, instead, you had chosen the term "fire" -- your statement would be false. So you still have to refer to the real world -- to the fact that you have actually, in reality, chosen to use the term "ice" to symbolize that imaginary referent, because your choice of terminology is really what your statement refers to in this case.

You're confusing a definition with a statement about the real world. If I'd define "fire" as the "solid form of water" the statement "fire is a solid" would be a true (analytical) statement. Of course this would be highly impractical, as we already use the term "fire" for something different, so that nobody would understand us in that case. But we should distinguish a formal definition of a concept from the concept itself, although it's of course practical to find a definition that fits closely an already existing concept.

But you don't have to include it in the definition of the concept in order for it to be a logically necessary part of the concept. Once again, a definition of a concept names only the essential characteristics of the entity, not every characteristic. If something is a characteristic of the entity, then a proposition ascribing that characteristic to the entity will be logically true, because its opposite would contradict the meaning of the concept designating the entity.

No, you confuse "logically true" with "logical reasoning". If we find some characteristic of the concept (that is not explicitly included in its definition), it would be logical to state that that entity has that characteristic. However, even if the evidence is overwhelming that this statement is true, it is not necessarily true, as our observation of that characteristic may be incorrect or incomplete. On the other hand, if a statement is logically true, that statement is a tautology, it will always be true in the context of the definition. It may happen that such a logically true statement does not correspond with what we observe in reality, but that means only that the definition is not consistent with reality.

I don't follow you. I can conclude that the proposition "Strawberries are red" is true, because I've seen what they look like. The fact that strawberries have properties that I'm not yet aware of does not alter the truth of that statement.

But it does: there exist also yellow strawberries, which shows that your statement "strawberries are red" is not necessarily true ("redness" is not implied in the commonly accepted definition of strawberries).

Do you really think that he was talking about high density ice that sinks in water? Seriously!

It doesn't matter one whit what he was thinking about; the only thing that counts is what he says.

He's so sloppy in his argument that he even doesn't give a definition of ice.

Does he have to?

Of course! If you want to analyze what analytical and synthetic statements mean, the definition is an essential part of the argument. Without definition the whole discussion becomes meaningless.

Do you really think that anyone besides yourself thought that he might be referring to high density ice? Do you think that Peikoff or the average reader is even aware of such a thing?

As I already said: what Peikoff thinks is completely irrelevant, we're talking about the logic of statements. For a logical analysis these should be judged on their own merits.

What do you mean -- "tentative knowledge”? The knowledge that normal ice, which is what Peikoff is referring to, floats on water is not tentative; it's an observable fact. Peikoff may define this kind of ice as "solid water," because he's unfamiliar with high-density ice. But as soon as he becomes familliar with it, he will have to revise his definition of normal ice to "solid water that floats." But that doesn't alter the fact that his knowledge that normal ice floats on water is logically true insofar as its denial is self-contradictory.

Now you're talking about "normal ice", that means that you smuggle in some extra qualifier, which was not in the original definition. That Peikoff only knows about ice that is "normal ice" is not relevant. With definition "ice is the solid form of water", the statement "ice does not sink in water" is incorrect, it is true for some forms of ice, but not for all forms of ice. We're concerned here only with exact definitions and statements, not with the imperfect knowledge of people who make these statements.

A child who sees flying birds might define them as "things that move through the air," in order to distinguish them from things that he is aware of on the ground. But once he discovers kites, he will have to revise his definition to "things that fly under their own power" in order to distinguish flying birds from kites. Does that mean that his knowledge that these creatures fly through the air is "tentative"? No, it is still logically true, because its denial is self-contradictory.

This is merely repeating the definition "things that move through the air" are "things that fly through the air", so this is a trivial example of an analytical truth. It is not a good definition of "bird", as it is in contradiction with the commonly accepted definition of "bird", which also implies ostriches for example.

The same can be said for our definition of normal ice, as it is revised from "solid water" to "solid water that floats." Both definitions are exact for their respective times and contexts of knowledge.

Not so fast. The point is not whether a definition is "exact" (that is a question of unambiguous and consistent formulation), but whether it is practical for describing a certain concept. In general the best definition is that one which uses the minimal description that still unambigously refers to the concept we want to describe. "Ice is the solid form of water" is such a definition. Now you may give a new definition: "ice is the solid form of water that floats in water" to exclude the possibility of sinking ice. With such a definition the statement "ice floats in water" becomes an analytical truth. But the disadvantage is then that high-density "ice" no longer is "ice", because it contradicts the definition of "ice". From a physical viewpoint it would be impractical to make such an exception for one of the many different kinds of ice.

