Why logic works

[source]

Although it was not a starting point to the thread of thought which brought me to write this post, I remembered my physics professor once saying that nobody knows why laws of nature can be described using mathematics. According to him, it is just accepted because it seems to be so.

My original confusion (which brought me here) was about logic. Why does logic work? Ultimately, why do axioms work? Why do things have identity; why are they what they are? I assume it is more than simply a matter of us putting it neatly into words in this way, but I'm not quite sure what.

Did we arrive at the idea of axioms by observation of reality, which then led to logic, and then on to mathematics - so it is BECAUSE we derived mathematics from axioms we arrived to by observation that mathematics describes laws of nature - or is it something else? Can someone please elaborate more on this?

[DragonMaci]

There is no why to the axioms. Why presuposes a cause and a more basic level of knowledge. The axioms have no cause and are the most level of knowledge. They cannot be reduced.

[source]

There is no why to the axioms. Why presuposes a cause and a more basic level of knowledge. The axioms have no cause and are the most level of knowledge. They cannot be reduced.

I'm not asking for a proof of the axioms. I know the axioms cannot be reduced. I'm asking how is it that we formulated them, and why in the form in which we did. I'm not asking about the axiom, I'm asking about its formulation. We say things are what they are - do we come to this claim by mere observation of things that are, or is there more to it? Does this then explain why logic and mathematics are then tools good enough to help us deal with reality?

[DragonMaci]

I'm not asking for a proof of the axioms.

I never said you were. I said you were asking for their cause. I was also saying they have no cause. If you were not asking that I am sorry.

As for how we formulated them I am not sure how to word it. I really only know how to word how we formulate higher forms of knowledge. Sorry I cannot help you there. I will give it some thought though as I would like to know myself. I will get back to you if I come up with something. However, I am still only a student of Objectivism so I may not know some of the words I may need.

Edited May 6, 2007 by DragonMaci

[JMeganSnow]

Axioms in logic and mathematics describe nature because they are formulated by looking at nature. Just as you can figure out that a thing is itself by looking at a thing and saying, yup, it's itself, you can take two things and add them to two other things and voila, you have four things.

Given, describing nature by means of mathematics is not always straightforward. Logical positivists claim that if you can logically describe something via math then it should exist in reality, which is not necessarily true. Some higher mathematics involves the use of imaginary numbers, which don't describe anything that can exist, either. Then you get your non-repeating, non-terminating numbers . . . it's not a very organized math if the circumference of a circle divided by its diameter can only be described as "three and a bit". Looking at stuff like that should tell you just what the antecedents of math are and just how well existing mathematics describes reality.

[DavidOdden]

I'm asking how is it that we formulated them, and why in the form in which we did. I'm not asking about the axiom, I'm asking about its formulation.

You have to give us some example axioms, properly formulated. I think, if you can give some examples of ones that you might have doubts about, that I can explain the formulation apart from the symbol choice. Typically, this is a language exercise. The Kleene axioms are not, in fact, axiomatic, even if they are true formalisms.

[tps_fan]

My original confusion (which brought me here) was about logic. Why does logic work? Ultimately, why do axioms work? Why do things have identity; why are they what they are? I assume it is more than simply a matter of us putting it neatly into words in this way, but I'm not quite sure what.

Metaphysics and epistemology amount to having a proper method of recognizing and acknowledging reality. On a related note, I think that the idea of "first cause" is tied to the fallacy of begging the question which (in this context) exists thanks to religion. (Mystics generally believe in a higher power i.e. supernature; Objectivists don't believe any such thing... because there isn't a reason or cause that gives rise to such belief.) Existence exists. Existence equals identity, and a consciousness can only recognize the things which exist. Dr. Leonard Peikoff cites page 942 of _Atlas Shrugged_ at near the beginning of his book _Objectivism: The Philosophy of Ayn Rand_, so you can read that part of _A.S._ and the first chapter of _O:PAR_ for elaborations.

