Why does the world conform to logic?

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Re: Why does the world conform to logic?

Postby Lomax on February 15th, 2018, 6:55 pm 

Braininvat » February 15th, 2018, 10:58 pm wrote: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?"

Fair enough - we're just proceeding from different premises then. From anything I can see in this thread in remains to be evidenced that the world does conform to logic (rather than the other way around, or neither). Either way I don't think meaning and reference should be confused, and I don't think we always need one to have the other.
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Re: Why does the world conform to logic?

Postby Lomax on February 15th, 2018, 7:06 pm 

Lomax » February 11th, 2018, 11:27 pm wrote:I'm surprised by the number of points that haven't been raised in this thread. Firstly, we (humans, philosophers, scientists, sense-makers) don't all agree which logic is the correct one

...


In the mathematical logic of quantum mechanics multiplication is not commutative, and the distributive law does not hold.

...

This is significant, because RJG says that the primary purpose of logic is to identify and discard logical impossibilities (my italics). That would render it somewhat trivial - we might as well say that the purpose of Scientology is to rule out Scientological impossibilities. Presumably what RJG means is that the purpose of logic is to rule out impossibilities - in which case we need some explanation as to how it does so, as opposed to merely ruling out inconceivabilities.

And I've yet to see any of these points addressed.
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Re: Why does the world conform to logic?

Postby RJG on February 15th, 2018, 7:18 pm 

Lomax wrote:Two different statements, with two different truth-values.

Correct.

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

Lomax wrote: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.

I've said it at least a couple of times already. T is whatever the "statement" is referring to, within the statement S!

"T" is this "statement" embedded within S. And this "statement" can be referring to anything! Just write in whatever you want this statement to be. But, whatever it is, Statement S says that it is false!

Maybe if you look at the word "statement" within "this statement is false" as a variable name (that you can plug anything into), instead of the word "statement", then it may make it clearer.
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Re: Why does the world conform to logic?

Postby RJG on February 15th, 2018, 7:33 pm 

Thanks all for the interesting conversation. I'll be out of touch (internet coverage) for a few days. Feel free to bad-mouth me all you want while I'm gone. :-)
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Re: Why does the world conform to logic?

Postby Lomax on February 15th, 2018, 8:00 pm 

RJG » February 16th, 2018, 12:18 am wrote:
Lomax wrote:Two different statements, with two different truth-values.

Correct.

Hence, a contradiction of the form P & ~P. QED.
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The Liar Paradox

Postby PatrckCaton on February 15th, 2018, 8:53 pm 

Patrick Caton
A Solution To the Liar Paradox

Let's solve the famous Liar paradox. The paradox can be expressed this way. Someone says, "This statement is a lie." If the speaker is lying as he claims then the statement is objectively true, in spite of the fact that it claims to be false; but if the speaker is telling the truth then the statement cannot be a lie, as it claim to be. Paradox!
The solution is straightforward. I have heard novelists describe their writing challenges in something like the following terms: "Telling the truth is hard. I will have in my mind some truth about the human situation that I try to express in words on a page. My first attempt usually fails. My second attempt may bring me closer, but not close enough. My third attempt may begin to close the gap on one side but lose ground on the other. I may do better on attempt number fifteen or forty but I eventually have to settle for some degree of flawed compromise that approximates what I was really trying to say. I may come close, but I can never get it dead right." So is our novelist telling the truth, or is he lying? Both. He is telling the truth about his inescapable lying! His description of his predicament is as true as truth an be, but it describes the lies he is telling now and must tell always whenever he takes up the language in an attempt to convey the truth. On shallow levels the liar paradox is not legitimate but on deeper cosmic levels it is a mature, sophisticated, accurate and "true" description of reality. On these levels the paradox is solved, which means it is shown to be both logical and accurate about reality-as-such. Metaphysics also operates on these deep levels and uses paradox as one of its major principles.
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Re: Why does the world conform to logic?

Postby Positor on February 16th, 2018, 12:01 am 

Lomax » February 15th, 2018, 10:52 pm wrote:
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.

I think RJG misunderstands the liar paradox. He seems to have in mind, for example, the following:

T: The earth is flat.
S: The statement "the earth is flat" is false.

But in the liar paradox, the word "this" of course refers to the very sentence containing that word. The sentence is self-referential - that is the whole point of the paradox. If "this statement" is taken to mean "The earth is flat" or any other false external sentence, then there is obviously no paradox; T is straightforwardly false, and S is straightforwardly true. The correct interpretation in the liar paradox is:

T: This statement is false.
S: The statement "This statement is false" is false.

