Let me convince you that none of you are Classical logicians!

[henry quirk]

It's the same cup.

Why?

Cuz my cup 'is' my cup (the same cup), full or empty, hot or cold.

'My cup is full' and 'my cup is empty' are statements about 'a' cup, 'my' cup, a singular cup, statements of 'condition' or 'status', not 'identity'.

Contents (or lack of) is the 'circumstance' of my cup, not the cup itself.

[Speakpigeon]

To me: the L of I is not about the placeholder but the 'thing' the placeholder is applied to.

That's what he doesn't get even though it's basic. If he knew any logic he would know Frege and Frege wrote a detailed analysis of the difference between what a word means and what the same word refers to. Old news and still news to him.
EB

That is what you don't get even though it's basic.

You don't know what it meant to prove (In the Mathematical sense of the word) that 1 = 1, and that 99^99 = 99^99

You don't know what it means that there are integers for which "x = x" is UNDECIDABLE IN THIS UNIVERSE'S LIFETIME.
Do you know what undecidable means? https://en.wikipedia.org/wiki/Halting_problem

Because you don't know what computational complexity is.

The computational complexity of "x = x" JUST IN THE CONTEXT OF INTEGERS is infinite.
Which means that in infinite amount of time, across an infinite number of universes "x = x" cannot be proven true even for the INTEGERS.
But you assume it true.

Because you don't know what computational complexity is.

And you don't know that if it is infinite for the integers, it is infinitely more infinite for the natural numbers, infinitely infinitely infinitely more infinite for the real numbers. Infinitely more infinite complex numbers.

Because you don't know what computational complexity is.

AND WE HAVEN'T EVEN GOTTEN TO FUCKING ENGLISH WORDS YET. We haven't gotten to physics, chemistry, biology, human nature, phenomenology, experience!

You truly have missed the forest for the trees. You truly have mistaken the complex for the simple.

That has always been the claim of Postmodern thinkers. There is TOO MUCH meaning; There is INFINITE meaning.
Through infinity rendering truth a trivial matter!

By accepting "for all x: x = x" as an axiom you trivialize ALL truth.

Because you don't know what computational complexity is.

You conflate identity with value.

Philosophy without technical input is sophistry. It is because you can't reason and think for yourself is why you keep appealing to "experts".

https://repl.it/@LogikLogicus/INTEGERS

Oh wait, I forgot. Computational logic is not your forte.

Try the English version: http://gamahucherpress.yellowgum.com/wp ... smbook.pdf

You haven't proved human logic contradictory, so why should I let go of it?
EB

[Logik]

You haven't proved human logic contradictory, so why should I let go of it?
EB

I never said it was contradictory.

You should let go of classical logic because it is a false dichotomy.

In addition to true and false there IS a third option: unknown.
There is a fourth also: unknowable.

There is a 5th one also: answer being entirely different to what you imagined or expected

Alas. I have something which you MIGHT consider as valid evidence.
Empirical evidence where your intuition produces the wrong result.

On the surface, you probably you would claim that digit(1) == integer(1)
It's intuitive, right ?

1 = 1 is not TYPED and so the meaning of "=" becomes ambiguous.

Here is the proof that digit(1) != integer(1)

https://repl.it/@LogikLogicus/INTEGERS

'##### Complexity of digits'
{ '0': 2.958004188258201e-06,
'1': 2.87300645140931e-06,
'2': 2.073000359814614e-06,
'3': 2.1270025172270834e-06,
'4': 2.1759988158009946e-06,
'5': 2.225999196525663e-06,
'6': 2.3930042516440153e-06,
'7': 2.4279943318106234e-06,
'8': 2.425993443466723e-06,
'9': 2.506996679585427e-06}
'##### Complexity of Integers'
{ '1': 7.4079944170080125e-06,
'10': 6.597998435609043e-06,
'100': 6.5400017774663866e-06,
'1000': 6.77400385029614e-06,
'10000': 6.656999175902456e-06,
'100000': 6.733003829140216e-06,
'1000000': 6.702997779939324e-06,
'10000000': 6.971997208893299e-06,
'100000000': 6.8640001700259745e-06}

[Eodnhoj7]

You haven't proved human logic contradictory, so why should I let go of it?
EB

I never said it was contradictory.

You should let go of classical logic because it is a false dichotomy.