Did we arrive at the idea of axioms by observation of reality, which then led to logic, and then on to mathematics - so it is BECAUSE we derived mathematics from axioms we arrived to by observation that mathematics describes laws of nature - or is it something else? Can someone please elaborate more on this?

I think it's always worth going back to the scientific method which is a paradigm of induction. Yes, it ultimately goes back to observation.... Principles are derived from consistent natural patterns. The basic axioms are the most universal and abstract principles; they aren't reducible. Axioms are used to conceptualize and concretize.

Why do axioms exist? They exists because men have stuff to do, and because men aren't omniscient, and because men are conceptual!

In the softcover edition of _O:PAR_, LP says on page 8, "Axioms are perceptual self-evidencies. There is nothing to be said in their behalf except: look at reality." It's also worth noting that, "'Validation' I take to be a broader term than 'proof,' one that subsumes any process of establishing an idea's relationship to reality, whether deductive reasoning, inductive reasoning, or perceptual self-evidence. In this sense, one can and must validate every item of knowledge, including axioms. The validation of axioms, however, is the simplest of all: sense-perception." That's also from page 8, of_O:PAR_.

You would navigate an ocean with a compass or some other related device, right? A compass is a tool. Likewise, principles are tools for navigating reality in scientific and conceptual terms.

Please read chapter 1 of _O:PAR_; it's really worth your time. It's a _very_ eloquent and easy-to-read overview of the general subject.

[BrassDragon]

If you're looking for the "proof" of the 3 central axioms of Objectivism (existence, consciousness, and identity), it's that these axioms are presupposed in all knowledge.

Because the axioms are presupposed in all knowledge, anyone who tries to argue that one of them is false can easily be defeated in an argument.

For example, a skeptic must assume that existence exists in saying "Existence does not exist." For something to not exist, something has to exist, etc.

I could be more helpful if I had OPAR handly, but like tps_fan said, it's WELL worth your time to read the first chapter and see how eloquently the axioms can be shown to be absolutely bulletproof.

[DragonMaci]

I could be more helpful if I had OPAR handly, but like tps_fan said, it's WELL worth your time to read the first chapter and see how eloquently the axioms can be shown to be absolutely bulletproof.

Yeah. That is the only part of OPAR I have read. It helped me understand the axioms, which had been a stumbling point for me before then.

[source]

Thank you, you have been very helpful.

I did read OPAR a while ago, in fact, but I don't have it with me at the moment. What I didn't understand was that logic works as a tool which helps us deal with reality because deep on an axiomatic level, it correlates with reality. Thanks for clearing this up.

[DragonMaci]

Thank you, you have been very helpful.

I did read OPAR a while ago, in fact, but I don't have it with me at the moment. What I didn't understand was that logic works as a tool which helps us deal with reality because deep on an axiomatic level, it correlates with reality. Thanks for clearing this up.

Yeah that is one of the first thing you will learn about this forum; the people here are quite willing to help you with such things; they like doing it. And even though I am still learning myself I am becoming one of them; I am quite happy to help people with the things I do know about.

Edited May 7, 2007 by DragonMaci

[cmdownes]

Because the axioms are presupposed in all knowledge, anyone who tries to argue that one of them is false can easily be defeated in an argument.

For example, a skeptic must assume that existence exists in saying "Existence does not exist." For something to not exist, something has to exist, etc.

This is somewhat unfair. Strictly speaking, a skeptic isn't beholden to argue "existence does not exist", merely that we have no grounds to accept the claim "existence exists". The situation is analogous to how a lot of theism/atheism debates go - the skeptical atheist is not obligated to prove the negation of "god exists", but merely refuses to grant the claim.

I'm not sure if this makes the Pyrrhonian skeptic's job any easier, but one should accurately represent the philosophy's rhetorical obligations.

[tps_fan]

This is somewhat unfair. Strictly speaking, a skeptic isn't beholden to argue "existence does not exist", merely that we have no grounds to accept the claim "existence exists". The situation is analogous to how a lot of theism/atheism debates go - the skeptical atheist is not obligated to prove the negation of "god exists", but merely refuses to grant the claim.