There is no "other" statement referred to.
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Re: Why does the world conform to logic?

Postby Positor on February 16th, 2018, 12:37 am 

Lomax » February 15th, 2018, 3:13 pm wrote:
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.

I agree with you up to a point. But I would like to distinguish contradictions in which the opposing truth-values are conceptually sequential, with each truth-value implying the next one (as in the case of "This statement is false") from contradictions in which the truth-values are conceptually simultaneous, and one does not imply another (as in the case of "It is raining and it is not raining"). Contradictions of the latter type require a different justification (if indeed they can be justified).

Lomax wrote:
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.

Thanks for the link. I was thinking of series such as:

+1, -1, +1, -1, +1, -1...

where the sum is indeterminate between two different values. But perhaps that is getting off-topic.
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Re: Why does the world conform to logic?

Postby RJG on February 16th, 2018, 2:27 pm 

...back real quick to stir up trouble!

Positor wrote:I think RJG misunderstands the liar paradox. He seems to have in mind, for example, the following:

T: The earth is flat.
S: The statement "the earth is flat" is false.

No, I understand it. My point was to prove that there are TWO different meaning statements, an S statement and a T statement.


Positor wrote:But in the liar paradox, the word "this" of course refers to the very sentence containing that word. The sentence is self-referential - that is the whole point of the paradox.

Agreed. (...and it is this word "this" that is causing the perceived paradox!).


Positor wrote:If "this statement" is taken to mean "The earth is flat" or any other false external sentence, then there is obviously no paradox; T is straightforwardly false, and S is straightforwardly true.

Yes! I am glad you see this. ...if T has its own meaning 'separate' from S (i.e. TWO different meanings), then there is "obviously no paradox". ...so hang onto to this thought!


Positor wrote:The correct interpretation in the liar paradox is:

T: This statement is false.
S: The statement "This statement is false" is false.

Agreed. So, then we can write the logical relationships as such:

T: This statement is false.
S: The statement "This statement is false" is false.
Therefore: S: The statement T is false

***

T: The earth is flat
S: The statement "The earth is flat" is false
Therefore: S: The statement T is false

The logical form and relationships are identical. Why would one be a paradox, and not the other? So now, do you agree, that there is "obviously no paradox" here?

Bottom-line is -- If we can identify a separate T statement (with its own meaning) within the S statement (with its own meaning) then there is NO PARADOX. It does not matter what T is! It does not matter if T is "the earth is flat" or if T is "this statement is false".
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Re: Why does the world conform to logic?

Postby Mossling on February 17th, 2018, 12:10 am 

Great thread :)

My two cents:

If logic requires dualism and an arrow of time in order to produce cause and effect, and we have logically deduced that dualism and time did not exist before the big bang, then there is some foundational truth 'out there' that transcends logic and which governs our logical world.

In this respect, ultimate truth lies beyond logic - in the realm of pure existence free from conceptual constructs - as John Gray puts across in his book Straw Dogs: Thoughts on Humans and Other Animals, for example. Logic is a human construct, but the universe is not human - it's bigger than that.

Image

It seems that we wish the ultimate truth to conform to logic because then at least the universe is more sympathetic to our human condition. Alas, it appears to not be the case - thus, humility is in order.
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Re: Why does the world conform to logic?

Postby Positor on February 17th, 2018, 11:37 pm 

RJG » February 16th, 2018, 6:27 pm wrote:So, then we can write the logical relationships as such:

T: This statement is false.
S: The statement "This statement is false" is false.
Therefore: S: The statement T is false

***
T: The earth is flat
S: The statement "The earth is flat" is false
Therefore: S: The statement T is false

The logical form and relationships are identical. Why would one be a paradox, and not the other?

If someone points at the statement "The earth is flat" and says "This statement is false", then you are correct: "this statement" has two meanings - (a) the statement "The earth is flat", and (b) the statement "This statement is false".

But in the liar paradox, "this statement" has only one meaning, i.e. the statement "This statement is false". Nobody is pointing to, or otherwise indicating, any other statement. There is no ambiguity in the word "this" here.
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Re: Why does the world conform to logic?

