The Opposite of Nothing Is/Isn't Everything

[Dragonfly]

Fine. In the statement "this statement is false" what objective reality independent of anyone's attribution does the word "this" refer to? Sorry, deictics are always context dependent. The ratio of a circle's circumference to its diameter is universal. "This" is radically relative to an asserting mind.

No, it's just a particular expression of a self-referential proposition that denies its own truth, which implies that A is not-A, a contradiction. The contradiction doesn't depend on the symbols or the language that is used to express it, it is universal. As for any mathematical or logical statement we should carefully define the terms and the grammar we use, but the essence is in the relations that we define that way, not in the symbols or the language itself.

[kiaer.ts]

deleted

[Michael Stuart Kelly]

Ted,

Is this pure linguistics as opposed to applied linguistics?

Michael

[kiaer.ts]

That's the second time you've done this Michael. Are you in need of attention? It is very frustrating to try to make myself clear, on the assumption that people want to understand themselves, only to be bumped by facetious nonsense. Please don't keep doing this. I am going to delete and repost that response.

[kiaer.ts]

Fine. In the statement "this statement is false" what objective reality independent of anyone's attribution does the word "this" refer to? Sorry, deictics are always context dependent. The ratio of a circle's circumference to its diameter is universal. "This" is radically relative to an asserting mind.

No, it's just a particular expression of a self-referential proposition that denies its own truth, which implies that A is not-A, a contradiction. The contradiction doesn't depend on the symbols or the language that is used to express it, it is universal. As for any mathematical or logical statement we should carefully define the terms and the grammar we use, but the essence is in the relations that we define that way, not in the symbols or the language itself.

Do you not understand that there is a radical difference between constants and variables, as they say in mathematics, or deictics and nouns as they say in linguistics? Terms like "this" and "that" or even "I" and "you" are radically context dependent. They have no meaning in themselves. They are like variables, rather than constants in math.

You seem, with your insistence on symbols or language to think that I am talking about concrete phrases in a given language such as English. This is not the case. The meaning of the phrase "this statement is false" is ambiguous and context dependent no matter whether you say "this statement is false" or "esta declaración es falsa." The problem here is that nothing inherent in the phrase causes there to be some real "this" which is in reality, false.

If you say to me, "this statement is false" my proper response to you is not "you have uttered a contradiction" but "what statement are you referrrring to?" You can keep repeating "this one" all you like, but no fact of reality is established.

Indeed, such concatenations of words are not even statements. A statement is an assertion of some factual state. But the words "this statement is false" would have to have the form "this statement (that x is the case) is false" in order to be a statement. Statements are always about something. The phrase is not well formed. It is not a statement. For it to be a statement, that x is the case must be specified. You end up with an infinite regress if you attempt to give the set of words some definite meaning. You end up with "this statement (that "this statement (that "this statement...ad infinitum" and you never get to the predicate false. No actual statement has been made. The only attempted (but not existentially real) contradiction would be if I were to assent that "this statement is false" is eithefr an unambiguous or finite statement. But either "this" is ambiguous or you haven't made a complete statement the truth or falsehood of which has any existence.

[Dragonfly]

You seem, with your insistence on symbols or language to think that I am talking about concrete phrases in a given language such as English. This is not the case. The meaning of the phrase "this statement is false" is ambiguous and context dependent no matter whether you say "this statement is false" or "esta declaración es falsa." The problem here is that nothing inherent in the phrase causes there to be some real "this" which is in reality, false.

That is just a matter of careful definitions how you construct such statements so that their meaning will be unambiguous. That is no different from what you do in mathematics when you construct a set of axioms and rules from which you derive mathematical statements. Such a formal system is not the same as everyday language, even if it uses the same words, just as the mathematically exact notion of a 'line' is not the same as the word 'line' we use in daily language with all its ambiguities. Creating a consistent logical system of definitions may be an interesting exercise in itself, but it is not really relevant to the essence of the statement, which is well understood by the informal clarification that the term "this statement" refers to the statement in which it occurs, and which can be summarized as "a statement that denies its own truth", and that essence is universal.

[kiaer.ts]

You seem, with your insistence on symbols or language to think that I am talking about concrete phrases in a given language such as English. This is not the case. The meaning of the phrase "this statement is false" is ambiguous and context dependent no matter whether you say "this statement is false" or "esta declaración es falsa." The problem here is that nothing inherent in the phrase causes there to be some real "this" which is in reality, false.