I'm not sure if this makes the Pyrrhonian skeptic's job any easier, but one should accurately represent the philosophy's rhetorical obligations.

I've only started to contemplate your response, but I'm willing to concede your basic point in a restricted sense. That is, I'm fine with abiding by argumentative constraints. Nevertheless(!), your argument still plays into the hands of an Objectivist.

You want to claim logical agonisticism here. No problem!

The above-mentioned reference to self-contradiction as illustrated by Ayn Rand, Leonard Peikoff, et al. _still_ holds here. That is, by claiming that the argumentative burden is on the Objectivist position doesn't change the facts and context of the matter. (cracks knuckles) It's like this: 1) Existence and identity aren't mutually equal via sleight of hand but instead because they are what they are. How would you claim one without the other?!? By the same token, these sorts of Modernist arguments can easily be assailed by someone simply taking a positive action e.g. the act of speaking affirms _both_ existence and identity. Don't believe me? Check this: _I'm_ posting this message, AND I'm posting _this message_. Follow me? In other words, it is _I_ who is making this effort, and (likewise) this effort is _mine_.

All the evidence in the universe works to Aristotle's favor in this regard. What do the Modernists have?: their opinions. Hoo-boy!

This argument IS analogous to that of the "Ontological argument". In both cases, a false alternative is asserted: In both cases, the burden of proof being with the mystic is avoided.

(Honestly, I ate my opposition's arguments like this for snacks a 1/4 of a century ago! )

C'mon man, get off the fence. (It hurts after awhile!)

[DavidOdden]

Strictly speaking, a skeptic isn't beholden to argue "existence does not exist", merely that we have no grounds to accept the claim "existence exists".

I don't your evidence for making that claim.

[cmdownes]

Greg,

I've only started to contemplate your response, but I'm willing to concede your basic point in a restricted sense. That is, I'm fine with abiding by argumentative constraints. Nevertheless(!), your argument still plays into the hands of an Objectivist.

Haha, alright, we'll see. I'm not a skeptic in the classical sense, I was just saying that BrassDragon had misrepresented their burden in the discussion of foundational truths. But I think Pyrrhonism generates an interesting discussion contra Rand on foundational truths. I'll defend it here for the sake of argument.

You want to claim logical agonisticism here. No problem!

My (arguendo) position isn't agnosticism about the truth of logic, as such. It's agnosticism about all propositions.

The above-mentioned reference to self-contradiction as illustrated by Ayn Rand, Leonard Peikoff, et al. _still_ holds here.

Are you referring to BrassDragon's "Because the axioms are presupposed in all knowledge, anyone who tries to argue that one of them is false can easily be defeated in an argument." ? If so, I don't know how it can still apply. One can't contradict oneself unless one makes a claim. Since a Pyrrhonian skeptic doesn't assert any propositions, they can't contradict themself. Well, they grant themselves one sort of proposition, but I don't think it alone can ever generate a genuine contradiction. A Pyrrhonian can advance the claim, "P, or not P, or neither P nor not P". They just withold judgment on which elements of the disjunct obtain.

That is, by claiming that the argumentative burden is on the Objectivist position doesn't change the facts and context of the matter. (cracks knuckles) It's like this: 1) Existence and identity aren't mutually equal via sleight of hand but instead because they are what they are. How would you claim one without the other?!?

Well, the Pyrrhonian skeptic doesn't claim one or the other. I'm not quite sure where you're going with this. And clearly a change in argumentative burden doesn't change the facts under discussion. It can, however, determine to what extent we are able to hold beliefs about those facts.

By the same token, these sorts of Modernist arguments can easily be assailed by someone simply taking a positive action e.g. the act of speaking affirms _both_ existence and identity. Don't believe me? Check this: _I'm_ posting this message, AND I'm posting _this message_. Follow me? In other words, it is _I_ who is making this effort, and (likewise) this effort is _mine_.