Quote:

We were entirely correct in thinking that normal ice floats on water. We did not think that all forms of ice (including high-density ice) float on water, because we were not aware of all forms of ice. We were aware only of normal ice, and were correct in thinking that all ice of that kind floats on water.

This shows only that there is a sharp distinction between analytical and synthetic truths. The statement "ice floats on water" is a typical synthetical truth: we were not aware that there exists also ice that sinks in water, it is an example of the fact that all our empirical knowledge is tentative. This in contrast to the same statement coupled to the definition "ice is the solid form of water that floats in water", which is an analytical truth, it is a tautology, so it will always be true. The price we have to pay for that is that "high-density ice" then no longer is "ice".

[John Dailey]

~~ My impression since the prob was mentioned in ATL-II was that much of the reading prob had to do with reading on/from the monitor itself (light directed to the eyes); I have no impression that the prob is 'reading' (say, books) per se.

~~ Ergo, may I re-suggest to just 'print out' from a printer those sections one's interested in.

LLAP

J:D

[Eudaimonist]

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".

[Dragonfly]

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, so the statement "a truth is a synthetic truth" would be a good example of an ana... ehm... ehm....hmmm...

We seem to be headed for a contradiction. We could try to solve it by giving "analytical truth" a different name, like "tautology". But this doesn't seem to me to be a satisfactory solution, as this would imply either that "a truth is a synthetic truth" is not a true statement or that a true statement is not a "truth". With the latter option you can remain consistent, but it doesn't seem very satisfactory to me.

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.

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, or (B) that there even doesn't exist a 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"); in (B) the definition is still logically consistent, but doesn't correspond to anything in reality, which makes is useless for practical purposes.

In general these kind of trivial analytical statements which are quite obvious are not interesting, they don't tell us anything new and are only useful as the basis upon which we can build our knowledge about the subject with synthetic statements, e.g. "ice is the solid form of water, now what can we discover about this solid form of water" (hoping that our definition is good enough so that we don't have to revise it to keep in touch with reality). But the fact that those analytical truths are trivial doesn't imply that the notion of an analytical truth is meaningless.

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).

[Eudaimonist]

Eudaimonist: 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.

Dragonfly: Well, that's a matter of definition of course.

Why is this a matter of definition? Does the concept of "truth" describe something about the real world, or not? Are there right and wrong understandings of what a truth is, or not?

I was hasty and should have written that truths are true of entities and their relations. Truth is a relation. It seems to me that I'm not merely creating an arbitrary definition, but am describing an empirical truth about human beings and their ability of cognition. If we want to know what truths are, this is where we must look.

[Dragonfly]

Why is this a matter of definition? Does the concept of "truth" describe something about the real world, or not? Are there right and wrong understandings of what a truth is, or not?

There exist different definitions of "truth". That doesn't mean that only one of them is the "correct" definition.

Is in your opinion "there is no largest prime number" a truth?

[DavidMcK]

Now there are 14 (+ - ) forms of ice; I'm not sure if the latest two float or not, the article doesn't describe the properties of the latest two: http://www.physorg.com/news12103.html

David

[Aaron]

Thanks David. I remember reading the old sci-fi idea of room-temperature-solid 'ice 9' in Vonnegut's Cat's Cradle. It was really interesting to learn that more unique forms than that have been found in reality.

[Eudaimonist]

There exist different definitions of "truth". That doesn't mean that only one of them is the "correct" definition.

Perhaps several of them are correct, and several are incorrect. I don't see why there shouldn't be such a thing as an incorrect definition.

Is in your opinion "there is no largest prime number" a truth?

That depends. Has it been proven? I will let a mathematician answer that one. What I do know is that it can't simply be "defined" as true.

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

[Dragonfly]

That depends. Has it been proven true? I will let a mathematician answer that one. What I do know is that it can't simply be "defined" as true.

Of course not. It has been proven true, and the proof is in fact quite simple (see for example: http://mathforum.org/library/drmath/view/57092.html).

[Michael Stuart Kelly]

Dragonfly,

Your article is receiving attention elsewhere. I shall save our critic, a young man named Dan Edge who is basically a good kid, further embarrassment by stating here that (1) you originally wrote this article for another place (NB's list) and Ellen Stuttle asked you to post it here, and (2) you are not an OL writer from the standpoint of expressing the viewpoint of the whole site, but you most definitely are my friend, one of my valued house guests and I admire your intelligence and talent.

