## Why does the world conform to logic?

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### Re: Why does the world conform to logic?

Lomax wrote:Gilbert Ryle argued something similar to your position: he said that if we unpack "this statement is false" it reads "A is false", where "A" reads "B is true", where "B" reads "C" is false, and so on ad infinitum. He argues that our assignment of truth value would depend on how much unpacking we do. But this to me seems like no answer at all: if the unpacking process is potentially infinite, then at no point have we effectively unpacked it at all, so every step suffers the same problem as the first.

The Liar's Paradox is just an equivocational "sleight-of-hand" parlor trick.

The author intentionally equivocates 'multiple' meanings from the 'singular' word "statement", by implanting the (trick) word "this" into his sentence. For what is it exactly that "this" is referring to?

From the original statement "this statement is false", does "this statement" refer to 'itself' [Meaning A]? ...or does it refer to the entire statement "this statement is false" [Meaning B]? ...or….

Meaning A = this statement ("statement"; itself) is false → which means: statement A is false
Meaning B = this statement ("this statement is false") is false → which means: statement B is false
Meaning C = this statement ("this statement ("this statement is false") is false") is false → which means: statement C is false

Because of the non-specific 'reference' (of the word "this"), we automatically fall into the trap (trick) of equivocating ALL the meanings, which then takes us down the infinite path into 'paradoxal-ness'.

The ultimate "meaning" of this (seemingly) "paradoxal" statement is wholly dependent upon the ultimate reference point of "this".

Lomax wrote:Graham Priest, on the other hand, argues that it's simpler just to allow that some statements meet the condition "P & ~P". As he writes, the metastructure of the universe does not implode around him. His tongue doesn't tie itself in a knot. His mind doesn't consume itself. So isn't there an Occamist case to be made for his position - just restrict the law of non-contradiction and get on with life?

In essence, Graham Priest correctly argues that "nonsense" (P & ~P) exists, so get over it, and move on with life.
Last edited by RJG on February 14th, 2018, 1:32 pm, edited 1 time in total.

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### Re: Why does the world conform to logic?

Lomax,

My second post was the more genuine one. The first one was made in jest, a poke at the follies of semantics. I completely agree with the use of a logic multi-tool.

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### Re: Why does the world conform to logic?

Braininvat wrote:
So sentences like "this sentence is false" are essentially void of meaning. A set of mirrors arranged to reflect each other, if there is no object in the field of view, show nothing but the mirrors infinitely receding. The field of view is a visual analogy to the Kripkean "undefined."

Maybe it helps to think of the Liar as a statement (or proposition), which means we're to imagine somebody asserting it. To assert P is to say that P is true. We could imagine a context similar to an English teacher saying "This sentence has no clauses." It works.

I don't think there's any solution to it anymore than there's a solution to Russell's Paradox.
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### Re: Why does the world conform to logic?

Braininvat wrote:So sentences like "this sentence is false" are essentially void of meaning.

What if the sentence said "that sentence is false"? ...would it still be "void of meaning"?

Is it "void of meaning" because we do not know which sentence "this" refers to? ...or is it "void of meaning" because "this" refers to multiple (seemingly) contradicting 'nested' sentences?

Asparagus wrote:I don't think there's any solution to it...

Hint: "this" is the secret to solving the paradox.

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### Re: Why does the world conform to logic?

Braininvat » February 14th, 2018, 6:22 pm wrote:Lomax,

My second post was the more genuine one. The first one was made in jest, a poke at the follies of semantics. I completely agree with the use of a logic multi-tool.

Glad we're agreed, but I couldn't fully assent to your second post. I don't think it matters that "this sentence is false" fails to refer to anything, because "P = P" doesn't appear to refer either. Actually I don't think a theory of meaning requires a theory of reference.

We'll be stuck arguing about the liar paradox forever now, with people saying increasingly incoherent things. But if "P" entails "P is true" then "this sentence is false" entails "this sentence is false and true". It doesn't matter whether "this sentence" refers - we have a statement of the form "P is false and true" - or, for short, "P & ~P". It's a simple contradiction. Priest says "then allow contradictions"; others will differ.

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### Re: Why does the world conform to logic?

RJG wrote:Hint: "this" is the secret to solving the paradox.

