The Analytic-Synthetic Dichotomy

[Daniel Barnes]

Ba'al:

>Untypical of what or who?

People who I've debated with on this topic often don't have a grasp of the basics, such as the difference between existential and universal statements, or the logical assymetry between falsification or confirmation, etc.

[Wolf DeVoon]

To learn anything about morality, we have to accept the idea that reality is real: that acorns grow into oak trees, and never become halibuts or eagles. Growth does not occur backwards, with mature trees shrinking into seeds and leaping from the ground back into parental buds. Photosynthesis does not emit light back to the Sun, and time cannot be reversed, despite a half-century of science fiction. Your moral life is real: it grows from innocent childhood to maturity. (from The 51% Solution)

Want exemption from morality? Best way to do that is mock man's ability to ascertain the facts, ridicule concept formation, deny the validity of abstraction, and claim that logic consists of truth tables.

"Predicate" is the first principle of language and classical logic. It is also the central bone of contention in Western philosophy, theology, and politics. Say, for instance, that you are at a birthday party with a number of others. You decide to count the number attending the party: 1, 2, 3, 4, 5, 6, 7, 8. But eight units of what? — of men and women, boys and girls. You could have also said that there were eight "people" at the party, but children aren't quite the same as adults, and therefore we habitually count them as members of a different class. Likewise, it is customary and useful to distinguish between male people and female people, referring to them respectively as "men" and "women" on the doors of segregated rest rooms. Not so many years ago, it was customary to distinguish between caucasians and negroes, referring to them respectively as Whites and Colored on the doors of segregated rest rooms. Whether we prefer to call someone a "woman", a "female", a "negro", an "American", or a "person" is not the point. Rather, the point is that predicates are inescapable, when you count persons, things, or values. (Id.)

All men are mortal. True or false?

W.

[tjohnson]

All men are mortal. True or false?

W.

It depends.

[Michael Stuart Kelly]

Bob,

Apparently, your logical system has to be absolute to work. You don't see a contradiction there in your statements about the absoluteness of negatives? That to propose a system is to propose a positive?

Also, you rely a great deal on direct observation. Objectivist epistemology does too.

Michael

[Brant Gaede]

All men are mortal. True or false?

W.

It depends.

I have to agree. All men are mortal if all men are mortal--but no one knows "all" men. As for myself, I think but don't know I am mortal. I only know this to the extent of the extant evidence. On that basis I am mortal and when I die that will be that.

--Brant

[Daniel Barnes]

Wolf:

>All men are mortal. True or false?

Well, it seems to be the case so far, but is by no means necessarily true. For example, not all living creatures have to die even now, so it's perfectly possible that at some point man might not have to either. Further, human life expectancy has been increasing for some time, and perhaps that trend will continue until mortality is no longer an issue. Further, the respected physicist Frank Tipler has put forward an argument from straight physics that asserts human immortality is indeed a possibility. So the answer to your question is: possibly false.

[BaalChatzaf]

[

All men are mortal. True or false?

W.

To determine that is true I would have to examine every man who ever was, now is or ever will be. Then in -each- case I would have to wait an indeterminate interval of time to see if they die. Therefore I cannot determine whether that is true -empirically- in each and every case. So the answer is: I don't know. Is it possible for a (human) man to exist as long as the physical cosmos? There is no logical reason why it can't be so, so I cannot dismiss the proposition a priori. On the other hand there is no way to determine this -universally quantified- assertion empirically. So the answer is: undetermined and not determinable by any finite empirical means.

Now if you put the -existentially quantified- proposition: There is exist a man who is not mortal, I would give you the same answer. One would have to look at the population of all men who ever were, currently are and who will be. This is equally impossible to determine by empirical means. So the answer is undetermined and not able to be determined by finite empirical means. Again there is no logical a priori reason to deny the possibility but there is no evidence to support it either.

If you ask the question: do there exist or have there existed mortal men (which is existentially quantified), the answer is yes indeed. Visit any graveyard and dig up the bones. There is you evidence.

If you ask the question: Is a particular man mortal, say your father. If you is already dead the answer is yes. If he is not yet dead wait 100 years. With high probability you will have an affirmative answer. I can answer the question in the case of my own father. He was mortal and he died in 1977. I saw the body.

Ba'al Chatzaf.

[BaalChatzaf]

Wolf:

>All men are mortal. True or false?

Well, it seems to be the case so far, but is by no means necessarily true. For example, not all living creatures have to die even now, so it's perfectly possible that at some point man might not have to either. Further, human life expectancy has been increasing for some time, and perhaps that trend will continue until mortality is no longer an issue. Further, the respected physicist Frank Tipler has put forward an argument from straight physics that asserts human immortality is indeed a possibility. So the answer to your question is: possibly false.