That is just a matter of careful definitions how you construct such statements so that their meaning will be unambiguous. That is no different from what you do in mathematics when you construct a set of axioms and rules from which you derive mathematical statements. Such a formal system is not the same as everyday language, even if it uses the same words, just as the mathematically exact notion of a 'line' is not the same as the word 'line' we use in daily language with all its ambiguities. Creating a consistent logical system of definitions may be an interesting exercise in itself, but it is not really relevant to the essence of the statement, which is well understood by the informal clarification that the term "this statement" refers to the statement in which it occurs, and which can be summarized as "a statement that denies its own truth", and that essence is universal.

You are repeating yourself.

Please answer yes or no.

Do you understand that terms like "this" are contextually ambiguous? That they cannot be defined like terms such as "line" or "pi," but must be referred to some contextual antecedent?

If you don't understand and concede that words such as "this" is radically deictic and contextual you will not understand my point.

[Dragonfly]

Please answer yes or no.

Do you understand that terms like "this" are contextually ambiguous? That they cannot be defined like terms such as "line" or "pi," but must be referred to some contextual antecedent?

The term "this sentence" can be unambiguously defined in a formal system that I mentioned, and that is all you need.

[kiaer.ts]

Please answer yes or no.

Do you understand that terms like "this" are contextually ambiguous? That they cannot be defined like terms such as "line" or "pi," but must be referred to some contextual antecedent?

The term "this sentence" can be unambiguously defined in a formal system that I mentioned, and that is all you need.

Then please provide an example.

You will not be able to avoid the use, explicit or implied, of a deictic. The deictic will be ambiguous, and when you attempt to refer the deictic back upon the phrase, you will run into an infinite regress in which you will never reach a predicate, and will never have made a complete assertion with an objective unambiguous meaning.

In essence you will say "this (by which I mean this(by which I mean this...." and you will never in fact get to "is false."

[BaalChatzaf]

Then please provide an example.

You will not be able to avoid the use, explicit or implied, of a deictic. The deictic will be ambiguous, and when you attempt to refer the deictic back upon the phrase, you will run into an infinite regress in which you will never reach a predicate, and will never have made a complete assertion with an objective unambiguous meaning.

In essence you will say "this (by which I mean this(by which I mean this...." and you will never in fact get to "is false."

There is some "setting up" to do. Please refer to

http://www.sm.luth.se/~torkel/eget/godel/theorems.html

wherein the famous Go'del Sentence that asserts its own unprovability is asserted.

This is Go"dels transformation of the Liar Paradox which produces his incompleteness theorem.

Just to make it brief a sentence in the formal system (formalized arithmetic in first order logic) can be encoded by a Go"del Number. A sentence of the form B(x) says that the sentence whose Go"del number is x is unprovable. But B(x) is a sentence so its Go"del number can be placed where x is and the result is a sentence that says (in an indirect fashion) that it is unprovable. If the formal system is consistent it can be shown that the sentence is true, but it is not a theorem since it truly asserts its own unprovability.

Neat trick. Kurt Go"del was very smart.

See also the introduction and essay the Franzen wrote on the use and misuse of the Go"del Incompleteness theorem.

http://www.sm.luth.se/~torkel/eget/godel.html

Torkel Franzen was the Avenging Angel of Mathematical Logic on the Internet pouncing on nonsense postings concerning mathematical logic. He died some time back (nearly ten years I think) of bone cancer at a relatively young age. It was a loss. No one has picked up his Sword of Truth unfortunately.

Ba'al Chatzaf

[Michael Stuart Kelly]

That's the second time you've done this Michael. Are you in need of attention? It is very frustrating to try to make myself clear, on the assumption that people want to understand themselves, only to be bumped by facetious nonsense. Please don't keep doing this. I am going to delete and repost that response.

Ted,

And I will do it as often as I wish.

You don't run things around here.

I have no idea what value was achieved by deleting one post and making the same one later. I suspect you are trying to control thread flow. Here's the short technical version. You can't do it with forum software. (I think I mentioned this once before a couple of months ago, but apparently this fact has not been assimilated yet.)

And if you had noticed the similarity between pure math and the linguistic problem with symbols you mentioned, you would have understood that my quip had much more depth (supporting you, in fact) than you allowed yourself to see. I find the concept of "pure math" to be just as strange as "pure linguistics" (as in "cut off from reality") and this was a great way to show it.

