What is P and -P?

What is the basis for reason? And mathematics?

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Scott Mayers
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Re: What is P and -P?

Post by Scott Mayers »

Skepdick wrote: Thu Jan 21, 2021 11:25 pm
Scott Mayers wrote: Thu Jan 21, 2021 10:16 pm If anything 'obeys' does it follow what it obeys consistently? You ARE referring to laws of physics as a system itself.
I have no fucking idea what that even means.

What measurement/experiment do you propose so that we can distinguish the two cases?

How would you tell apart if something obeys the laws of physics consistently from something which obeys the laws of physics inconsistently?

What does "inconsistent" obedience to physical laws look like?
How is it different from consistent obedience of "inconsistent" laws?

I am mentioning the physics laws vaguely and in passing - merely to point out that the symbol-manipulation system I am showing you does what it does, according to the symbol-manipulation rules that I have DESIGNED.

The system obeys MY rules.
My rules "obey" reality - by virtue of being real!

The underlying hardware architecture/electrical engineering/transistors/logic gates underneath it is absolutely moot! The system is Turing-complete - it's universal.
You missed the point(s) nor can likely get it.

I haven't been here for a couple days and looking back to remind me the context, you kept using CODE that cannot be used to propose actual ARBITRARY systems that DEFY the laws of logic minimally agreed to on the level of the machine. So my point I believe was about you thinking that you can make up rules that go against the primary logic of Identity and its correlated rules regarding contradictions. When you attempted to demonstrate something with code to 'prove' your case, I pointed out that any CODE effectively operating on a real computer requires those laws still. All you are doing is USING the system's laws to UNDEFINE specific labels.



Totality doesn't require rules. Our particular Universe only 'obeys' (that is, has 'laws') due to the fact that for an infinity of Universes, there will be some with patterns that have a consistency that appears as laws. But given this consistency, it has certain definite features that are based on the three universal laws. (of which Turing machines default to as well.)



I'm doubting that anything I say will matter. So I'm certain that I'm wasting my time. You haven't demonstrated that you can set up a system of axioms of logic that is not based on those three main laws of ALL logics (that I asked for). I argued that you cannot USE a program that is runable on a computer to demonstrate your issue because the computer IS based on those laws regardless or they could not even compile. All you are doing is redefining LABELS to the laws that basically act indifferent to encrypting your language by using terms that have opposite meanings to the normal meanings. You are not actually taking away the meanings.
Scott Mayers
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Re: What is P and -P?

Post by Scott Mayers »

Eodnhoj7 wrote: Sun Jan 24, 2021 2:03 am
Scott Mayers wrote: Thu Jan 21, 2021 7:06 pm
Eodnhoj7 wrote: Thu Jan 21, 2021 6:06 pm
P must be expressed through the law of identity but the law of identity is nonsensical.

"=" is undefined except through P. It is the repetition of P which allows "=" to have any meaning and only through P. The absence of repetition of "=" necessitates "=" as being empty of meaning. This repetition of P necessitates P as having the primary identity as it occurs through repetition.. "P is P" necessitates more than one P existing as there are multiple instances of P under "P is P" thus one P is different from another due to different positions of P in time and space.

When referring to the identity of P, as in one instance, it is best just to use "P" alone.
This HAS been tried but 'equally' fails (mind the pun). The use of it CAN be done if one uses 'absolutes' but people interpret this concept in worse defiance than your point. That is, you CAN define everything as 'absolutely unique', but as soon as I use any language, like English here, to set up the colloquial part of explaining the theory/system, you are forced to use the 26 letters of the alphabet in which the argument could only use each letter once. That would be 26 letters maximum to explain the whole system!

Those main 'laws of logic' are about the language we use to express the meaning of identity only. Otherwise you can only mention the term exactly once (as an 'absolute' instance) and just PRAY that others could somehow intuit what you mean by mere chance.