Postby Lomax on February 18th, 2018, 12:29 am 

I should think the salient point is that the relationships are not identical. The point of the liar paradox is that S is implicit in T. We should be writing it like this:

Premise one, "T": This statement is false.
Conclusion one, "S": Therefore, the statement "This statement is false" is false.
Conclusion two: Therefore, "S": The statement "T" is false

***
Premise one, "T": The earth is flat
Premise two, "S": The statement "The earth is flat" is false
Conclusion one: Therefore, "S": The statement "T" is false

Notice that these two syllogisms, now properly expressed and both valid, are of distinct forms.
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Re: Why does the world conform to logic?

Postby RJG on February 18th, 2018, 12:32 am 

RJG wrote:So, then we can write the logical relationships as such:

T: This statement is false.
S: The statement "This statement is false" is false.
Therefore: S: The statement T is false

***
T: The earth is flat
S: The statement "The earth is flat" is false
Therefore: S: The statement T is false

The logical form and relationships are identical. Why would one be a paradox, and not the other?

Positor wrote:If someone points at the statement "The earth is flat" and says "This statement is false", then you are correct: "this statement" has two meanings - (a) the statement "The earth is flat", and (b) the statement "This statement is false".

But in the liar paradox, "this statement" has only one meaning, i.e. the statement "This statement is false". Nobody is pointing to, or otherwise indicating, any other statement. There is no ambiguity in the word "this" here.

If "this statement" has only "ONE meaning" and refers ONLY to the ENTIRE statement, "this statement is false", then we could then replace the original sentence with --

"This statement, "this statement is false", is false.
Or simply, "This statement, "X", is false"

-- and if so, then the paradox disappears!

It is precisely the interplay between the TWO different references (meanings) of the word "this", that creates the perceived paradox.

In other words, if we can specify which meaning "this statement" refers to, then there is no paradox. Letting the meaning of "this statement" flip-flop between TWO different reference points (meanings), creates the paradox.

********
RJG and Lomax wrote:Therefore: S: The statement T is false

Lomax, both our conclusions are the same. Both prove there is no paradox. (S does not equal ~S).
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Re: Why does the world conform to logic?

Postby hyksos on February 18th, 2018, 4:03 am 

Braininvat » January 31st, 2018, 10:06 pm wrote:It's being asked if logic is "built into" the universe, i.e. that it's ontic foundation is innately mathematical. In that case, our symbol sets are the tools to grasp the logic inherent in the universe.

The project you are describing has not been successful.

... if our brains structure our perceptions in a lawful and logical manner, then they were probably grown/developed in a universe that is lawful and logical.

That does not follow, at all.

So I would say that our brains conform the symbol systems of logic that they use to the logic of reality.

That does not happen, not even today.
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Re: Why does the world conform to logic?

Postby hyksos on February 18th, 2018, 5:12 am 

Asparagus » January 30th, 2018, 10:47 pm wrote: Why does the world conform to logic? I would extend the title with: assuming that it does.

A vast number of participants have pointed out (correctly) that this logic issue has something to do with human minds. To begin to approach this question with any seriousness, you would need to read a lot of Immanuel Kant. Kant will help you realize how perception is related to knowledge, and that you know far far less than you think
you do. Kant himself was surrounded by people who (fallaciously) assumed knowledge of the outside world is beamed into our heads in some unfiltered form. Today nobody believes this. The human eye cannot see ultraviolet light, it cannot see infrared. We cannot perceive small things like bacteria directly, and we cannot see in the dark. (..and that's just vision.) Dogs can smell things we cannot and hear sounds we cannot.

Long story short, you don't perceive the world at all. You get sense perceptions created by sense organs.

Anyway, moving on from Kant. If anyone is under the impression that human brains evolved logic due to some simple four-step evolutionary stage from "World Logic" --to---> "Brain Logic" you could not be more wrong.

Let's start with some observations. This thing we moderns call "physics" only really existed for about 4 centuries. (anecdote A professor emphasized this in the first week of a physics course.) Vis-a-vis that anecdote, we might ask this little historical quandary:

Why did it take human civilization 4000 years to develop an airplane?
In particular, why did it take us 4000 years when we saw birds, bats, and insects flying all around us all day long?

Here is the answer: Before the advent of modern "physics", (a wopping 400 years ago,) people believed that wings were some kind of magic body part that imparted magical "flying ability" to a bird. These were literate people, by the way. Nobody ever thought that the birds can fly in air because their mechanical interaction with the air was consistent with the laws of physics. Prior to the Copernican/Galilean/Newtonian Revolution, a concept like "The Laws of Physics" was in nobody's mental vocabulary. The bulk of the agrarian population, none of whom were reading Latin and "ancient Greek" basically lived in what Carl Sagan called a "demon haunted world", where all phenomenon were perceived as acts of inexplicable magic.