No. It's not about a contextless sentence. It's about the proposition expressed by the utterance of the sentence. It's not meaningless.
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### Re: Why does the world conform to logic?

Lomax wrote:But if "P" entails "P is true" then "this sentence is false" entails "this sentence is false and true.

Not so. You are falsely equivocating two different sentences/meanings as one-in-the-same"sentence". You fail to see is that there are two different sentences/meanings; two different P's.

P1: sentence A is false
P2: sentence B ("sentence A is false") is false

Again, what does "this sentence" actually refer to? Is it sentence A - OR - sentence B? ...pick one, but don't pick both!!!

Asparagus wrote:It's about the proposition expressed by the utterance of the sentence. It's not meaningless.

Agreed, but 'WHICH' meaning??? Does "this sentence is false" mean:

P1: Sentence A is false - OR - P2: Sentence B is false?

If one falsely equivocates BOTH meanings, then one falsely sees a paradox.

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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 8:12 am wrote:P1: sentence A is false
P2: sentence B ("sentence A is false") is false

Again, what does "this sentence" actually refer to? Is it sentence A - OR - sentence B? ...pick one, but don't pick both!!!

But what is sentence A? Is it "Sentence A is false"? If so, P2 says it is the same as sentence B.

If sentence A is not "Sentence A is false", what sentence is it? (It must be a complete sentence, by definition.)
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### Re: Why does the world conform to logic?

Lomax » February 14th, 2018, 1:42 pm wrote:Positor, what constitutes a "stage"?

Something along the lines of Gilbert Ryle's A, B, C etc that you mention.

Lomax wrote:I mean, however long you look at it, "this statement is false" is the same utterance. So when you say
Positor wrote:4. Hence it falsely implies that it is false-at-the-first-stage. But it consequently acquires a truth-value, i.e. "false". So now there is a second stage, at which it is false. But the fact still remains that it was not false at the first stage; therefore there is no contradiction.

everything before your "therefore" seems to show that there is a contradiction. I mean, you said it yourself: now it reveals itself to be false, despite the fact it was not false. But it is still it: it hasn't changed.

No, but there are different implied qualifications at each 'stage'. The sentence is false with regard to some aspect, and true with regard to some other aspect. I am happy to call it "true and false" in the sense that we say "this bird is black and white", i.e. we do not mean that it is wholly black and (in the same sense) wholly white.

Incidentally, would dialetheism allow "It is and it is not the case that this statement is false"?

Lomax wrote:Gilbert Ryle argued something similar to your position: he said that if we unpack "this statement is false" it reads "A is false", where "A" reads "B is true", where "B" reads "C" is false, and so on ad infinitum. He argues that our assignment of truth value would depend on how much unpacking we do. But this to me seems like no answer at all: if the unpacking process is potentially infinite, then at no point have we effectively unpacked it at all, so every step suffers the same problem as the first.

OK, but in mathematics only a finite part of an infinite series can be analysed, and that does not seem to be a problem.
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### Re: Why does the world conform to logic?

RJG wrote:P1: sentence A is false
P2: sentence B ("sentence A is false") is false

Again, what does "this sentence" actually refer to? Is it sentence A - OR - sentence B? ...pick one, but don't pick both!!!

Positor wrote:But what is sentence A?

Sentence A is the sentence that the author is pointing at. Maybe he's pointing at (referring to) a sentence in a book that he is reading.

Positor wrote:Is "Sentence A is false"?

Yes. (...according to the one saying it).

Positor wrote:If so, P2 says it is the same as sentence B.

No, it is not the same.

If sentence A is the sentence in the book, sentence B is the author's sentence saying "this sentence is false".

These are two different sentences; two different meanings. Conflating one as the other is the root (trick) of the paradox.

Either the book's sentence is false OR the person saying (it is false) is false. We don't know, until we know who/what "this" is specifically referring to. In other words, does "this" refer to the sentence in the book - OR - to the spoken word of the one who spotted this book error.

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### Re: Why does the world conform to logic?

Positor » February 15th, 2018, 1:41 pm wrote:No, but there are different implied qualifications at each 'stage'.