As an implied criticism of you, he stated:

When I "chew" on a topic with which I am not very familiar, I do not write with a tone of authority on that topic.  I make a point that I'm stating opinion and ask for constructive criticism.

He does not use this method when he talks about OL, though, preferring another more emotional and less reason-based one at a hostile venue (apparently based on some kind of "morbid fascination"). For example, he complained about me:

The fact that the moderator MSK sanctioned the article was very distressing to me.

Of course, if he had bothered to read the thread, he would have seen this from my post above:

I dug up the original essay by Peikoff, but I don't have time to reread it with full concentration just yet. I will do so and get back to this thread.

I also mentioned the criticism of Gary Merrill of Rand and Peikoff's low standards of scholarship and overly-broad statements of other philosophers (and I do agree with Merill's conclusions).

Dan's got a good head, basically. The reason he makes this kind of mistake is from adopting the preconceptions of others - especially the "insult first, then check facts" policy. I know because I used to do it. Once I saw the errors I was making by using that method, I formally eschewed it and corrected myself.

Also, should anyone who comes here do the basic reading, he will easily understand that the main purpose of OL is to foster the creation of works and hang out with creators and their friends, especially in the realm of creative and nonfiction endeavors.

We humbly leave the task of preaching to the young to the new proprietors and gurus of Objectivism, the new intellectual heirs of Ayn Rand.

Ah yes... OL is also a haven for the Brandens. (Proudly so.)

//;-))

Michael

[Roger Bissell]

Michael -- who is Gary Merill/Merrill?

REB

[Michael Stuart Kelly]

Roger,

Here is how his entry is signed:

Gary H. Merrill [Principal Systems Developer, Compiler and ToolsDivision] SAS Institute Inc. / SAS Campus Dr. / Cary, NC 27513

I am sending you the full post by email.

For those interested, here is the full post by Merrill on Rober Bass's website. It is a pretty famous piece of valid Rand criticism.

Also, here is a criticism by Robert Bass of Objectivist Epistemology. I need to stop everything to get into this, which I have not done yet, but it seems very reasonable on skimming. At least good questions are asked.

Michael

[Roger Bissell]

Michael, thank you for sending the Merrill piece. It was quite interesting. I have always been concerned about the level of scholarship in Rand's and Peikoff's writings. At the very least, it often seems as though they are writing "in a bubble," instead of in a historical context.

I was motivated to email an academic philosopher friend of mine who, long ago and far away, loaned me his copy of Peikoff's dissertation, and I asked him to refer to it to see if Peikoff mentioned Quine's "Two Dogmas" essay dating from about 1950. I will let you all know what my friend reports on this.

Considering how prominent a piece Quine's was, it would be a major failure of scholarly grounding (especially failing to acknowledge priority of critique of the Analytic-Synthetic Dichotomy) if Peikoff did not mention Quine's essay in either his dissertation or his later essay. For that matter, if he did mention it in his dissertation, why in the world didn't he also mention it in his later essay? Either way, I'm scratching my head while shaking it...

Also, let me here and now go on record as being firmly in disagreement with Dragonfly's attempted critique of Peikoff's essay. I appreciate Bill Dwyer's efforts, and I regret that I don't have the time and energy to address Dragonfly's posts myself. But I think he's as wrong about this as he is about Objectivism's axioms and their relevance to scientific theory. Dan Edge convinced me to speak up, which I should have done before this, when he wrote:

if you value OL as you say, then it's in your interest to at least state your disagreement on OL...Cal [Dragonfly] has written a technical, relatively well-organized attack on Objectivist epistemology. I don't see how you can let that sort of thing stand without so much as an "i disagree."

Amen. I don't know if or when I'm going to be able to engage Dragonfly adequately on these issues, but I'm no longer going to allow my silence to imply agreement with or indifference to critiques of Objectivism that I think are wrong-headed.

REB

[Michael Stuart Kelly]

Roger,

Working over these ideas is what we are all about. As with Dragonfly, you are one of my treasured friends whose mind I admire.

I would like to mention a few items.

On skimming over Dragonfly's essay again, I see that he refers to "Mike." That "Mike" is not me. It must be another member of the NB forum, so this could be a source of confusion.

Dan Edge is a good kid, like I said. So I am making an exception to a general rule I have about not doing a back-and-forth thing with other forums, as this always leads to bickering. In this case, there is a promise of intelligent discussion.