Point being, human beings are not born logical. Our brains have no innate logic. In the absence of modern education and literacy, we are as dumb as rocks.

Let's investigate a little bit more about this C/G/N Revolution. Prior to the 1600s, there was geometry (Given by the Greeks) and there was algebra (imported from north Africa by the Moors). Prior to about 1590 AD, nobody assumed that algebra was related to geometry. Nobody assumed that if something is true on the Geometry Chalkboard, that those truths must be faithfully reproduced on the Algebra Chalkboard. Those two separate disciplines had to be connected. The connection had to be formulated by some of the greatest geniuses in Europe.

Today, junior high school kids have algebra and "graphing functions" beat into them by rote, and are never told about the time in which they were considered separate things.

But most importantly in regards to the discussion in this thread --> Why should algebra and geometry be related? Why must it be that if something is geometrically true, that truth will be algebraically true? And why if something is algebraically true, it must be geometrically true?

Why is that?

(Go to a quiet room and think about it.)

Shapes can be transformed into equations, and those equations can be manipulated in terms of quantified variables and only as quantified variables. If any consequences are born from that manipulation of symbols, the shapes will conform as well. No logic can connect these two things. Only faith in a "deeper logical platonic realm" will connect the two in a strong way that we modern people connect them. In other words, there is no reason (cue Kant) that the two should be so faithful to each other.

Faith ... not logic ... connected Algebra to Geometry.

As logical or smart the people of the late medieval ages were (or were not) their lack of the concept of "Laws of Physics" was the missing ingredient for them to begin to construct technology and medicine. As someone has already pointed out in this thread -- if you put garbage into a machine, it will give garbage out, even when its intervening functions are perfectly logical.

Logic is a method. When it comes to reality and the universe, there is also another element present, which itself is not logic, it is a je-ne-sais-quoi . It is as alive today as it was in the notebooks of Leonardo da Vinci, where he is trying to design a helicopter.

We can investigate why a scientific revolution enabled human beings to build technology and multiply our population numbers exponentially. Why should the scientific method work in this universe, in the first place? People pretend to know, they really do not. It just does work. We happen to find ourselves in a universe where "that is the case", as it were.

(Cuing Kant again), it is not the case that human science is successful, due to the fact that humans directly experience and comprehend the very tiniest fabric of space and time and matter. Not only do we not measure that part of reality (Like our eyes not seeing infrared) , but our best more cutting-edge theories cannot describe it either.

Our very best theories (our best logical inferences) about space at the smallest scales says that there should be so much energy down there that atoms themselves should be ripped to pieces. {{ a link for the doubting Thomases : https://en.wikipedia.org/wiki/Cosmologi ... nt_problem }} Yet here we sit, surrounded by gazillions of stable atoms, as far out as our fancy telescopes can see.

So all our modern concepts of electrons, and gravity, and Einstein, and quantum fields. These things are deduced logically , not perceived directly. If this process were a straight shot down Deduction Street, we would have finished all of physics by 1932. It's not a straight shot. There is always need for a new approach, a new concept not dreamed of before now, a new "way" of thinking about an old problem.

What is happening there? The brain is not mechanically churning through a deduction spreadsheet. Is it imagining? Dreaming? Having faith?

In any case, that unusual organ in your head is doing something.. something unusual, something alien... something that is not logic.
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Re: Why does the world conform to logic?

Postby RJG on February 18th, 2018, 9:28 am 

Logic is not derived through 'faith'. Logic is just our innate (apriori) means of "making sense" (reasoning). We have no choice to accept, or to not accept. Logic is 'given' to us; 'imposed' upon us.

Without it, there could be no algebra or geometry, or the connecting of algebra to geometry. Without logic, there could be no science/physics, nor understanding of any kind. Without logic, Hyksos's 'well said' words above would be non-sensical; without meaning.

If we wish to "make sense", then 'logic' is our best (and only!) means to do so.
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Re: Why does the world conform to logic?

Postby Positor on February 18th, 2018, 10:23 am 

RJG » February 18th, 2018, 4:32 am wrote:If "this statement" has only "ONE meaning" and refers ONLY to the ENTIRE statement, "this statement is false", then we could then replace the original sentence with --

"This statement, "this statement is false", is false.
Or simply, "This statement, "X", is false"

OK, so X is false. But X states that X is false. So it correctly states its truth-value, i.e. it states it truly. So X is true! That is the paradox.
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Re: Why does the world conform to logic?