The light is not missing. Your eyes are shut. Keep them shut or open them, the choice is yours. But don't you be telling me to shut mine.

Once more, in case I was not clear. You don't run things around here.

Now back to the discussion if you wish.

Michael

[tjohnson]

This sounds like the same problem that Russell created the Theory of Types to address.

As an example, Russell gives the two-valued law of 'excluded third', formulated

in the form that 'all propositions are true or false'. We involve a vicious-circle

fallacy if we argue that the law of excluded third takes the form of a proposition,

and, therefore, may be evaluated as true or false. Before we can make any statement

about 'all propositions' legitimate, we must limit it in some way so that a statement

about this totality must fall outside this totality.

Another example of a vicious-circle fallacy may be given as that of the

imaginary sceptic who asserts that he knows nothing, but is refuted by the

question—does he know that he knows nothing? Before the statement of the sceptic

becomes significant, he must limit, somehow, the number of facts concerning which

he asserts his ignorance, which represent an illegitimate totality. When such a

limitation is imposed, and he asserts that he is ignorant of an extensional series of

propositions, of which the proposition about his ignorance is not a member, then

such scepticism cannot be refuted in the above way.

[BaalChatzaf]

Since you are so contemptuous of Objectivists are you here only for the reason you aren't welcome anywhere else? Do you have any admiration for Objectivists? Did they get anything right? Or do you acquire stature by standing on the shoulders of Objectivists while shitting on them?

--Brant

Objectivists operating in their domain of competence make very important points. This domain is the domain of politics, economics and morality. It is not the domain of physical science and mathematics. On more than one occasion I praised Rand's "money speech" placed in the mouth of Fransisco. She got the nature and function of money pegged right on and proper. On the issue of government scope, size and function I tend to agree with O'ists more than I disagree. On the absoluteness of physical/material reality the O'ists and I are on the same page.

When some O'ists start to defecate upon physical science and mathematics of which they know little, I get testy. They are excreting on my trade and doing so out of ignorance. In order to properly criticize any doctrine, theory or other mental artifact one must first understand it.

Ba'al Chatzaf

Edited May 27, 2009 by BaalChatzaf

[tjohnson]

I find the concept of "pure math" to be just as strange as "pure linguistics"

Micheal, if I called it "the study of exact relations" instead of "pure mathematics" would you find it so strange?

[Michael Stuart Kelly]

GS,

The term certainly sounds better.

I have problems, though, with trying to graft this kind of term on to an Objectivist concept since the conceptual daisy chain (originating with reality for Obectivism and not originating with reality for your meaning) is different.

Michael

[Rich Engle]

Man, I knew something in my gut was making me ignore this thread (as in did not read it at all).

And here I thought you had enough of your bandwidth being vampirized via those coupla other dealios.

Well, you know how it goes, Maestro...it is embarrassing and annoying when your monkeys get out of control. Summer comes, it gets hot, they riot.

So far so good.

rde

Edited May 27, 2009 by Rich Engle

[Brant Gaede]

Since you are so contemptuous of Objectivists are you here only for the reason you aren't welcome anywhere else? Do you have any admiration for Objectivists? Did they get anything right? Or do you acquire stature by standing on the shoulders of Objectivists while shitting on them?

--Brant

Objectivists operating in their domain of competence make very important points. This domain is the domain of politics, economics and morality. It is not the domain of physical science and mathematics. On more than one occasion I praised Rand's "money speech" placed in the mouth of Fransisco. She got the nature and function of money pegged right on and proper. On the issue of government scope, size and function I tend to agree with O'ists more than I disagree. On the absoluteness of physical/material reality the O'ists and I are on the same page.

When some O'ists start to defecate upon physical science and mathematics of which they know little, I get testy. They are excreting on my trade and doing so out of ignorance. In order to properly criticize any doctrine, theory or other mental artifact one must first understand it.

Ba'al Chatzaf

No. While some Objectivists have views on math and science that you rightly denigrate, these disciplines are not Objectivism, but you disparage Objectivists collectively.

--Brant

[merjet]

I find the concept of "pure math" to be just as strange as "pure linguistics" (as in "cut off from reality") and this was a great way to show it.

Pure arithmetic: 3 - 5 = -2

Applied arithmetic:

3 degrees - 5 degrees = -2 degrees (Celsius or Fahrenheit)

3 dollars - 5 dollars = -2 dollars (net worth)

Such math doesn't apply to degrees Kelvin or chairs or physical dollar bills.