The skepticism I'm defending here is really more ancient Greek than Modernist in bent. But regardless, I don't know to what extent your claim can convince a Pyrrhonian who has no position on the validity of his senses, the existence of other persons, the reality of mental states etc.

All the evidence in the universe works to Aristotle's favor in this regard. What do the Modernists have?: their opinions. Hoo-boy!

Well, Pyrrho was more of a All the evidence in the universe is ultimately subject to the same mulish refusal to grant assent to its alleged truth and the demand for further justification. The Pyrhhonian doesn't even have opinions, in the end, just a state of "ataraxia" attained through their methodological skepticism. Ataraxia is what Pyrrhus called the detached and balanced state of mind that supposedly arises from the tranquility of total, global skepticism.

Pyrrhonism is not an argument. Pyrrhonians are not concerned with convincing you of the truth or falsity of any propositions. They are not Socrates, saying "I know nothing but the fact of my own ignorance." They would see even that as a sort of dogmatism, since it holds at least one foundational belief. It's just the methodological employment of universal skepticism. But it is a really old and interesting challenge to foundationalist epistemologies, like Rand's, and it can't be dismissed quite so brusquely.

C'mon man, get off the fence. (It hurts after awhile!)

It hurts a bit, but being wrong hurts a lot. I'm not a Pyrrhonian, like I said, but witholding judgment in the absence of compelling reasons for belief is sometimes appropriate.

David,

I don't your evidence for making that claim.

I don't your sentence. What kind of evidence do you want me to give for the claim that a school of philosophy doesn't advance a given claim? I assume you're not looking for a bibliography on philosophical skepticism. What do you want from me?

Edited May 18, 2007 by cmdownes

[Robert J. Kolker]

There is no why to the axioms. Why presuposes a cause and a more basic level of knowledge. The axioms have no cause and are the most level of knowledge. They cannot be reduced.

What gives philosophical axioms their privileged status is that in order to deny them, you have to assert them.

For example: Anyone who denies the existence of existence has to account for the existence of the denier who made the denial of existence in the first place.

Bob Kolker

[DavidOdden]

I don't your sentence. What kind of evidence do you want me to give for the claim that a school of philosophy doesn't advance a given claim? I assume you're not looking for a bibliography on philosophical skepticism. What do you want from me?

Would you like me to provide the missing verb? "See", or "understand". After that, notice that you say 'Strictly speaking, a skeptic isn't beholden to argue "existence does not exist", merely that we have no grounds to accept the claim "existence exists".' If I'm not happy with the evidence that you give, I will let you know. But to begin with, I simply want you to provide some evidence of this claim you're made. I want you to understand the nature of the skeptic's argument. Let me repeat, so that you don't get lost in your confusion. My question is remarkably simple. I'm not calling you a liar, but the content of my question is hard to distinguish from that, I understand. I am saying that you have made a claim of that cannot be at all supported, and I am challenging you to support this claim. To maintain context, I will repeat your claim and my question:

I don't [see] your evidence for making that claim.

Now then, please support your claim about skeptics. If that involves a bibliography, so be it, or a few references, whatever. I'm denying the validity of your claim, so what is your basis for making the claim? Put your foot in it.

[cmdownes]

Would you like me to provide the missing verb? "See", or "understand". After that, notice that you say 'Strictly speaking, a skeptic isn't beholden to argue "existence does not exist", merely that we have no grounds to accept the claim "existence exists".' If I'm not happy with the evidence that you give, I will let you know. But to begin with, I simply want you to provide some evidence of this claim you're made. I want you to understand the nature of the skeptic's argument. Let me repeat, so that you don't get lost in your confusion. My question is remarkably simple. I'm not calling you a liar, but the content of my question is hard to distinguish from that, I understand. I am saying that you have made a claim of that cannot be at all supported, and I am challenging you to support this claim. To maintain context, I will repeat your claim and my question:I don't [see] your evidence for making that claim.Now then, please support your claim about skeptics. If that involves a bibliography, so be it, or a few references, whatever. I'm denying the validity of your claim, so what is your basis for making the claim? Put your foot in it.