Postby RJG on February 18th, 2018, 10:57 am 

RJG wrote:If "this statement" has only "ONE meaning" and refers ONLY to the ENTIRE statement, "this statement is false", then we could then replace the original sentence with --

"This statement, "this statement is false", is false.
Or simply, "This statement, "X", is false"

Positor wrote:OK, so X is false. But X states that X is false. So it correctly states its truth-value, i.e. it states it truly. So X is true!

Yes, so then --

X is true, and
S is true

Note: X is true because S is true! (X is true when S is true, and X is false when S is false. The truth value of X is conditional on the truth value of S)

If "this statement" refers to "X", then it does NOT refer to S: "this statement X is false. "This statement" can only refer to ONE statement, NOT to TWO different statements!

Positor wrote:That is the paradox.

No. A paradox is the mutual condition of --

X is true
X is false

...and we never have the mutual condition where X is true and X is false, hence No Paradox.

*****
Note: This is no different than saying that "the statement "the earth is flat" is false". One statement says one thing "the earth is flat", and second statement corrects that false statement. There is no paradox here.
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Re: Why does the world conform to logic?

Postby Lomax on February 18th, 2018, 3:34 pm 

Well RJG and I both seem to be arguing along the lines of Arthur Prior now so it's nice to have acquired some common ground. As to whether to call the liar paradox a paradox, I have no idea. Often definitions of "paradox" are something like "something which seems like a contradiction but may not be". Well I think this is the other way around - something that seems like an insoluble regression but is actually just a contradiction.
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Re: Why does the world conform to logic?

Postby Asparagus on February 18th, 2018, 8:40 pm 

This is a cool paradox: Russell's:

Wiki wrote:According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves.
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Re: Why does the world conform to logic?

Postby Lomax on February 18th, 2018, 9:29 pm 

I think it's structurally similar. Russell was inclined to find a way of saying there can be no such set; the equivalent here is saying "the statement is not true". Which I think is correct.
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Re: Why does the world conform to logic?

Postby RJG on February 19th, 2018, 9:06 am 

Lomax wrote:
Asparagus wrote:This is a cool paradox: Russell's:
I think it's structurally similar.

Agreed.

Liar's Paradox
1. Statement T: "This statement is false".
2. Statement S: "This statement, "This statement is false", is false."
3. → Statement S: "This statement, T, is false."
4. → No paradox. No contradiction.

Russell's Paradox
1. Set T: Sets that don't contain themselves.
2. Set S: The set of sets that don't contain themselves.
3. → Set S: The set of T
4. → No paradox. No contradiction.

These paradoxes are falsely presumed to exist via an 'equivocation fallacy'. T is not S. Falsely equivocating them as the same, is the logical error.
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Re: Why does the world conform to logic?

Postby Asparagus on February 19th, 2018, 10:07 am 

Lomax » February 18th, 2018, 9:29 pm wrote:I think it's structurally similar. Russell was inclined to find a way of saying there can be no such set; the equivalent here is saying "the statement is not true". Which I think is correct.

It's ruled out artifically for the sake of set theory. R exists in the same way any other set exists: as an abstract object.
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Re: Why does the world conform to logic?

Postby Lomax on February 19th, 2018, 12:51 pm 

Asparagus » February 19th, 2018, 3:07 pm wrote:
Lomax » February 18th, 2018, 9:29 pm wrote:I think it's structurally similar. Russell was inclined to find a way of saying there can be no such set; the equivalent here is saying "the statement is not true". Which I think is correct.

It's ruled out artifically for the sake of set theory. R exists in the same way any other set exists: as an abstract object.

Russell's words were "From this I conclude that under certain circumstances a definable collection does not form a totality".
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Re: Why does the world conform to logic?

Postby Lomax on February 19th, 2018, 12:56 pm 

RJG » February 19th, 2018, 2:06 pm wrote:
Lomax wrote:
Asparagus wrote:This is a cool paradox: Russell's:
I think it's structurally similar.

Agreed.

...


4. → No paradox. No contradiction.