The better way is to permit a class of 'variables' that have NO direct meaning as containers of particular concepts to refer to WHAT the variables MEAN, not their literal symbols. As such, a set theory type of expression of identity is their, "Postulate of 'extenstion'" ["extension" referring to the nature of the symbols to EXTEND to the meaning, beyond the symbol, just as our senses act as symbols of reality EXTERNAL to ourselves.] Here is an example of their first postulate (of most if not all systems of set theories):

(A = B) means identically that ((Given x is any element of A, that has the same element in B) AND [also that](Given y is any element of B, that has the same element in A))

This keeps the variable's distinct in a relatively 'absolute' way, that DEFINES the meaning of the equal sign, "=". But notice the repetition of the symbols cannot be avoided regardless. This particular set theory definition does this to clarify that the meanings of A and B refer to their contents or members, not the symbol as a whole class.

Now, if you still disagree, I can only ask if YOU can express any logical system that improves upon these. And, as I've asked before of others, can you define ANY system without reference to the postulated "laws of logic" referring to the meaning of "consistency, inconsistency, and contradiction"? All we need is one clear example that cannot be confusing.
1. False, one word can have a variety of meanings thus subjecting it to equivocation. Your answer of A=B shows the repetition of underlying sub variables which leaves "=" as undefined. "=" can only be defined through repetition where "= p =" is necessary for "=" to having any underlying identity.

2. As to the logical system: viewtopic.php?f=26&t=30276
Like I asked Skepdick, show me a system with postulates. But I see you attempt to at the above link but I cannot make sense of your own language or meaning in the OP to bother without alot more questions, like, for instance, what is 'context' to you? What does "all is context" mean when the term itself is specifically our word to mean something like, "the circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed."

You likely use context to mean, "the parts of something written or spoken that immediately precede and follow a word or passage and clarify its meaning." But this still is begging given such a definition is not an 'object'. You are likely referring to syntax, which still requires defining the MEANING of your symbols to MAP to defining symbols TO the basic universal logical laws.

Note that I understand the metaproof 'completeness of Propositional logic that begins first by describing HOW the system uses symbols to define what is 'well-formed'. This then gets mapped to truth tables that simply list all POSSIBLE sets of binary values of which 'true' and 'false' are applied. What it does NOT do is to interpret the propositions as these provide the literal meaning.

The question here is whether you can express a metalogic that can be 'complete' and 'consistent'. But, like me arguing with Skepdick, who assumes that ANYTHING goes, you are missing that the system has to at least have some meaning of 'identity', not that you CAN use arbitrary symbols and syntax to describe your system. That is, how can you have a system that has no meaning to 'identity' without losing sense to the meaning of even the user of your system to follow your expected rules 'consistently'? You would fail on your first 'rule' for the fact that rules are "a set of CONSISTENT behaviors expected of those agreeing to abide by them. What could be your 'first rule' to beg the system has no identity?

Rule 1 example: there is no such thing as 'consistency' ....no such thing as 'identity'. Then there should be no reason for anyone to play the game unless the game is merely be randomly do anything you want regardless of rules.
Skepdick
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Re: What is P and -P?

Post by Skepdick »

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am You missed the point(s) nor can likely get it.
You are unlikely to make them communicable.
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am I haven't been here for a couple days and looking back to remind me the context, you kept using CODE that cannot be used to propose actual ARBITRARY systems that DEFY the laws of logic minimally agreed to on the level of the machine.
Exactly that.

I am showing you a system in which A!=A and it doesn't blow up.

I am also using a theorem from distributed computer science to re-define the very notion of "consistency" (which is incoherent in classical logic because the notion of "same time" is undefined)
It's no longer "absence of contradictions" - it's consistency as logical monotonicity (CALM)

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am So my point I believe was about you thinking that you can make up rules that go against the primary logic of Identity and its correlated rules regarding contradictions.
Of course I can. I did.

The "rules" of logic are abstract, not concrete - they are subject to alteration.

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am When you attempted to demonstrate something with code to 'prove' your case, I pointed out that any CODE effectively operating on a real computer requires those laws still.
You are reifying the laws of logic as if they are the laws of physics. You've made the mortal error of every logician.

You've confused the world of logic with the real world.
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am All you are doing is USING the system's laws to UNDEFINE specific labels.
YES! I am doing precisely that. The system's laws are the laws of physics - even if i don't know what those laws ARE, I know how to exploit them to manipulate symbols/rules in formal languages.