David,

I hope you find the supplied excerpts satisfactory.

"The Pyrrhonian is not (and cannot consistently be) assenting to the claim that foundationalism [Randian epistemology, argued to be grounded in axiomatic truths, is a foundationalist view -Colin] is false. Rather, a Pyrrhonian employing this mode would be attempting to reassure herself (and perhaps show the Epistemist [The author of the article uses this term to refer to those who think knowledge of epistemically interesting facts is possible -Colin]) that the so-called foundational proposition stands in need of further support. In other words, the Pyrrhonian believes that a foundationalist cannot rationally practice his foundationalism because it inevitably leads to arbitrariness — i. e., assenting to a proposition which can legitimately be questioned but is, nevertheless, assented to without rational support.

So, how could the Pyrrhonian proceed? To begin to answer that question it is important to note that foundationalism comes in many forms. But all forms hold that the set of propositions can be partitioned into basic and non-basic propositions. Basic propositions have some autonomous bit of warrant that does not depend (at all) upon the warrant of any other proposition.[23] Non-basic propositions depend (directly or indirectly) upon basic propositions for all of their warrant.

Suppose that an inquirer, say Fred D'Foundationalist, has given some reasons for his beliefs. Fred offers q (where q could be a conjunction) for his belief that p, and he offers r (which could also be a conjunction) as his reason for q. Etc. Now, being a foundationalist, Fred finally offers some basic proposition, say b, as his reason for the immediately preceding belief. Sally D'Pyrrhonian asks Fred why he believes that b is true. Sally adds the "is true" to make clear to Fred that she is not asking what causes Fred to believe that b. She wants to know why Fred thinks that b is true. Now, Fred could respond by giving some reason for thinking that b is true even if b is basic, because basic propositions could have some non-autonomous warrant that depends upon the warrant of other propositions. But that is merely a delaying tactic since Fred is not a coherentist. In other words, he might be able to appeal to the conjunction of some other basic propositions and the non-basic propositions that they warrant as a reason for thinking that b is true. But Sally D'Pyrrhonian will ask whether he has any reason that does not appeal to another member in the set of basic propositions for thinking that each member in the set is true. If he says that he has none, then he has forfeited his foundationalism because he is really a closet coherentist. Being true to his foundationalism, he must think that there is some warrant that each basic proposition has that does not depend upon the warrant possessed by any other proposition.

The crucial point to note here is that Sally can grant that the proposition has autonomous warrant but continue to press the issue because she can ask Fred whether the possession of autonomous warrant is at all truth conducive. That is, she can ask whether a proposition with autonomous warrant is, ipso facto, at all likely to be true. If Fred says "yes," then the regress will have continued. For he has this reason for thinking that b is true: "b has autonomous warrant and propositions with autonomous warrant are somewhat likely to be true." If he says "no" then Sally can point out that he is being arbitrary since she has asked why he thinks b is true and he has not been able to provide an answer."-SEP "Skepticism", Sec. 8

"He [Pyrrho] himself has left nothing in writing, but this pupil Timon says that whoever wants to be happy must consider these three questions: first, how are things by nature? Secondly, what attitude should we adopt towards them? Thirdly, what will be the outcome for those who have such an attitude? According to Timon, Pyrrho declared that things are equally indifferent, unmeasurable and inarbitrable. For this reason neither our sensations nor our opinions tell us truths or falsehoods. Therefore for this reason we should not put our trust in them one bit, but should be unopinionated, uncommitted and unwavering, saying concerning each individual thing that it no more is than is not, or both is and is not, or neither is nor is not. The outcome for those who actually adopt this attitude, says Timon, will be first speechlessness [aphasia], and then freedom from disturbance; and Aenesidemus says pleasure. (Eusebius, Prep. Ev. 14.18.2-5, Long & Sedley)"-Quoted in SEP, "Ancient Skepticism"