We are not agreed. Consider the following assertions:

1. P & ~P
2. This statement is true and it is not the case that this statement is true
3. This statement is true and this statement is false
4. This statement is false

(1) is a contradiction and therefore false by virtue of its form alone. (2) is of the same form as (1). (3) is equivalent to (2). (4) implies (3). All four statements are contradictory, and so, formally false.
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Re: Why does the world conform to logic?

Postby Asparagus on February 19th, 2018, 1:23 pm 

Lomax » February 19th, 2018, 12:51 pm wrote:
Asparagus » February 19th, 2018, 3:07 pm wrote:
Lomax » February 18th, 2018, 9:29 pm wrote:I think it's structurally similar. Russell was inclined to find a way of saying there can be no such set; the equivalent here is saying "the statement is not true". Which I think is correct.

It's ruled out artifically for the sake of set theory. R exists in the same way any other set exists: as an abstract object.

Russell's words were "From this I conclude that under certain circumstances a definable collection does not form a totality".

By "does not form a totality," was he saying that R doesn't exist? We're talking about it. We can ask questions about it. We can be either wrong or right in our assessment of it. It has all the hallmarks of an abstract object.
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Re: Why does the world conform to logic?

Postby RJG on February 19th, 2018, 1:45 pm 

Lomax wrote:We are not agreed. Consider the following assertions:

1. P & ~P
2. This statement is true, and it is not the case that this statement is true
3. This statement is true and this statement is false
4. This statement is false

(1) is a contradiction and therefore false by virtue of its form alone. (2) is of the same form as (1). (3) is equivalent to (2). (4) implies (3). All four statements are contradictory, and so, formally false.

Not so. (4) does 'not' imply (3). (4) implies (a) OR (b), but NOT both (a) + (b):

    (a) this "statement" (itself) is false, or
    (b) this statement "this statement is false" is false.

If (4) implies (a), then there is no contradiction, and the "statement" is false.
If (4) implies (b), then there is no contradiction, and the statement "this statement is false" is false.

In no case is there a contradiction. The contradiction/paradox only occurs when one equivocates TWO meanings (a) + (b) to the single word "this".
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Re: Why does the world conform to logic?

Postby Lomax on February 19th, 2018, 2:40 pm 

Asparagus » February 19th, 2018, 6:23 pm wrote:By "does not form a totality," was he saying that R doesn't exist? We're talking about it. We can ask questions about it. We can be either wrong or right in our assessment of it. It has all the hallmarks of an abstract object.

That's what I take him to mean - if "totality" doesn't mean "set" then I cannot parse the meaning of his statement. We can ask questions about "square circles", or about "nonexistent unicorns", but it doesn't mean they exist.
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Re: Why does the world conform to logic?

Postby Lomax on February 19th, 2018, 2:43 pm 

RJG,

Do you not agree that for all x, if x then x? In other words do you deny the principle of reflexivity?

If we can assert

1. P

Then we can conclude

2. P is true

This is the case for all P. Remember the definition of validity is that it is impossible for the conclusion to be false while the premises are all true.
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Re: Why does the world conform to logic?

Postby RJG on February 19th, 2018, 3:21 pm 

For added clarification of the fallacy of Russell's Paradox:

The equivocation 'trick' to Russell's paradox is contained within the first sentence. It is here where we fall hook, line, and sinker into accepting (believing in) a logical impossibility. We falsely believe (via equivocation of 'sets' with 'members of sets') that it is possible for Sets to actually contain themselves.

1. Set T: Sets that don't contain themselves

This is a nonsense statement. This is as nonsensical as saying "pigs that don't have wings". It implies that sets can somehow contain themselves. But 'sets' cannot contain themselves. T cannot contain T. Sets can only contain Members (T can only contain ~T's !!)

It is impossible to be both "inside" a box (as a 'member') while "outside" the box (as a 'set'). In other words, it is not logically possible to be in two places at one time. It is one or the other, but never both! Russell's Paradox would like us to believe otherwise.

Russell's Paradox is just the creation of nonsense, out of nonsense.


**********

Lomax wrote:If we can assert

1. P

Then we can conclude

2. P is true

This is the case for all P. Remember the definition of validity is that it is impossible for the conclusion to be false while the premises are all true.

Agreed. If the premises are sound and valid, then the conclusion is sound and valid.

(I'm assuming you will present some premises/conclusion that makes your point, shortly? ...if so, I'm anxious to see it, ...and if you prove me wrong, I will gladly and respectfully admit it to you.)
Last edited by RJG on February 19th, 2018, 3:51 pm, edited 2 times in total.
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