However, it also seems that there is an attempt to control what goes on at OL from over there. People are free or not to post whatever they like over there, but not one of them will dictate policy over here.

Dragonfly's value is that he makes good arguments and he is my friend. OL is not in the business of trouncing strawmen or preaching to the Objectivist choir - or gratuitously insulting others. Frankly, we need intelligent challenges like Dragonfly poses. Of what use is a weak argument? That's for preachers, not intellectuals. We discuss ideas here and each person is free to accept or reject them. OL posters are all highly intelligent people of good faith. You are. I am. Dragonfly is.

I am glad you intend to engage him on this. I also intend to one day, however, this subject is not on my priority list. I'm too busy writing my next "sob story."

Still, in Dragonfly's defense, there is a viewpoint based on making an intellectual theoretical opening for artificial intelligence that I am beginning to discern in his arguments. The reason I am beginning to discern this is because I am leaving my mind open for now - without abandoning things like core Objectivist concepts - until I understand what he is talking about.

The discussion of this is presently going on in the Science section. I know that his epistemological viewpoint is shared by many, many scientists - the ones who are actually building the marvels of our current technological wonders, especially through computing.

Just as in Rand's fiction, here we sit, enjoying the fruits of the labors of such scientists and spitting in their faces. We damn the ideas in their heads without even giving them a decent hearing. Why? Because we are the Church of Rand. Ha!

Scientists tend to look at Objectivist people - these Internet forums and some of the different Objectivist preachers who are trying to establish a religion out of a philosophy - then they merely blink their eyes and go back to their labs.

I strongly believe that it is in our benefit to analyze the issue of epistemology from their angle thoroughly. If Objectivist ideas are strong, they will stand up - and I believe the core ones will. If they are weak, they will need to be supplemented - and I believe that there is some serious work that still needs to be done.

Facts are facts, regardless who says them. But there is one thing scientists have going for them. They have practical results - and we are communicating on one of them right now - the Internet. They make a theory, test it, then turn it over to industry to build with it. What do we have on the Objectivist side? What practical results can we show? Who are the loudest among us?

That bears repeating. Who are the loudest among us?

Just a bunch of mediocre crummy little people - mostly underachievers, low-talent has-beens and BS artists - who like to bicker. That's who. I'm not even going to play that game. We have to build. One of ideas behind my efforts is to foster achievement, not bickering.

(I refere to the loudmouths, not civil intelligent Objectivists.)

How about at least a best-seller? Just one? Some kind of achievement that we can show scientists if we want to tell them that they are full of crap and that Peikoff is right? Hell, even the organization Peikoff founded is a charity firm living off donations. It's not even a profit-making business based on the capitalistic values it preaches. No wonder scientists don't pay attention.

Regarding fundamental axioms, I have discerned from Dragonfly's arguments (with me at least) that he does not deny their truth. He merely places low intellectual value on them and is a bit heavy-handed in expressing this. I admit that all this is slow going because my priorities are other.

(As an aside, for example, I need to do my thing on your microcosm article and I have been delaying it because that discussion must be done correctly, thus it requires a high amount of study. I simply have not finished my preparation. Also - I might as well say it - I have a nice "sob story" on your CD coming. It's already outlined.)

I sincerely believe that Dragonfly's heavy-handed expression during discussion is a result of being cussed out and mocked at other places by nasty dogmatic Objectivists who use axioms to turn their minds off and preach instead of listening and trying to understand.

You are my friend, Roger, and I have stated that you have the free run of this site. We disagree on a few fundamental things, but that does not impede the value I hold for you, nor will it ever interfere with my stated position. If that young man wishes to debate this issue with civility, nothing stops him from debating it here. To be clear, this is not an invitation. It is an observation. (But I also have no restriction against him or anyone who comes in peace and goodwill. I do have a restriction against people of ill will.)

I am now closing down my own inter-forum comments on this issue and shall attend to my other projects. But first, let me thank you for such kind words over there. I have been working hard for us intelligent folks to have a decent place to hang out and it is good to see it recognized spontaneously.

The only thing I ask is that you do not allow this young man or anybody to dictate policy on OL indirectly by telling you what and how to post here. (I know that this is not the case right now, but the seeds are there, so it needs saying.) We have something very special and we are all special here. There are people who do not have the ability to build something like what we have, so they wish to destroy it. Such people are free to make their own forums to their own taste or stay on the bicker forums.

Michael