"…the dogmatists say that they [the skeptics] abolish life, in the sense that they throw out everything that goes to make up a life. But the skeptics say that these charges are false. For they do not abolish, say, sight, but only hold that we are ignorant of its explanation…. We do sense that fire burns, but we suspend judgement as to whether it is fire's nature to burn…. “We only object,” they say, “to the non-evident things added on to the phenomena [the appearances]…. For this reason, Timon in his Pytho says that he has not diverged from what is customary. And in his Likenesses he says, "But the apparent utterly dominates wherever it goes." And in his work On the Senses he says, “That honey is sweet I do not posit; that it appears so I concede.” (D.L. 9.104-5, Inwood & Gerson)" -ibid.

"Sextus reports two of Carneades' central arguments against the Stoics' cataleptic impressions and any alternative “criterion” of knowledge proposed by the dogmatic philosophers (AM 7.159-165). [Here we've switched from the Pyrrhonians to the Academic skeptics, those making positive claims about the unknowability of things -Colin] According to the first argument, there can be no criterion which establishes certain truth because reason, the senses, and any other possible criterion sometimes misleads us. According to the second argument, the impressions (or “presentations”) that inform our judgments are not completely objective, and reflect their own nature as well as the nature of the reality they reflect — as light shows both itself and the things it illuminates. The subjectivity emphasized in the latter argument may have been underscored by an appeal to the standard Academic argument that any impression which appears true can be paired with (and opposed by) an indistinguishably similar impression which is apparently false." -ibid

Regardless of what one thinks of the strength of the skeptics' views, it simply cannot be claimed that they argued the the law of identity is false. Skepticism as articulated by those in whose context Aristotle was writing in would not have supported any such claim.

Edited May 18, 2007 by cmdownes

[DavidOdden]

I hope you find the supplied excerpts satisfactory.

I don't see why that constitutes a basis for making your claim about skeptics.

[cmdownes]

I don't see why that constitutes a basis for making your claim about skeptics.

Then I have to ask whether you're a being a skeptic yourself and simply refusing to assent to any proposition or whether you've misinterpreted my original claim. And if you intended to make this a sort of object lesson, it would have been far more polite and intellectually honest to simply say that skepticism endorses a stance of invincible ignorance.

As I happen to neither be a skeptic, nor be literate in Attic Greek, nor be a scholar on the subject of pre-Socratic thought, I feel little shame in arriving at beliefs on what constitutes skeptical philosophy on the basis of what experts in the field say the positions of skeptical philosophers were - or at least what people literate in Attic Greek say that the contemporaries of the skeptics said about them. I thought those excerpts pretty well outlined that skepticism doesn't negate the basic claims made by foundationalist epistemologies (i.e. Rand's axioms) but rather calls into question our ability to determine their truth or falsity.

Edited May 18, 2007 by cmdownes

[DavidOdden]

And if you intended to make this a sort of object lesson, it would have been far more polite and intellectually honest to simply say that skepticism endorses a stance of invincible ignorance.

Anybody who comes to a forum dedicated to discussion of Objectivism should not have the temerity to even raise the specter of that irrational philosophy skepticism, much less object to having the only method of operation of the skeptics actually applied to their feelings.

[cmdownes]

Anybody who comes to a forum dedicated to discussion of Objectivism should not have the temerity to even raise the specter of that irrational philosophy skepticism, much less object to having the only method of operation of the skeptics actually applied to their feelings.

That rhetorical move is a cheap trick and you know it. If I were actually a skeptic it wouldn't work in the first place, since there wouldn't be any propositions of mine to interrogate. The effectiveness of your sophistic ploy is dependent on the fact that I'm actually not a skeptic - which pretty much makes the whole thing pointless in the first place.

What other irrational philosophies am I forbidden to even broach the notion of?

Edited May 19, 2007 by cmdownes

[DragonMaci]

This is somewhat unfair. Strictly speaking, a skeptic isn't beholden to argue "existence does not exist", merely that we have no grounds to accept the claim "existence exists".