In addition to true and false there IS a third option: unknown.
There is a fourth also: unknowable.

There is a 5th one also: answer being entirely different to what you imagined or expected

Alas. I have something which you MIGHT consider as valid evidence.
Empirical evidence where your intuition produces the wrong result.

On the surface, you probably you would claim that digit(1) == integer(1)
It's intuitive, right ?

1 = 1 is not TYPED and so the meaning of "=" becomes ambiguous.

Here is the proof that digit(1) != integer(1)

https://repl.it/@LogikLogicus/INTEGERS

'##### Complexity of digits'
{ '0': 2.958004188258201e-06,
'1': 2.87300645140931e-06,
'2': 2.073000359814614e-06,
'3': 2.1270025172270834e-06,
'4': 2.1759988158009946e-06,
'5': 2.225999196525663e-06,
'6': 2.3930042516440153e-06,
'7': 2.4279943318106234e-06,
'8': 2.425993443466723e-06,
'9': 2.506996679585427e-06}
'##### Complexity of Integers'
{ '1': 7.4079944170080125e-06,
'10': 6.597998435609043e-06,
'100': 6.5400017774663866e-06,
'1000': 6.77400385029614e-06,
'10000': 6.656999175902456e-06,
'100000': 6.733003829140216e-06,
'1000000': 6.702997779939324e-06,
'10000000': 6.971997208893299e-06,
'100000000': 6.8640001700259745e-06}

You forgot the third option of "both true and false (deficient in truth, but true as gradation)".

[Logik]

You forgot the third option of "both true and false (deficient in truth, but true as gradation)".

That is kind of what I am doing by constructing the language bottom up. Measuring it.

https://en.wikipedia.org/wiki/Transcomp ... al_problem
https://en.wikipedia.org/wiki/Ultrafinitism

[Eodnhoj7]

You forgot the third option of "both true and false (deficient in truth, but true as gradation)".

That is kind of what I am doing by constructing the language bottom up. Measuring it.

https://en.wikipedia.org/wiki/Transcomp ... al_problem
https://en.wikipedia.org/wiki/Ultrafinitism

I will post a thread observing, using the number line and corresponding symbols, that the grounding of measurement is in Chaos Theory...Will take a few minutes...but Aristotelian Logic is correct when viewed as an extension of a higher logical system.

[Logik]

Aristotelian Logic is correct when viewed as an extension of a higher logical system.

Correct. Aristotelian logic is the arbiter. But its utility is RIGHT at the end. Once you are done with deduction/induction.
It tests completeness. It ensures there's no undistributed middle. It does NOT test for consistency. It doesn't have to if you have made no errors.

Like so ( from https://repl.it/@LogikLogicus/INTEGERS ):

Code: Select all

  # Positive claim A == A => True
  A = False
  with Timer() as t:
    A = digit_eq(axiom, axiom)
  COMPLEXITY_OF_DIGITS[axiom] = {}
  COMPLEXITY_OF_DIGITS[axiom]['A'] = t.elapsed

  # Negative claim A != A => False
  B = True
  with Timer() as t:
    B = digit_ne(axiom, axiom)
  COMPLEXITY_OF_DIGITS[axiom]['B'] = t.elapsed
  
  # Validate excluded middle
  if A and B:
    raise ProofInvalid('A: {}, B: {}'.format(A, B))
  COMPLEXITY_OF_DIGITS[axiom] = t.elapsed

[Eodnhoj7]

Aristotelian Logic is correct when viewed as an extension of a higher logical system.

Correct. Aristotelian logic is the arbiter. But its utility is RIGHT at the end. Once you are done with deduction/induction.
It tests completeness. It ensures there's no undistributed middle. It does NOT test for consistency. It doesn't have to if you have made no errors.