Pure arithmetic concerns the relations between numbers, not how the numbers might be applied. In pure arithmetic you can regard the numbers as abstract nouns. In applied arithmetic the numbers are concrete adjectives.

[Michael Stuart Kelly]

Merlin,

In other words, there is a category of math so pure that it can never be applied to reality or speculations about reality?

All you described to me was rules of method, not a separate discipline.

Michael

[merjet]

Merlin,

In other words, there is a category of math so pure that it can never be applied to reality or speculations about reality?

All you described to me was rules of method, not a separate discipline.

Michael

That is not a paraphrase of what I said. Like I said here the distinction between pure and applied math is intent, not content. It seems you are trying to distinguish by content.

[Michael Stuart Kelly]

Merlin,

Others in this discussion treat pure math and applied math as if the issue were content, not intent, especially when they claim there is no correspondence between pure math and reality.

That is precisely what I question. If there were no correspondence, pure math only applies to reality in some cases by accident, but not by correspondence.

I believe this kind of reasoning is flawed.

I am surprised you have not noticed this.

Michael

[Roger Bissell]

Then please provide an example.

You will not be able to avoid the use, explicit or implied, of a deictic. The deictic will be ambiguous, and when you attempt to refer the deictic back upon the phrase, you will run into an infinite regress in which you will never reach a predicate, and will never have made a complete assertion with an objective unambiguous meaning.

In essence you will say "this (by which I mean this(by which I mean this...." and you will never in fact get to "is false."

Ted, I am in complete agreement with you, and you have stated your position very clearly. I first studied and wrote on this issue back in 1971, in an essay published in The Individualist. Here is a link to the essay posted on my website: To Catch a Thief: an Essay in Epistemological Crime-Busting

Over the years, I have had a number of little debates with people claiming to be able to set up specifically self-referential sentences ("This sentence is...") that were true or false, and the same logical principle knocked them all down, like kewpie dolls at the fair. It got boring after a while. But at least the purportedly meaningful self-referential "This sentence is..." "sentences" were fairly easy to understand--i.e., to understand what they were trying to establish, which failed. But this Goedel stuff is sheer gibberish. I don't want to buy a used car from anyone "smart" enough to write or understand it! Gak. Talk about "argument from intimidation"! More like "The Emperor's New Clause." :rofl:

There is some "setting up" to do. Please refer to

http://www.sm.luth.se/~torkel/eget/godel/theorems.html

wherein the famous Go'del Sentence that asserts its own unprovability is asserted.

This is Go"dels transformation of the Liar Paradox which produces his incompleteness theorem.

Just to make it brief a sentence in the formal system (formalized arithmetic in first order logic) can be encoded by a Go"del Number. A sentence of the form B(x) says that the sentence whose Go"del number is x is unprovable. But B(x) is a sentence so its Go"del number can be placed where x is and the result is a sentence that says (in an indirect fashion) that it is unprovable. If the formal system is consistent it can be shown that the sentence is true, but it is not a theorem since it truly asserts its own unprovability.

Neat trick. Kurt Go"del was very smart....

Ba'al, IMHO, if you cannot say it in simple language (like Ted does and like I tried to do in my 1971 essay and like Henry Veatch did in Intentional Logic in the early 1950s), then you can't say it. Please provide an intelligible translation of the above, or spare us such space fillers in the future. We are trying to ~understand~ here, and whether or not we make mistakes, it helps to talk to one another in common verbiage, not impenetrable symbolisms.

I already posted an unanswerable refutation of Goedel's slingshot argument, in which he (like others) attempted to prove that all true propostions refer to the same fact, and it was in clear, simple English prose. Interestingly, no one has tried to point out where it might be in error--even while we are treated to a dense cloud of verbal fog that purports to show how Ted is in error about specifically self-referential sentences.

REB

[Roger Bissell]

Correction: I do NOT define 0/0 as 1, because I do not define 0^n as 0! 0^n does not equal 0. 0^1 does not equal 0. 0 to any power is 1, just as any number to the zero power is 1.

Question: what is the square of 0? It is 0*0. And what is 0*0 ? It is 0. In fact 0^n, for n > 0 is 0.

Proof: 0^1 = 0 so the thing is true for n = 1.