Okay, but then they're all implied by the original stage (such is the nature of implication). For example if we say that A implies B and B implies C, then we can deduce that A implies C. Which means the true and false "stages" are all implicit in the original "stage". Rendering "this statement is false" as semantically equivalent to "this statement is false and true" - a straightforward contradiction. CC: RJG.

Positor » February 15th, 2018, 1:41 pm wrote:Incidentally, would dialetheism allow "It is and it is not the case that this statement is false"?

Yes, I think so. But different dialetheists can have different dialetheisms. My basic intention in this thread is to argue against logical monism - and if logic were a property of the our universe, rather than our ways of thinking, then there would only be one true logic.

Positor » February 15th, 2018, 1:41 pm wrote:OK, but in mathematics only a finite part of an infinite series can be analysed, and that does not seem to be a problem.

I'm not sure what you mean by this. Here's an example of analysing an infinite series, in mathematics.

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### Re: Why does the world conform to logic?

Lomax wrote:Okay, but then they're all implied by the original stage (such is the nature of implication). For example if we say that A implies B and B implies C, then we can deduce that A implies C. Which means the true and false "stages" are all implicit in the original "stage". Rendering "this statement is false" as semantically equivalent to "this statement is false and true" - a straightforward contradiction. CC: RJG.

Lomax, if I were to make the true statement that said "the statement 1+1=3 is false", would this be a (true & false) contradiction?

I am sure you would say NO - this is not a contradiction, because these are two different statements.

And the same goes with the Liars Paradox! ...if we make the true statement B, that statement A is false, would this be a (true & false) contradiction? ...NO - these are two different statements.

We are only conned (tricked; deceived) into believing that statement A and statement B are the 'same' statement by the multi-referencing word "this".

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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 5:09 pm wrote:Lomax, if I were to make the true statement that said "the statement 1+1=3 is false", would this be a (true & false) contradiction?

No, because "(1+1=3) is false" does not entail "(1+1=3) is true". Positor admits that after one "stage" of inference from "this statement is false" (which we can call S1) we get a statement equivalent to "S1 is true".

Let "S" stand for "This statement is false". Positor argues (and I agree) that at the first analysis:

Premise 1: S
Conclusion one: Therefore, S is false

Or for short, not-S. So we have

P1: S
C1: Therefore, ~S

The next analysis leads Positor to "S is false" is false. Or for short, "S". So we get

C1: ~S
C2: Therefore, S.

Since both of our conclusions so far have followed from a single premise, we can now say

C3: S > (S & ~S)

From C1 and C2 we can also say

C4: ~S > (S & ~S)

So (S > (S & ~S)) & (~S > (S & ~S)). In other words, under all conditions we get the outcome (S & ~S). So we are faced with a contradiction: something which is false - even if it claims to be. (I am reminded of Orwell: "Some things are true even if the Telegraph says they are true".) I understand it still looks odd: this is why I say the paradox is a psychological phenomenon rather than a logical (or metaphysical) one.

The difference should be quite obvious.

If you're having trouble parsing the contradiction, you can do what logicians do to prove assertions - plot it on a truth table. You'll find it yields "false" for every field.

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### Re: Why does the world conform to logic?

RJG wrote:Lomax, if I were to make the true statement that said "the statement 1+1=3 is false", would this be a (true & false) contradiction?

Lomax wrote:No, because "(1+1=3) is false" does not entail "(1+1=3) is true".

Absolutely Agree! The 'true' statement "X is false" does not entail "X is true". So now apply the same reasoning:

Case 1: The 'true' statement "the statement (1+1=3) is false" does not entail "that statement (1+1=3) is true"

Case 2: The 'true' sentence "the sentence (that is written in the book) is false" does not entail "that sentence (that is written in the book) is true".

We have TWO different sentences/statements; one is 'true', one is 'false'. The problem arises when we conflate (equivocate) the 'true' sentence/statement with/as the 'false' sentence/statement.

*******

Lomax wrote:Let "S" stand for "This statement is false".

Okay, but let's also let "T" stand for the "statement" within the S statement. So now we have:

S = "This statement (T) is false".
T = "statement"

Note: We have TWO different statements here; S and T --- S is 'true', T is 'false'.

