The Analytic-Synthetic Dichotomy

[Michael Stuart Kelly]

Brant,

There is no pouring. Here is an analogy. Just because you went somewhere really far away and stayed a long time, that does not mean you did not take the first step. You had to take the first step to get there.

Why deny that? As a matter of fact, what is gained (and who gains) by denying that?

The same goes for math.

Even more. The argument seems to be that man can take a structure and make it so complex that it becomes real even though it is not real at the same time. Does that make any sense to you?

Michael

[Brant Gaede]

Some mathematical structures are well matched to physical reality. Some are very abstract and not matched at all.

Bob,

Where have I said differently?

Still, at the base, there are numbers. If you have numbers, you have mental units that were developed by counting things.

There are conceptual structures that are not matched to reality at all. Look at the unicorn example that is always provided. Just because we can mentally create make-believe, does that mean that concepts per se are divorced from reality because they can be employed in make-believe? Of course not.

But that seems to be the argument for math I keep reading. Why can't there be make-believe in mathematics? What do you call a logical projection divorced from reality?

I call it make-believe.

Michael

Make believe is not divorced from reality. That's a contradiction. Nothing is divorced or devorceable from reality.

--Brant

Edited June 16, 2007 by Brant Gaede

[Michael Stuart Kelly]

Brant,

I meant divorced from external reality as opposed to exist as a pure mental projection. Unicorns don't exist as entities, only as ideas.

Michael

[Brant Gaede]

Brant,

I meant divorced from external reality as opposed to exist as a pure mental projection. Unicorns don't exist as entities, only as ideas.

Michael

I raise unicorns.

--Brant

[Wolf DeVoon]

Earlier today the subject of unicorns came up with my 5-year-old. She's riding a horse tomorrow morning, and having thought about it further, decided she wanted to ride a unicorn instead. I explained make-believe as cartoons on television, and that unicorns didn't exist outside (existential jungle, roads).

Anyhow, Brant's unicorn ranch puts me in mind of Tiny Tim:

All I want is 50 million dollars

and sealskins to protect me from the cold

With Rockefeller waiting on my table

and a backyard with a mountainful of gold

If I only owned the Western Union cable

and if Tuesday Weld would only be my wife

If I could only stay 16 forever

Then I know that I'd be satisfied with life

[Daniel Barnes]

Baal

>Some mathematical structures are well matched to physical reality. Some are very abstract and not matched at all.

And some of these initially "unmatched" abstractions turn out to have important physical applications that are discovered centuries later, leading to - quite understandable - Platonic suspicions.

[Michael Stuart Kelly]

And some of these initially "unmatched" abstractions turn out to have important physical applications that are discovered centuries later, leading to - quite understandable - Platonic suspicions.

Daniel,

That couldn't possibly be because math is initially grounded in reality, could it?

Michael

[william.scherk]

Looks like a proponent of CR needs warm bodies around him.

I am having another attack of pig-ignorance. What is referred to by C R, please?

[Michael Stuart Kelly]

William,

Critical Rationalism. Popper's thang...

Michael

[william.scherk]

William,

Critical Rationalism. Popper's thang...

Michael

Thanks, Michael. I feel so stoopid.

I wonder if you have followed up on your discovery of Susan Haack. If so, you may have come across her writings on Popper.

(If I had to choose between Popper, Haack and Rand, I would choose Haack. Not because she is a better philosopher that Rand, or has deeper and more effulgent insights than does Popper, but because she is alive and writing and actually responds to fan mail from the pig-ignorant like me.

I will pass by this thread to the gorgeous and wise Ophelia Benson, another of my faves. I wonder if she will come down on the side of Michael Stuart Kelly, or on that of Daniel Barnes.)

In my blessed ignorance, I thought that all Objectivists were Popperians in Rand's clothing. Thanks for enlightening me.