If the second law of thermodynamics holds eventually sufficient free energy to keep such a thing alive will dissipate. Eventually the cosmos will become cold and dark, and life could not be maintained. That takes a certain amount of free energy (energy at low entropy and high enough temperature). So based on the truth of the second law of thermodynamics (which is NOT a priori true, but assumed as a hypothesis) it would not be possible for any living man to be immortal. The question is: is the second law of thermodynamics true? Answer: so far it is supported by evidence (lots of it!) and has never been empirically falsified. So there is no pressing reason not to suppose it is true. But it cannot be logically derived a priori from the principle of non-contradiction. It is an a posteriori synthetic proposition which (by evidence) appears to be true. So far so good.

The very same thing is the case with all our favorite conservation laws too. Non of them are a priori but all are supported by vast amounts of empirical evidence and they have never been empirically falsified nor do they lead to a logical contradiction. So it would be unreasonable to deny the truth of the conservation laws. In addition to which, if the conservation laws -were falsified- we would have to rebuild physics from the ground up.

As a betting man, I would stake my life on the truth of the laws of thermodynamics and the truth of the conservations principles. I already do. I use dangerous machinery and I sometimes fly in aircraft.

Ba'al Chatzaf

[tjohnson]

All men are mortal. True or false?

W.

Why does everything have to be 2-valued, yes or no, true or false, etc. ? Life is not like that and it seems to me that a life orientation devoted to 'reality', like objectivism, should have realized that by now?

[BaalChatzaf]

All men are mortal. True or false?

W.

Why does everything have to be 2-valued, yes or no, true or false, etc. ? Life is not like that and it seems to me that a life orientation devoted to 'reality', like objectivism, should have realized that by now?

Define living forever to mean being coexistent with the physical cosmos. Now either a human can live forever or he can't. I.E. he will last as long as the rest of the cosmos or he will die sooner (that is much likelier). There ain't any in-between. Some propositions are true or false. Some have some kind of numerical degree. For example; it is hot in here. Well, what is hot? This is not well defined. One can say the ambient temperature in this room (specify the room) is between 75 and 80 degrees F.. This is either true or it isn't. But hot unqualified is a fuzzy term. One must attach some measure to make it definite and meaningful.

Ba'al Chazaf

[tjohnson]

Some propositions are true or false.

Propositions may be true on one level but false on another. Someone can always argue with even the most self-evident statements. 'Truth' depends on agreement so you and I could agree something is true while others may think it's false. You can argue till you are blue in the face that there is no god yet billions of people on earth believe this is so. In science there is a well developed system to evaluate 'trueness' and 'falseness' but we are free to accept this system or reject it (to the detriment of all).

[Dragonfly]

Of course a non-analytic propostion would not yield a contradiction upon denial (though I deny that there are any such propositions), but how does that prove that non-defintional truths are non-analytic, rather than being a kind of analytic truths??

Simple: a non-definitional truth is by definition a synthetic truth.

You seem to have very circular reasoning--that is, you are assuming what you are trying to prove: I say you haven't proved that non-defintional are synthetic (i.e. not analytic), and your reply starts off by assuming that definitional truth are not analytic, the very thing I asked you to prove.

There is nothing to prove, it is a matter of definition (I suppose you meant "non-definitional truth").

Also, 'analytic' does not mean certain: if its denial is contradictory then it is analytic, whether we know it or not. (Remember, logical properties, such as being analytic, being self-contradictory and entailment, apply to propositons or relations between them, and they are independent of knowledge: for example, if p logicall entails q, that is true regardless of whether anyone knows it or not.)

The point is that anyone can derive the truth of an analytic statement from the statement and the given definitions alone and be certain about the outcome, as long as that person doesn't make logical errors. No empirical validation is needed. In that sense an analytical statement is certain, contrary to synthetic statements.

More importantly, that sentence was only an illustration. His general claims are:

(1) If a statement is true, then it is analytically true

A statement can be true while we don't know that it is true. In that case we can't logically derive the truth of that statement, and therefore it is not an analytic statement.

Again, a statement can be analytic even if we don't know it. For example, the propositions of trigonometry, being mathematical, are analytic and always were , even before anybody had deduced any of them from the properties of a triangle.

The propositions of trigonometry can be logically derived from the definitions. It is not relevant whether someone has or has not derived those propositions already. On the other hand a universally quantified statement (thanks to Bob for the terminology; this is what I meant, but I didn't know the correct term - I'll use this definition implicitly when I'm talking about synthetic statements) about the real world can never be logically derived from the definitions, as this would imply omniscience. That is the essential difference.