Like logic!
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am Totality doesn't require rules.
Precisely! Rules are abstract entities, you keep reifying them.

Humans are the makers of those "rules"!

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am Our particular Universe only 'obeys' (that is, has 'laws') due to the fact that for an infinity of Universes, there will be some with patterns that have a consistency that appears as laws. But given this consistency, it has certain definite features that are based on the three universal laws. (of which Turing machines default to as well.)
Precisely! Rules are abstract entities, you keep reifying them.

Humans are the makers of those "rules"!

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am You haven't demonstrated that you can set up a system of axioms of logic that is not based on those three main laws of ALL logics (that I asked for).
So showing you a symbolic system where A=A is false is not a demonstration? OK.

What would be a sufficient demonstration to convince you that you are wrong?

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am I argued that you cannot USE a program that is runable on a computer to demonstrate your issue because the computer IS based on those laws regardless or they could not even compile.
You really really really don't understand the universality of Turing completeness (or any model of computation) a priory any axiom schema.

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am All you are doing is redefining LABELS to the laws that basically act indifferent to encrypting your language by using terms that have opposite meanings to the normal meanings. You are not actually taking away the meanings.
Your lack of understanding is astounding.

The symbol "=" in A=A doesn't have such a thing as "opposite meaning" - it's just a predicate,
identical(A,A) performs an operation/measurement/comparison on the parameters and returns a result.

To assert identity is to make a DETERMINATION. Measurement!

A!=A re-written in predicate form is just identical(A,A) -> False

So yeah! I have given the "opposite meaning" to your axiom. Which is exactly the same damn thing as rejecting it! Because it's false!
Scott Mayers
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Re: What is P and -P?

Post by Scott Mayers »

Skepdick wrote: Tue Jan 26, 2021 6:38 am
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am You missed the point(s) nor can likely get it.
You are unlikely to make them communicable.
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am I haven't been here for a couple days and looking back to remind me the context, you kept using CODE that cannot be used to propose actual ARBITRARY systems that DEFY the laws of logic minimally agreed to on the level of the machine.
Exactly that.

I am showing you a system in which A!=A and it doesn't blow up.

I am also using a theorem from distributed computer science to re-define the very notion of "consistency" (which is incoherent in classical logic because the notion of "same time" is undefined)
It's no longer "absence of contradictions" - it's consistency as logical monotonicity (CALM)

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am So my point I believe was about you thinking that you can make up rules that go against the primary logic of Identity and its correlated rules regarding contradictions.
Of course I can. I did.

The "rules" of logic are abstract, not concrete - they are subject to alteration.

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am When you attempted to demonstrate something with code to 'prove' your case, I pointed out that any CODE effectively operating on a real computer requires those laws still.
You are reifying the laws of logic as if they are the laws of physics. You've made the mortal error of every logician.

You've confused the world of logic with the real world.
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am All you are doing is USING the system's laws to UNDEFINE specific labels.
YES! I am doing precisely that. The system's laws are the laws of physics - even if i don't know what those laws ARE, I know how to exploit them to manipulate symbols/rules in formal languages.

Like logic!
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am Totality doesn't require rules.
Precisely! Rules are abstract entities, you keep reifying them.

Humans are the makers of those "rules"!
To me, you are placing the MEANING of consistency as OWNED by humanity rather than physics. Physics is of those worlds that have 'consistent' laws of which we are SUBJECT to follow.

You also keep thinking that a human's capacity to undefine what will be CALLED 'consistent or not, or choose to use some made word for the meaning, implies that the meaning itself doesn't exist to OUR shared world of reasoning.

Physical laws ARE due to 'abstract' realties and is just the PERFECT MODEL of reality, but a 'model' nontheless.

"Logic" refers to manipulating symbols but do NOT refer to the symbols being used (necessarily) but to what one can variably replace them with IN MEANING.

Scott Mayers wrote: Tue Jan 26, 2021 3:04 am Our particular Universe only 'obeys' (that is, has 'laws') due to the fact that for an infinity of Universes, there will be some with patterns that have a consistency that appears as laws. But given this consistency, it has certain definite features that are based on the three universal laws. (of which Turing machines default to as well.)
Precisely! Rules are abstract entities, you keep reifying them.