Lomax wrote:Positor argues (and I agree) that at the first analysis:
Premise 1: S
Conclusion one: Therefore, S is false

Incorrect! - This is where the equivocation/conflation error occurs. Remember:

S = "This statement (T) is false", so S is 'true'. --- It is T that is 'false'!!!

Lomax wrote:Or for short, not-S. So we have
P1: S
C1: Therefore, ~S

Because you have inadvertently equivocated T and S as the 'same' statement, all the logic that follows is flawed.
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### Re: Why does the world conform to logic?

Lomax wrote: » February 15th, 2018, 2:09 pm[/url]"][quote="
Let "S" stand for "This statement is false". Positor argues (and I agree) that at the first analysis:

Premise 1: S
Conclusion one: Therefore, S is false

Or for short, not-S. So we have

P1: S
C1: Therefore, ~S

Yep. If S is true, then S is false. If S is false, then S is true.
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### Re: Why does the world conform to logic?

Asparagus wrote:Yep. If S is true, then S is false. If S is false, then S is true.

But is the S that is true the same (or different!) as the S that is false?

The "S" cannot represent TWO different statements! Pick the one you want to be S, and call the other one something else.

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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 8:38 pm wrote:
RJG wrote:Absolutely Agree! The 'true' statement "X is false" does not entail "X is true". So now apply the same reasoning:

Case 1: The 'true' statement "the statement (1+1=3) is false" does not entail "that statement (1+1=3) is true"

Case 2: The 'true' sentence "the sentence (that is written in the book) is false" does not entail "that sentence (that is written in the book) is true".

Case 2 does not follow from Case 1. At least under Positor (and Ryle's) scheme, the statement "this statement is false" does entail the statement "this statement is true". I laid it out in the barest logical terms for you above, in a slow, careful, step-by-step inference.

What is your "T"? Can you write it out?

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### Re: Why does the world conform to logic?

Asparagus » February 15th, 2018, 8:48 pm wrote:
Lomax wrote: » February 15th, 2018, 2:09 pm[/url]"][quote="
Let "S" stand for "This statement is false". Positor argues (and I agree) that at the first analysis:

Premise 1: S
Conclusion one: Therefore, S is false

Or for short, not-S. So we have

P1: S
C1: Therefore, ~S

Yep. If S is true, then S is false. If S is false, then S is true.

Therefore we have a biconditional. So in both cases, "S & not-S" is entailed. Therefore the truth-value of the "paradox" is simply zero. QED.

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### Re: Why does the world conform to logic?

We accept that contradiction happens, perhaps out of our intuition about language and semantics. And that intuition is that a sentence that is self -referential is, by its nature, not about anything. (Sentences are not people, who can successfully self-refer) The subtext we bring to " This sentence is true." is "True in what way? What is it true about? If it is only saying that it is true in itself, then that truth is empty and trivial." The subtext for "this sentence is false" differs slightly: "False in what way? What can it be false about? If it is only saying that it's false in itself, then that falsity is a trivial contradiction that has no relation to an external state of affairs."

What I'm getting at is a theory of acts. A sentence does not act, it is not an agent. It just sits there, without real meaning, until it is part of a larger event, a speech act. Only an agent, only a speaker, can make a proposition about the world or a possible world (keeping modalists happy?). And when I speak to you and utter "I am lying to you right now, Norman," or utter "this sentence is false," then this becomes an act that exists in the world and thus reveals itself as a meaningless loop, a bad faith exercise of the gift of gab. (Norman is the android in the original Star Trek series who is broken by the utterance of the paradoxical sentence, thus revealing his lack of true sentience)

Does this plain language approach help to clarify our human intuitions about language?

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### Re: Why does the world conform to logic?

RJG wrote:Absolutely Agree! The 'true' statement "X is false" does not entail "X is true". So now apply the same reasoning:

Case 1: The 'true' statement "the statement (1+1=3) is false" does not entail "that statement (1+1=3) is true"

Case 2: The 'true' sentence "the sentence (that is written in the book) is false" does not entail "that sentence (that is written in the book) is true".

Lomax wrote:Case 2 does not follow from Case 1. At least under Positor (and Ryle's) scheme, the statement "this statement is false" does entail the statement "this statement is true". I laid it out in the barest logical terms for you above, in a slow, careful, step-by-step inference.