Here is a couple snippets from Haack's extremely interesting "Trial and Error: The Supreme Court's Philosophy of Science." Oh how I would love to have her on this list for an afternoon of rigour. Unfortunately, she plays in a different leaque and we can only sit in the stands and cheer her on.

Popper also describes his philosophy of science as "Deductivist," by contrast with

"Inductivism," whether in the strong, Baconian form that posits an inductive logic for arriving at

hypotheses or in the weaker, Logical Positivist form that posits an inductive logic of confirmation.

According to Popper, Hume showed long ago that induction is unjustifiable. But science doesn't need

induction; the method of conjecture and refutation requires only deductive logic -- specifically, modus

tollens, the rule invoked when an observational result predicted by a theory fails.

[ . . . ]

The pejorative tone of the phrase "pseudo-science,"

which presumably refers to activities which purport to be science but aren't really, derives in part from

its imputation of false pretenses, generally, and in part from the favorable connotations of "scientific,"

specifically. But rather than sneering unhelpfully that this or that work is "pseudo-scientific," it is always

better to get down to those "brass tacks" Bridgman talks about, and specify what, exactly, is wrong with

it: that it is not honestly or seriously conducted; that it rests on flimsy or vague assumptions --

assumptions for which there is no good evidence, or assumptions which aren't even susceptible to

evidential check; that it seeks to impress with decorative or distracting mathematical symbolism or

elaborate-looking apparatus; that it fails to take essential precautions against experimental error; or

whatever.

PS -- this is my favourite thread by far of all the Randt-ish threads I have read in the past month. I think I have learned more about Objectivist thought here than in all my other reading. Bear in mind, though, that a close second favourite is the demented screed now unfolding at our Sisters-in-Rand site, where He Who Knows Opera is currently posturing and preening.

[edited for sloppy spelling, syntax and general crimes against humanity]

Edited June 17, 2007 by william.scherk

[Daniel Barnes]

Mike:

>That couldn't possibly be because math is initially grounded in reality, could it?

Mike, what problems do you think this vague comment solves, and how does it solve them?

[Daniel Barnes]

William cited Haack:

>According to Popper, Hume showed long ago that induction is unjustifiable.

The reply to Haack is that this is of no nevermind because, fortunately, induction is 'grounded in reality.'

>But science doesn't need induction; the method of conjecture and refutation requires only deductive logic -- specifically, modus tollens, the rule invoked when an observational result predicted by a theory fails.

This is ok too, because apparently deductive logic is also 'grounded in reality.'

>The pejorative tone of the phrase "pseudo-science," which presumably refers to activities which purport to be science but aren't really...

Someone should tell Haack that the way to tell pseudo-science from true science is, obviously, that the latter is 'grounded in reality.'

And so on and so forth.

Edited June 17, 2007 by Daniel Barnes

[BaalChatzaf]

William cited Haack:

>According to Popper, Hume showed long ago that induction is unjustifiable.

The reply to Haack is that this is of no nevermind because, fortunately, induction is 'grounded in reality.'

>But science doesn't need induction; the method of conjecture and refutation requires only deductive logic -- specifically, modus tollens, the rule invoked when an observational result predicted by a theory fails.

This is ok too, because apparently deductive logic is also 'grounded in reality.'

>The pejorative tone of the phrase "pseudo-science," which presumably refers to activities which purport to be science but aren't really...

Someone should tell Haack that the way to tell pseudo-science from true science is, obviously, that the latter is 'grounded in reality.'

And so on and so forth.

Using Induction one can start from true premises (the partial observations) and end up with false conclusions (not all crows are black, it turns out). And THAT is why Induction is not a valid mode of reasoning. It is a useful mode and also a necessary mode. All of our "Learning the Hard Way" is an exercise in Induction. Without Induction we would perish. But that still does not make it valid.

Deductive logic deals with -valid- arguments. Logic, per se, does not guarantee soundness of the argument, i.e. logic cannot guarantee the truth of the premises especially when the premises are synthetic statements, rather than a priori true statements. The Objectivist definition of logic is just plain wrong.