Humans are the makers of those "rules"!
And you are 'reifying' the abstraction of NATURE as due to humans in an anthropomorphic interpretation that ALL 'logic' is just some featureless game to which we'd have to include chaotic behavior, like a child scribbling on paper. "Logic" (intentional) is the particular models about reality to which we substitute symbols to reference things, use the system to draw conclusions, and then replace the symbols in those conclusions to be about the world. The minimal 'logic' has to be about some intent to symbolize reality in a ONE-TO-ONE correspondence of which the Law of Identity is a minimal rule in ANY system that says, WE AGREE TO THESE RULES. That 'agreement' of asserting IDENTITY is AT LEAST to say you have SOME RULE or even if you assumed it to BE just a 'game', it would have no referent.

Your example of asserting X = !X actually just asserts that you want the symbol on the LEFT to be the IDENTIFYING substitute for what is on the right. The identity relation here is like assigning the memory space NAMED, "X", to contain "!X" in its memory as data. It does not imply that they are IDENTICAL concepts because the left-hand 'X' is a label of a container while the right is the contents. The law of Identity would mean that the container's label 'X' where used to refer to addresses is fixed and identifies WHATEVER its content means.

That kind of 'assignment' is VARIABLE and means that the contents can vary or do not have to be the same. But try to impose the meaning of the literal address space, whether constant or variable, to be 'variable' only suggests that you are also mistaking the POINTERS to other addresses in the opposite way: content of some labeled pointer to defining which address to refer to.
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am You haven't demonstrated that you can set up a system of axioms of logic that is not based on those three main laws of ALL logics (that I asked for).
So showing you a symbolic system where A=A is false is not a demonstration? OK.
You are interpreting identity as an assignment to some variable content. IF you are referring to say, an actual hardware example, you can treat a flip-flop memory gate as ACTING like this. when electricity is limited IN TIME to flow through some circuit AND it gets fed back to itself as an input, Input-y as initially zero CAN output an Output-Y that feeds back to ALTER the function of the circuit. In this way, you may think this is a system DEFINED inconsistently, right? The reality tells us that given this IS a contradiction, it is not necessarily paradoxical because TIME itself resolves this in a way that permits this to be non-contradictory: Input-y(t=0) differs from Input-y(t=1). The whole label including its content are themselves distinct variables, "Input-y(t=0)" != "Input-y(t=1)" even while the partial label, "Input-y" they share is fixed.
What would be a sufficient demonstration to convince you that you are wrong?
PROVE that you understand me correctly before you impose your internal impression of what you believe I mean maps to your meaning. Unfortunately, you'd be just PROVING that the 'law of identity' applies because then we'd have ...

"(Scott-Mayers)view = (Skepdick)expression-of-(Scott-Mayers)view".

The value in each of these named variables as labels have to be what is called, 'identical', not the labels of the variable. But when we do, we'd state the labels as 'identical' when we have

(Scott-Mayers)view == (Scott-Mayers)view,

for example. Note that the traditional "=" in most computer ASSIGNMENT statements are more like "implications" meaning that IF (some variable is used) then (it means some constant), and is done by assigning the meaning of the right side's content value as a constant, into the variable on the left.

You're best 'proof' [to convince me sufficiently] would simply be to disagree with me perpetually until the end of infinite time. As you do this well here in finite means, there is likely no way...and that is why the law of Identity is itself a perpetual law BY MEANING!
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am I argued that you cannot USE a program that is runable on a computer to demonstrate your issue because the computer IS based on those laws regardless or they could not even compile.
You really really really don't understand the universality of Turing completeness (or any model of computation) a priory any axiom schema.
"Turing completeness" is NOT relevent and actually undoes what you appear to be asserting and favors my position:
In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine. ... Virtually all programming languages today are Turing-complete.
I stick with using "universal machine" given this definition is very specific to Turings literal expression in his paper on that. I have it, read it many times, compared it to other versions or expressions and it reduces in meaning you are implying as simply "universally complete", which happens to mean that those "universal laws" of logic necesarily apply or they cannot be proven 'complete'. I have advanced computer logic under my belt. The example I just gave above regarding the flip-flop is an example of extended logic BEYOND the normal 'Turing' design because his require Non-circular systems (cannot feed back the tape presented on its own because it would become 'finitely' expressed and unable to demonstrate his proof of the INCOMPLETENESS of any finite machine with respect to the infinite domain of realities that exist.