It doesn't follow, because you have falsely combined S and T, as S alone. You only see ONE statement/sentence when there are TWO.

Lomax wrote:What is your "T"? Can you write it out?

Sure --

Case 1:
Statement S = "the statement (1+1=3) is false" → is TRUE
Statement T = "(1+1=3)" → is FALSE

Case 2:
Sentence S = "the sentence (that which is written in the book) is false" → is TRUE
Sentence T = "(that which is written in the book)" → is FALSE

You are able to recognize and reject the paradox in Case 1, but somehow are blind to the same exact conditions in Case 2. Why? Why is Case 1 not a paradox, and Case 2 is? In both cases, there are TWO differing statements/sentences; S and T; S is True, and T is False.

In summary: each statement, S and T, have their own individual truth values. There is no "paradoxal" element (the mutual co-existence of S and ~S) in the "Liar's Paradox", but instead only the conflation/equivocation of S and T.
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### Re: Why does the world conform to logic?

Braininvat » February 15th, 2018, 9:52 pm wrote:We accept that contradiction happens, perhaps out of our intuition about language and semantics. And that intuition is that a sentence that is self -referential is, by its nature, not about anything. (Sentences are not people, who can successfully self-refer) The subtext we bring to " This sentence is true." is "True in what way? What is it true about? If it is only saying that it is true in itself, then that truth is empty and trivial." The subtext for "this sentence is false" differs slightly: "False in what way? What can it be false about? If it is only saying that it's false in itself, then that falsity is a trivial contradiction that has no relation to an external state of affairs."

Suppose we were discussing formal logic and we asserted, as a premise:

1. P

Would you say we cannot allow that P can function with a truth-value? My concern here is that the liar paradox was brought up (by me, because of Priest) in the context of formal logic - in which context the non-logical symbols usually don't refer. That's because the point of formal logic is to strip away semantics and see what we can prove false by its form alone. So I don't understand why the referent (or lack thereof) should be an issue here.

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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 10:18 pm wrote:
Lomax wrote:What is your "T"? Can you write it out?

Sure --

Case 1:
Statement S = "the statement (1+1=3) is false" → is TRUE
Statement T = "(1+1=3)" → is FALSE

Case 2:
Sentence S = "the sentence (that which is written in the book) is false" → is TRUE
Sentence T = "(that which is written in the book)" → is FALSE

And you accuse me of equivocation.

S was in fact "this statement is false". What is T?

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### Re: Why does the world conform to logic?

Lomax wrote:S was in fact "this statement is false".

Yes. S = "this statement is false", which is a 'true' statement? ...correct?

Lomax wrote:What is T?

T = the "statement" itself, which we know from S, is 'false', ...correct?

So that makes TWO (different) statements? ...correct?

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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 10:33 pm wrote:
Lomax wrote:S was in fact "this statement is false".

Yes. S = "this statement is false", which is a 'true' statement? ...correct?

No, it's a contradictory statement. Positor argues that on the second analysis (or "stage", if you prefer) that its falsehood implies its truth. On the next and previous analysis, vice versa. With this method we will never reach a final analysis, but we will very quickly reach a point at which S has been shown to imply both S and ~S, and we will remain at that point. If S entails S & ~S, it shares its truth conditions.

RJG » February 15th, 2018, 10:33 pm wrote:T = the "statement" itself, which we know from S, is 'false', ...correct?

So that makes TWO (different) statements? ...correct?

One last try. Can you put T into words for me? If I were to write out T, what specific string of words would I write?

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### Re: Why does the world conform to logic?

Lomax » February 15th, 2018, 2:23 pm wrote:
Braininvat » February 15th, 2018, 9:52 pm wrote:We accept that contradiction happens, perhaps out of our intuition about language and semantics. And that intuition is that a sentence that is self -referential is, by its nature, not about anything. (Sentences are not people, who can successfully self-refer) The subtext we bring to " This sentence is true." is "True in what way? What is it true about? If it is only saying that it is true in itself, then that truth is empty and trivial." The subtext for "this sentence is false" differs slightly: "False in what way? What can it be false about? If it is only saying that it's false in itself, then that falsity is a trivial contradiction that has no relation to an external state of affairs."