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

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

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

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

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

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

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

1. See above.

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

3. This is not coherent. Statements may be non-falsifiable without being true or certain. But only definitional truths are certain. See further above.

4. This formulation is vague. The definitional truth may refer to something that is known empirically, but its truth cannot be derived empirically, as it cannot be falsified by empirical observation.

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

For example, we can analyze the concept of triangles to come up with the basic truths of trigonometry, we can analyze the concept of bachelors to come up with statements such as ‘All bachelors are unmarried’, and we can analyze the concept of ice to come up with statements such as ‘All ice is solid’. Regarding the latter, you may not have certainty

Oh yes, you have. If you define ice as the solid form of water, you have certainty that ice is solid. Whether there exists a solid form of water is an entirely different question. That belongs to the realm of synthetic knowledge. This is an illustration of the fact that an analytic truth in itself doesn't tell us anything about the world. We may apply that analytic truth to see whether it corresponds to empirical evidence, and we might for example discover that it doesn't, but that doesn't invalidate its truth, only its applicability.

, or any degree of knowledge, because you have to discover the basic truths: you have discover that water is H20, and that gold has atomic number 7,

I have serious doubts about that...

Certainly not. Those truths follow logically from the axioms and definitions in mathematics, they cannot be falsified by empirical evidence.

I didn't say that they could be falsified by empirical evidence: I said that they were empirical--i.e., knowable from experience, without need for supplemental from any additional database or alleged database (such as innate ideas). Remember, I don't concede that all empirical statements must falsified; that remains on the list of claims for you to prove (see above).

What does "knowable from experience" mean? Do you think you can prove trigonometrical propositions by measuring enough triangles? Further I never said that empirical statements must be falsified, only that they must in principle be falsifiable, if they should have any meaning.

Peikoff never claimed to be authority (except on Ayn Rand). I would like to know where you and other people, such as Daniel, get the idea that is claiming to be.

Also, your claim that he is talking nonsense about science depends on your claim that he is wrong about the various dichotomies he has rejected, and you haven't yet done this (see above).

No, it doesn't at all depend on his being wrong on various dichotomies. See for example here and here. He even once said that he knew for philosophical reasons that the Big Bang theory had to be wrong, and that he was studying physics to be able to prove it. I kid you not!

[Wolf DeVoon]

All men are mortal. True or false?

W.

Why does everything have to be 2-valued, yes or no, true or false, etc. ? Life is not like that and it seems to me that a life orientation devoted to 'reality', like objectivism, should have realized that by now?

For the record, you are mortal, which means you can be killed by murder, misadventure, natural disaster, traffic fatality, combat, collateral damage, inattention while crossing a street, etc. All men are mortal. It has nothing to do with gambling or wishful thinking or prudent behavior. You will die someday.

W.

[tjohnson]

For the record, you are mortal, which means you can be killed by murder, misadventure, natural disaster, traffic fatality, combat, collateral damage, inattention while crossing a street, etc. All men are mortal. It has nothing to do with gambling or wishful thinking or prudent behavior. You will die someday.

W.

I don't think so, I don't believe in death. I believe I will move to a different form of existence. Can you prove I'm wrong? I can argue with everything you say and so you're statements are only 'true' to other believers of your statements. I believe there IS something going on independent of us but any statements about it are subject to assumptions and agreement by others. If there was only one person on earth he could state 'truths' all day long and they would definitely be true, since no one could argue with him. Of course, why would a single organism evolve ways to communicate with others?

No, I'm sorry but if you open your mouth and say something then it is your opinion, period. It may be a very well educated opinion, make all the sense in the world, but it is still opinion. Even the most exact sciences are subject to some opinion.

[BaalChatzaf]

I don't think so, I don't believe in death. I believe I will move to a different form of existence. Can you prove I'm wrong?

Since you make the extraordinary claim the burden of proof rests with you. Extraordinary claims require extraordinary evidence. Not only do you not have extraordinary evidence to back your claim, you have no evidence at all. Your belief is something you plucked out of the air with nothing solid to back it.

Shame on you!

Bob Kolker

[Daniel Barnes]

Wolf:

>For the record, you are mortal... All men are mortal.

It doesn't look like Wolf is too clear on the difference between existential vs universal statements yet. This seems to be a point of continuing confusion among the Objectivist camp, so we might as well clear it up.

Here is an existential statement:

"I see a black crow."

Here is a universal statement:

"All crows are black."

Do you see the difference?

Now there is no logically valid way to derive the latter from the former, no matter how many of the former we collect.

Further, there is no logically valid way to get to "All crows are probably black" either, with "probably" referring to any actual probability.