Pseudo Science is an exercise in the untestable. It is the lack of falsifiability that makes a discipline unscientific or pseudo scientific.

Ba'al Chatzaf

[Wolf DeVoon]

The Objectivist definition of logic is just plain wrong.

I'm baffled. Where is the O'ist definition of logic?

[Guyau]

Wolf,

Rand's definition of logic is given on page 1016 of Atlas:

"Logic is the art of non-contradictory identification."

She remarks also on that page:

"Logic rests on the axiom that existence exists."

It follows, I notice, that it is not logically possible that nothing exists. It is not logically possible that existence might not have been. One logician, David Bostock, remarks to the contrary in his Intermediate Logic (Oxford 1997). He maintains that "it is a possibility that nothing should have existed at all" (page 354). The two opposing views, Rand's and Bostock's, commend different ways of developing modal logic. I won't pursue that just now.

Let me indicate, instead, a little more of Rand's conception of logic. Her definition of logic as the art of non-contradictory identification is made in the context of having cast consciousness as identification. In this conception, logic is embedded in wider processes of identification, all of them relying on Rand's thesis that no existents are without identity.

[Michael Stuart Kelly]

Mike:

>That couldn't possibly be because math is initially grounded in reality, could it?

Mike, what problems do you think this vague comment solves, and how does it solve them?

Daniel,

The same problems you did here below and in the same manner. Meaning not much for either.

And some of these initially "unmatched" abstractions turn out to have important physical applications that are discovered centuries later, leading to - quite understandable - Platonic suspicions.

The Objectivist definition of logic is just plain wrong.

Bob,

So logic is the art of contradictory identification? Or is it the whim of non-contradictory identification? Or is it the art of non-contradictory non-identification? Or...

Hmmmmmmm...

Michael

[BaalChatzaf]

Mike:

>That couldn't possibly be because math is initially grounded in reality, could it?

Mike, what problems do you think this vague comment solves, and how does it solve them?

Daniel,

The same problems you did here below and in the same manner. Meaning not much for either.

And some of these initially "unmatched" abstractions turn out to have important physical applications that are discovered centuries later, leading to - quite understandable - Platonic suspicions.

The Objectivist definition of logic is just plain wrong.

Bob,

So logic is the art of contradictory identification? Or is it the whim of non-contradictory identification? Or is it the art of non-contradictory non-identification? Or...

Hmmmmmmm...

Michael

None of the above. People who are paid to do Logic and who publish in refereed mathematics journals define Logic as the science or discipline of valid inference. Logic is about propositions and how some are inferred from others.

Logic does not tell you how to identify which premises are true. That requires other arts and sciences.

Ba'al Chatzaf

[william.scherk]

William,

Critical Rationalism. Popper's thang...

One further question, if you will: what is your position on Critical Rationalism, 'standing on one foot'? Is Critical Rationalism useful or not, as a practical guide to knowledge?

I note that in your continuing discussion with Daniel, a problem of linguistic charity rears its head again. In an earlier exchange you suggested, with humour, that your and Daniel's mutual goal was 'Free Entertainment," whereas Daniel answered, "We are both trying to correct some underlying historical mistakes." Would you please leave off the smileys and give us a sincere answer?

**********************

I am confused by what I sense is a contempt for Daniel and his positions. I get the impression that you are annoyed with Daniel, and because you are annoyed, you don't have to play fair. I know this is not the impression you wish to leave, so I am puzzled . . .

One notion I would ask you to consider again, Michael, is that of mutual goals. Although you acknowledged a certain 'technical correctness'** in my critique of your thoughts on letters/words, I am not sure you grant my point. If you don't actually grant the point, and do not absorb its usefulness, I don't see any productive point to this thread.

Free entertainment? Sure. Good faith discussion aimed at mutual comprehension? There I am not sure at all.