Like so ( from https://repl.it/@LogikLogicus/INTEGERS ):

Code: Select all

  # Positive claim A == A => True
  A = False
  with Timer() as t:
    A = digit_eq(axiom, axiom)
  COMPLEXITY_OF_DIGITS[axiom] = {}
  COMPLEXITY_OF_DIGITS[axiom]['A'] = t.elapsed

  # Negative claim A != A => False
  B = True
  with Timer() as t:
    B = digit_ne(axiom, axiom)
  COMPLEXITY_OF_DIGITS[axiom]['B'] = t.elapsed
  
  # Validate excluded middle
  if A and B:
    raise ProofInvalid('A: {}, B: {}'.format(A, B))
  COMPLEXITY_OF_DIGITS[axiom] = t.elapsed

Its grounded in "or" properties through the law of excluded middle, it is a "perspective" of continual "divergence" as an extension of "materialism". It is strictly aristotle's perspective as a materialist...nothing more. Perspective's exist through other perspectives (people back up what other people say and take it as there own) and as such observe all "zietgeists" (and aristotelian logic is a "zietgeist") as existing through recurssion.

[Logik]

Its grounded in "or" properties through the law of excluded middle, it is a "perspective" of continual "divergence" as an extension of "materialism". It is strictly aristotle's perspective as a materialist...nothing more. Perspective's exist through other perspectives (people back up what other people say and take it as there own) and as such observe all "zietgeists" (and aristotelian logic is a "zietgeist") as existing through recurssion.

There is no dogma in the code above - leave what people say.

I have invented digits and integers from first principles using the alphabet 0 to 9.

You can invent ANY language you want with ANY alphabet you want.
It WILL be consistent and coherent.

[Eodnhoj7]

Its grounded in "or" properties through the law of excluded middle, it is a "perspective" of continual "divergence" as an extension of "materialism". It is strictly aristotle's perspective as a materialist...nothing more. Perspective's exist through other perspectives (people back up what other people say and take it as there own) and as such observe all "zietgeists" (and aristotelian logic is a "zietgeist") as existing through recurssion.

There is no dogma in the code above - leave what people say.

I have invented digits and integers from first principles using the alphabet 0 to 9.

You can invent ANY language you want with ANY alphabet you want.
It WILL be consistent and coherent.

That invention is strictly a redirecting of those digits/variables...all "invention" is grounded in the direction of key properties (numbers/variables) where a point of relativistic "equilibrium" is used to control entropy/negentropy.

The "one/many" or "negentropy/entropy" paradigm is a foundation of consciousness which may exist through variations but is a constant process that cannot be reinvented...just like the wheel cannot be reinvented.

He who becomes "the wheel" (symbolically speaking) bends reality.

[PeteJ]

I'm very late to the party but interested in the OP. I don't see the problem.

Nobody would argue...

Jane is yellow
Brian is yellow
Ergo Jane is Brian.

I expect I'm missing something,

[Skepdick]

I'm very late to the party but interested in the OP. I don't see the problem.

Nobody would argue...

Jane is yellow
Brian is yellow
Ergo Jane is Brian.

The point is that you don't get a choice in the matter. If you subscribe to classical logic, then the law of transitivity dictates that if A = B, and B = C, then A = C.

I expect I'm missing something,

It boils down to this question: "How do you formalize the verb is?" in the sentence . "Jane is yellow" ?
However you choose to formalize it, do you use that semantic consistently throughout your argument?

Because if you don't - that's the definition of equivocation.

Here is one way to formalize "Jane is yellow"
f(Jane) = Yellow
Then it follows that "Brian is yellow" is: f(Brian) = Yellow

So then... f(Jane) = f(Brian). Which would be the same thing as saying "Jane's yellowness is the same as Brian's yellowness".

Cool. We an work with that. f(x) = y is what's called a surjective function
It maps elements in the domain [Jane, Brian, Skepdick, Whoever,.....], to the co-domain of colors [Yellow, Blue, Red, Green, .....]

So back to the beginning then: f(Jane) = Yellow is the formalization of the English sentence "Jane is yellow".
And even more abstractly "is" is formalized as: f(X) = Y is a surjective function where X is a set of people and Y a the set of colors.

Is that how you use "is" all the time, or are you equivocating?

The problem boils down to the fact that "is" is ambiguous.
In exactly the same way the "=" sign in Mathematics is ambiguous.

https://ncatlab.org/nlab/show/equality

The dualism that exists between Sameness and Difference. It's very Deleuzian.

[PeteJ]

Is that how you use "is" all the time, or are you equivocating?

I use it to attach the attribute of yellow to Jane and Brian.

[Skepdick]

I use it to attach the attribute of yellow to Jane and Brian.

OK. Is that the only sense in which you use the verb "is"?

Because if you don't.... that's equivocal use of "is".

[PeteJ]

Okay.