If you can show how there is an inductive way to get from such existential statements (also called "observation statements") to universal statements (also know as "universal laws" or "universal truths") via a valid inference, please do. You will be the most famous philosopher of the past few centuries, and I can boast that I once was on the same internet forum as you.

This is the problem of induction.

Do you now see why saying things like "I see a black crow" or "You are mortal" does not even touch on the problem, let alone refute it?

Edited June 24, 2007 by Daniel Barnes

[Wolf DeVoon]

Aristoteleans are well acquainted with the meaning of universal and particular. I think our conversation on this topic is finished.

W.

[Daniel Barnes]

Wolf:

>Aristoteleans are well acquainted with the meaning of universal and particular.

Not all of them, it seems.

>I think our conversation on this topic is finished.

OK.

[Daniel Barnes]

Ba'al:

>Define living forever to mean being coexistent with the physical cosmos.

Ba'al, just FYI, if you haven't already encountered it you might be interested in Frank Tipler's controversial "Omega Point" theory here:

http://www.math.tulane.edu/~tipler/physicsofimmortality.htm

Tipler is not religious BTW.

[tjohnson]

Since you make the extraordinary claim the burden of proof rests with you. Extraordinary claims require extraordinary evidence. Not only do you not have extraordinary evidence to back your claim, you have no evidence at all. Your belief is something you plucked out of the air with nothing solid to back it.

Shame on you!

Bob Kolker

Who says it's an extraordinary claim? When the majority of people believe in god then it's the atheists who are not ordinary.

[BaalChatzaf]

Since you make the extraordinary claim the burden of proof rests with you. Extraordinary claims require extraordinary evidence. Not only do you not have extraordinary evidence to back your claim, you have no evidence at all. Your belief is something you plucked out of the air with nothing solid to back it.

Shame on you!

Bob Kolker

Who says it's an extraordinary claim? When the majority of people believe in god then it's the atheists who are not ordinary.

Uh uh. It one thing to say you believe there is no death, it is another thing to assert that it is true. To assert the truth of the proposition you must bring empirical evidence or show that it follows logically from an apodictic judgment. You have done neither.

So you believe it is true. There is no accounting for what people believe. Some people believe in the Tooth Fairy or Tinkerbelle. So what?

Ba'al Chatzaf

[tjohnson]

It one thing to say you believe there is no death, it is another thing to assert that it is true.

Ba'al Chatzaf

OK, what do mean by 'true'?

[BaalChatzaf]

It one thing to say you believe there is no death, it is another thing to assert that it is true.

Ba'al Chatzaf

OK, what do mean by 'true'?

In correspondence to the world. For example: the statement "There is a five dollar bill in my wallet" is true if and only if there is a five dollar bill in my wallet. This definition of true is due to Tarski, but is implicit in Aristotle.

In brief, a declarative sentence is true if and only if it asserts a fact.

Ba'al Chatzaf

[tjohnson]

In correspondence to the world. For example: the statement "There is a five dollar bill in my wallet" is true if and only if there is a five dollar bill in my wallet. This definition of true is due to Tarski, but is implicit in Aristotle.

In brief, a declarative sentence is true if and only if it asserts a fact.

Ba'al Chatzaf

And what if I am looking in your wallet and I say it's not a 5 dollar bill, it's counterfeit?

[BaalChatzaf]

In correspondence to the world. For example: the statement "There is a five dollar bill in my wallet" is true if and only if there is a five dollar bill in my wallet. This definition of true is due to Tarski, but is implicit in Aristotle.

In brief, a declarative sentence is true if and only if it asserts a fact.

Ba'al Chatzaf

And what if I am looking in your wallet and I say it's not a 5 dollar bill, it's counterfeit?

A five dollar bill is a bill with a numeral "5" and the word "five" prominently displayed upon it. A countereit fiver is still a fiver. Just don't try to spend it.

The point is true declarative sentences assert facts. False declarative sentences deny facts. Then there are sentences which are meaningful but have somewhat fuzzy terms in them. Such as "It is hot in in this room". "Hot" is a fuzzy term. Contrast this with the assertion "the temperature in this room is between 75 and 80 degrees (F)" based on a standard mercury thermometer which has been calibrated according to Bureau of Standards protocols. The first assertion is fuzzy and its truth or falsity can be debated. The second is not of this nature. It is either true or not true.

The point is there are declarative sentences which are either true or not true. There are also meaningful sentences which are not so definite. Sentences expressing opinions are of this nature. For example: "Liberty is good". True or not true? Taken at face, one could not say. The sentence would have to be contextualized, qualified and hedged up the ying-yang before a definite decision could be made.

Next?

Ba'al Chatzaf