Suppose 0^n = 0. Then 0^(n+1) = (0^n)*(0^1) = 0*0 = 0

The induction completes the proof. For all n >= 1 0^n = 0

Ba'al Chatzaf

0 does not have a square. 0*0 is undefined. 0^n is NOT 0*0 n times. It is 1 * n factors of zero. There is no number that corresponds to n factors of zero. 0*0 n times is just as undefined as 0*0 is. So 0^n = 1.

No induction necessary here.

REB

Your math is incorrect.

0*n = 0 when n is not 0. O.K. 0*n - 0*n = 0 since 0 - 0 = 0. But by the distributive law

0*n - 0*n = 0*(n - n) = 0 * 0 . So 0*0 = 0. You do like the distributive law, don't you? In a ring (a ring is an algebraic structure with + and * that is a group with respect to + and * distributes across +) 0*anything = 0. Are you saying that 0 - 0 is not defined?

Ba'al Chatzaf

Yes. 0 is an operation stopper. You cannot "do" zero to anything. Starting with 0, you can't add 0 to it, multiply it by 0, divide it by zero, or subtract 0 from it. 0 + 0 IF we start with zero, then (as they say in "Jolly Holiday") THERE WE STOP! Viz., you cannot subtract 0*n from 0*n, so your attempted application of the distributive law breaks down in the left-hand side of the attempted chain of equations.

REB

[Roger Bissell]

Correction: I do NOT define 0/0 as 1, because I do not define 0^n as 0! 0^n does not equal 0. 0^1 does not equal 0. 0 to any power is 1, just as any number to the zero power is 1.

Question: what is the square of 0? It is 0*0. And what is 0*0 ? It is 0. In fact 0^n, for n > 0 is 0.

Proof: 0^1 = 0 so the thing is true for n = 1.

Suppose 0^n = 0. Then 0^(n+1) = (0^n)*(0^1) = 0*0 = 0

The induction completes the proof. For all n >= 1 0^n = 0

Ba'al Chatzaf

0 does not have a square. 0*0 is undefined. 0^n is NOT 0*0 n times. It is 1 * n factors of zero. There is no number that corresponds to n factors of zero. 0*0 n times is just as undefined as 0*0 is. So 0^n = 1.

No induction necessary here.

REB

*sigh* Roger, now you're saying that 0*0 is undefined, but 0^n = 1. But 0^2 is just another way of writing 0*0. So, if 0*0 is undefined, then 0^2 must be undefined; it's the SAME THING. Are you saying that 0^n is undefined for n=2, but 1 for n not equal to 2??

Here's another grade-school example of why that just doesn't work.

What's (1-1) * (1-1) ? If we simplify what's inside the parentheses first, we get 0 * 0, which in RogerLand is Undefined. But, if we use the good old "FOIL" method to distribute it out, we get 1 - 1 - 1 + 1. Compute it left to right, we get 0 - 1 + 1, or -1 + 1, or 0. So (1 - 1) * (1 - 1) both equals zero and is undefined. In your math, can something equal zero AND be undefined? Or don't you believe that (x + y)*(z + w) = x*z + x*w + y*z + y*w?

Your system has a contradiction. Face up to it.

Distributive law, huh? I think you're being a bit careless with it. The way I learned it: (x + y) * (z + w) = (xz + xw) + (yz + yw), and you then perform the operations ~inside~ the parenthesis, only then combining the two results inside parenthesis. :yes:

Applying this to the present case: (1 - 1) * (1 - 1) = (1 - 1) + (- 1 + 1) = 0 + 0. Oops, oh my, here we are with another undefined (in RogerLand) expression. Can't add 0 to 0 any more than you can multiply 0 by 0. :no:

Sorry, Laure. The contradiction is not in my system, but in your misapplication of the Distributive Law. If you want to arbitrarily dispense with the parentheses, once ~you've~ had ~your~ way with them, then sure, you can prove a ~lot~ of things with a timely discarding of the oh-so-inconvenient parentheses. But rules are rules, and if you want to invoke them, you have to ~follow~ them! :poke:

REB

"Don't you know little fool, you never can win! Use your mentality, face up to reality!" (lyric to "I've Got You Under My Skin") :hug:

[Roger Bissell]

In your math, can something equal zero AND be undefined? Or don't you believe that (x + y)*(z + w) = x*z + x*w + y*z + y*w

The distributive law wrapped up in a pretty package.

Ba'al Chatzaf

Pretty is as pretty does, Ba'al. See my reply to Laure preceding.

REB