*******************************

Forgive me if I read all of this completely wrongly. Lately I am struggling with integrity in the workplace. I struggle to find solutions to 'people problems.'

In a nutshell, some folks agree to be bound by professional behaviour. The same folks fail at times, but will not admit the failure. Ensuing disdain, contempt, belligerent outbursts all seem to be designed to put the offender 'one up' on the target. But, of course, if the goal is to do the job most efficiently and with least heartache, being one up on the target simply poisons the work environment and leads to terminations, tears, rage-filled arguments, etcetera.

My challenge is to get everyone to the mutual goal. I don't yet know how to manage a couple of incorrigibles. Because all error emanates from the 'other,' their sole goal appears to be altering the other person's behaviour.

This is all well and good, but to alter the unwanted behaviour one must use good psychological tools.

Lately I am struck over and over again by a scene from the movie "The Wizard of Oz." This is when one of the Wicked Witches is splashed with water by Dorothy. Of course, being wicked, the witch dissolves into the floor and dies.

Some people seem to hold that admitting error will lead them to melt on the spot . . . and so, of course they resist. It is getting to the point where I consider the incorrigibles as wicked, and could not give a shit if they did melt and die.

_______________________________

** one can read your note on 'technical correctness' as a form of, 'You may be correct, but I am still right.' Another reading is, 'I don't care about being correct, I care about ending up on top in the wrassling.'

I know these readings are quite likely inaccurate/wrong, but the impression remains . . .

[Michael Stuart Kelly]

Bob,

I just did a small run-around on Google and wherever I say "valid" and "inference" (with respect to logic, especially deductive logic), I saw the word "premise" as one of the, er... premises of both.

So you are saying that logic uses premises, but is not a process that identifies them?

Hmmmmm...

It's not getting any better for me...

Michael

[Michael Stuart Kelly]

I am confused by what I sense is a contempt for Daniel and his positions. I get the impression that you are annoyed with Daniel, and because you are annoyed, you don't have to play fair.

William,

Don't mistake our banter for contempt. I have a lot of respect for Daniel and it is mutual. At times we have some very nice off-line communications. I think you have been hanging around some pretty nasty environments where people don't have any fun when they disagree, thus you get the impression that all Objectivist-oriented discussions are like that.

Instead of harsh moral condemnation, or contemptuous dismissal, or baring one's chest and cutting loose with a Tarzan holler, consider what Daniel and I do as friendly pokes in the ribs. I can't speak for him, but I am almost sure he will agree.

Actually, I post on Daniel's blog at times. I have not done nearly as much over there as I would like, but I will get around to doing more.

One further question, if you will: what is your position on Critical Rationalism, 'standing on one foot'? Is Critical Rationalism useful or not, as a practical guide to knowledge?

I believe that part of Critical Rationalism is extremely useful and part is baloney. Of course I am only speaking about what I know of it. For instance, in what Objectivism would be called "testing context or hierarchy" in knowledge, or something like that, the theory of concentrating on falsifiability is brilliant and an excellent rule for experiments. It is a wonderful way of checking premises.

The idea I read by Popper of never defining terms because it leads to infinite regress is pure baloney. I consider it hype to be shocking. If you read between the lines, you see that definitions are implicit in everything Popper does (that I have read or read about so far), including that particular passage.

There are other suspicions I have, but I prefer to read more before opining.

I wrote about the Popper essay I read on two types of definition. I think you must have read it. I consider Popper and Rand to be mostly talking about the same things, but using different words. I also believe their followers make jabs at each other because they look at the words and not the meanings—and both sides swallow the hype from their respective masters.

Michael

[BaalChatzaf]

Bob,

I just did a small run-around on Google and wherever I say "valid" and "inference" (with respect to logic, especially deductive logic), I saw the word "premise" as one of the, er... premises of both.

So you are saying that logic uses premises, but is not a process that identifies them?

Hmmmmm...