Actually, in saying, "we have no grounds to accept the claim 'existence exists'," one is saying "existence does not exist". Besides, we do have grounds to say "existence exists". The fact that we are here to debate the issue is proof. We clearly exist, evidetnly as do our surroundings. Without the existence of ourselves and our surroundings there could be no debate. Thus BrassDragon misinterpreted nothing. Rather he saw through to their root and their true meaning, which is obsured even from those that say it.

The situation is analogous to how a lot of theism/atheism debates go - the skeptical atheist is not obligated to prove the negation of "god exists", but merely refuses to grant the claim.

It is not analogous at all. We have evidence in abundance that proves that existence exists. We clearly exist or this debate would not be happening. Also, this debate is happening, so clearly it exists. The computers we are using to write our arguments and view the arguments of others clearly exist or there would be no debate. This forum clearly exists or again there would be no debate.

... and it can't be dismissed quite so brusquely.

Actually it can be. The mere act of being sceptical about the three axioms requires accepting them. They have to accept that they exist or there would be no one to be sceptical. They have to accept that they are concious or else they could not be sceptical. And finally they have to accept they have an identity or else there would be no one to be sceptical.

What gives philosophical axioms their privileged status is that in order to deny them, you have to assert them.

For example: Anyone who denies the existence of existence has to account for the existence of the denier who made the denial of existence in the first place.

I am fully aware of that, as my previous paragraph makes clear.

[DavidOdden]

What other irrational philosophies am I forbidden to even broach the notion of?

It's not, at least presently, a question of forbidding anything, though it is true that persistent use of this forum to promulgate anti-Objectivist philosophy will lead to consequences. My point is simply that your initial statement that a skeptic isn't beholden to argue anything and merely states that we have no grounds to accept anything is a cheap move, and clearly you have to know that. A skeptic simply does not have such a thing as an "argument" and doesn't use reasoning, but rather depends on juvenile automatic gainsaying. To give any recognition to this method and to sully the term "argument" by applying it to what skeptics do is an insult to the concept "argument". Whether or not you have fully embraced skepticism or are simply toying with it as an appealing idea doesn't matter -- you've at least given support to skepticism by claiming that they have an argument when they do not, and by ignoring the fact that skepticism is at heart no more sophisticated that replying "Not it isn't" or "That proves nothing" to every argument.

[cmdownes]

Kane,

Actually, in saying, "we have no grounds to accept the claim 'existence exists'," one is saying "existence does not exist".

The claim "I have no grounds to accept P" doesn't entail the assertion of ~P. That's just a non sequitur. As David pointed out several posts ago, the demand for justification is not the accusation of falsehood. EG, "I have no evidence my roommate is in the hall," does not mean I'm claiming my roommate isn't in the hall.

Besides, we do have grounds to say "existence exists". The fact that we are here to debate the issue is proof.

To the extent that you need to prove an axiom, it's not axiomatic. A foundational claim needs to be self-warranting, or it's not a foundational claim. Appealing to sense data makes the legitimacy of such data foundational, not "existence exists".

Actually it can be. The mere act of being sceptical about the three axioms requires accepting them.

As odd as it sounds, the skeptic is skeptical even that he is actually conversing with you and adopting the skeptical mode.

Dave,

The skeptic simply does not have such a thing as an "argument" and doesn't use reasoning, but rather depends on juvenile automatic gainsaying.

I wouldn't call it juvenile, but yes. You're right in that skepticism doesn't really advance an argument as such. In fact, I made that very statement earlier: "Pyrrhonism is not an argument. Pyrrhonians are not concerned with convincing you of the truth or falsity of any propositions... It's just the methodological employment of universal skepticism." So when you say,

you've at least given support to skepticism by claiming that they have an argument when they do not

...you misrepresent me. I think skepticism is interesting and worth exploring because it poses the primary question of epistemology. "How do you know that?" The entire history of epistemology in Western thought is a response to skepticism of different sorts. Ignoring skepticism is ignoring the driving force of that branch of philosophy.