Suppose we were discussing formal logic and we asserted, as a premise:

1. P

Would you say we cannot allow that P can function with a truth-value? My concern here is that the liar paradox was brought up (by me, because of Priest) in the context of formal logic - in which context the non-logical symbols usually don't refer. That's because the point of formal logic is to strip away semantics and see what we can prove false by its form alone. So I don't understand why the referent (or lack thereof) should be an issue here.

Well, the thread topic was logic and its relation to the world. So reference seemed pertinent to that, at least. If logic doesn't depend on reference or an act of reference by a conscious speaker, then its proofs seem rather austere and less relevant to the thread topic of how logical statements relate to external reality. My interest lies in how a logical proposition conforms to the world, which seems to reside in questions of " what do we mean when we say P?" Meaning seems to arise from conscious acts. Logically, simply examining sentence structure, it would seem easy to assert "Dogs lack opposable thumbs.". No need to refer (point) to actual dogs, we just look up dog, thumb, and opposable in a dictionary. But, being conscious, it gets messy, because we look to see how a statement conforms to reality. We ask what dog really means, and if a mutated dog who had a startling opposable thumb, is still really a dog. Our speech acts can shift and transform. Nothing that actually exists is a logical contradiction, is it? So we just pick the right formal logic scheme to handle canine mutations and make valid logical statements about them.

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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 3:53 pm wrote:
Asparagus wrote:Yep. If S is true, then S is false. If S is false, then S is true.

But is the S that is true the same (or different!) as the S that is false?

Same.
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### Re: Why does the world conform to logic?

Braininvat wrote:Nothing that actually exists is a logical contradiction, is it?

RJG's view is that we can't ask that question. I don't quite grasp why he thinks that.

Would you say that we can imagine that the world doesn't conform to logic? Sort of like Flatlanders? Or would you say it's not even truly imaginable?
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### Re: Why does the world conform to logic?

RJG wrote:S = "this statement is false", which is a 'true' statement? ...correct?

Lomax wrote:No, it's a contradictory statement.

It only appears contradictory because TWO different statements are involved in this deceptive statement. We don't know which statement (S or T) that we are referring to.

Lomax wrote:Positor argues that on the second analysis (or "stage", if you prefer) that its falsehood implies its truth.

It is because Positor is mixing apples with oranges; he's conflating the statement-of-the-statement with the statement itself. Or as the late great 'Obvious Leo' would say, "he's conflating the 'map' with the 'territory'."

RJG wrote:So that makes TWO (different) statements? ...correct?

Lomax wrote:One last try. Can you put T into words for me? If I were to write out T, what specific string of words would I write?

T can be ANY statement/sentence that we want. For example, if we want to make the statement T = "the earth is flat".

Then, if we want to make a statement (S) about this statement (T), then we can make the statement S = "the earth is flat is false!"

Such that:
Statement S = "the earth is flat is false!" → is TRUE
Statement T = "the earth is flat" → is FALSE

Again, these are TWO separate statements (not to be confused with one another! ...the map is NOT the territory).
Last edited by RJG on February 15th, 2018, 6:47 pm, edited 1 time in total.

RJG
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### Re: Why does the world conform to logic?

Braininvat wrote:Nothing that actually exists is a logical contradiction, is it?

Asparagus wrote:RJG's view is that we can't ask that question. I don't quite grasp why he thinks that.

Where did I say that? We can say/ask all kinds of stupid illogical stuff.

But Braininvat is right; the logically impossible (i.e. logical contradictions) are not actually possible in reality. Claiming they are, is one thing, and actually existing, is another. -- It is still not possible to do the impossible.

RJG
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### Re: Why does the world conform to logic?

RJG » February 15th, 2018, 11:29 pm wrote:
RJG wrote:S = "this statement is false", which is a 'true' statement? ...correct?

Lomax wrote:No, it's a contradictory statement.

It only appears contradictory because TWO different statements are involved in this deceptive statement.

Two different statements, with two different truth-values.

RJG » February 15th, 2018, 11:29 pm wrote:T can be ANY statement/sentence that we want. For example, if we want to make the statement T = "the earth is flat"

If S is "this statement is false" and T is the (or a) statement "within" S, then what is T, written out? If you are unable to answer the question, just say so, and I'll stop wasting my time.

Lomax