It's not getting any better for me...

Michael

I said it is not a process for determining the truth of premises. A valid argument with untrue premises is -unsound- (technical term). That means the conclusion cannot be detached from the inference. It is all based on modus ponens. If p implies q and p is true then one can infer that q is true. What if p is false? Then it is the case the p implies q (a false premise implies any conclusion). But you can't pull out q (the conclusion) because modus ponens requires two things: the truth of the premise and the truth of the implication.

It gets somewhat more complicated than this when quantification and modalities (other than true/false) enter into the logic. Google <modal logic> and Google <first order logic>.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

I will read this stuff, but I have yet to see anything that makes the Objectivist definition wrong.

Art = Skilled human activity

Non-contradictory = Evaluation of premises

Identification = Conclusion

Non-contradictory identification = Process (like syllogism, etc.)

I can agree that the Objectivist definition is not very technical. In terms of falsehood, I need a clearer explanation to understand what you are talking about.

Michael

[Wolf DeVoon]

Wolf,

Rand's definition of logic is given on page 1016 of Atlas:

"Logic is the art of non-contradictory identification."

She remarks also on that page:

"Logic rests on the axiom that existence exists."

It follows, I notice, that it is not logically possible that nothing exists. It is not logically possible that existence might not have been. One logician, David Bostock, remarks to the contrary in his Intermediate Logic (Oxford 1997). He maintains that "it is a possibility that nothing should have existed at all" (page 354). The two opposing views, Rand's and Bostock's, commend different ways of developing modal logic. I won't pursue that just now.

Let me indicate, instead, a little more of Rand's conception of logic. Her definition of logic as the art of non-contradictory identification is made in the context of having cast consciousness as identification. In this conception, logic is embedded in wider processes of identification, all of them relying on Rand's thesis that no existents are without identity.

Thanks, Stephen. Your scholarship is always on the money. What I had in mind was Rand's reference to the syllogism and the three 'book' titles of AS that refer to excluded middle proof. Existence exists is derived from it, IMO. I agree that Rand proposed noncontradiction as a system or method for building knowledge by observation, calibrated measurements, and precise definitions. But I think Aristotle did the heavy lifting.

W.

[Wolf DeVoon]

Google <modal logic> and Google <first order logic>.

Hmm. I would say Google <syllogism 14 valid>

Aquinas' Commentaries are the clearest presentation IMO.

It's beginning to bug me that critics are trotting out set theory to disprove or obliterate predicate logic. If you wander down the modal logic path, you'll end up with Hosper's doctrine of 'necessary and sufficient,' which is played dues wild. Conceptual knowledge is Aristotelean predicate - sometimes called Classical - logic. Add ITOE for the connection between sense data and rigorous, noncontradictory definitions. Presto! A complete system of knowledge based on the syllogism.

It is implicit in every post. No one chats in set theory or modal logic.

W.

Edited June 17, 2007 by Wolf DeVoon

[BaalChatzaf]

Google <modal logic> and Google <first order logic>.

Hmm. I would say Google <syllogism 14 valid>

Aquinas' Commentaries are the clearest presentation IMO.

It's beginning to bug me that critics are trotting out set theory to disprove or obliterate predicate logic. If you wander down the modal logic path, you'll end up with Hosper's doctrine of 'necessary and sufficient,' which is played dues wild. Conceptual knowledge is Aristotelean predicate - sometimes called Classical - logic. Add ITOE for the connection between sense data and rigorous, noncontradictory definitions. Presto! A complete system of knowledge based on the syllogism.

It is implicit in every post. No one chats in set theory or modal logic.

W.

That is because doing so requires technical machinery. You don't see people chatting in various symmetry groups or in differentiable manifolds either. There is simple no reasonable way of discussing these topics using ordinary language. A technical vocabulary must be used along with a grasp of mathematical methodology. Most people are ill equipped to discuss such things.

Ba'al Chatzaf