I don't know why I'm constantly getting accused of being 'dumb' or naive by you (or some others) when I grant charity to your own capacity to reason with at least better background than many others here on this topic? Don't worry about my educational background. I can prove my worth in context to our discussion without expecting authority.
Scott Mayers wrote: Tue Jan 26, 2021 3:04 am All you are doing is redefining LABELS to the laws that basically act indifferent to encrypting your language by using terms that have opposite meanings to the normal meanings. You are not actually taking away the meanings.
Your lack of understanding is astounding.
Dito. But unlike you, I actually think you have a likely understanding under the surface but misappropriate the meaning of those universal laws with a bias that is unwarranted. Although others HAVE argued this within their own proposed alternatives, ...like how some who dismiss traditional logic as FALSE rather than INCOMPLETE as they attempt to upsell their presumed superior idea as a complete replacement that undoes the old.
The symbol "=" in A=A doesn't have such a thing as "opposite meaning" - it's just a predicate,
identical(A,A) performs an operation/measurement/comparison on the parameters and returns a result.

To assert identity is to make a DETERMINATION. Measurement!

A!=A re-written in predicate form is just identical(A,A) -> False

So yeah! I have given the "opposite meaning" to your axiom. Which is exactly the same damn thing as rejecting it! Because it's false!
I am hoping that you eat these words after reading the above. But I'm certain you'll come back with something else. If you presume me 'incorrect' (ie, 'false' by our some universal meaning), you have yet to prove you understand the meaning of the universal laws that reference 'identity' and 'contradiction'. They are NOT the specific logics that one defines based on them. They are the essential mechanisms of nature, whether we symbolize them or not, referring to any consistent system in Totality. The realities that logic refers to (like physics) are the perfect 'symbols' of themselves in this respect. For them to make any 'sense', they need consistency or we could not use the sense's data of our literal senses to infer anything. When you see something at some given time, the memory you assign to it REFERS to the reality as an IDENTITY. This way, you do not have to literally require denoting the literal objects every single time you want to communicate something about them. Thus the agreement to any system of rules by all participants requires being IDENTICAL or the system cannot function as a system at all.

This is like if you were to 'agree' to play some game, like chess, we agree to the meaning of the same rules regarding all tokens as IDENTIFYING some particular set of behaviors. The 'identity' of a Bishop to move only diagnally, for example, requires being in sync with all players or they cannot have an effectively functioning "game of chess".
Skepdick
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Re: What is P and -P?

Post by Skepdick »

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am To me, you are placing the MEANING of consistency as OWNED by humanity rather than physics. Physics is of those worlds that have 'consistent' laws of which we are SUBJECT to follow.
Humanity is an abstraction. Humans are concrete entities. Some humans own the meaning of identity as you do Other humans (who call themselves "physicists") own the meaning that I do.

You are playing the same, stupid game as every theist in history. My God (axiom) is better than your God (axiom).

This disagreement is not resolvable philosophically, because axioms are always contingent upon pragmatic human choice.
If you don't back down and tolerate world-views alternative to the status quo - there will be violence.

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am You also keep thinking that a human's capacity to undefine what will be CALLED 'consistent or not, or choose to use some made word for the meaning, implies that the meaning itself doesn't exist to OUR shared world of reasoning.
It exists to YOUR shared world of reasoning - within YOUR echo-chamber.

it doesn't exist to MY shared world of reasoning - within MY echo-chamber.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am Physical laws ARE due to 'abstract' realties and is just the PERFECT MODEL of reality, but a 'model' nontheless.
Model indeed! Sounds like you don't understand the Löwenheim–Skolem theorem.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am "Logic" refers to manipulating symbols but do NOT refer to the symbols being used (necessarily) but to what one can variably replace them with IN MEANING.
Logic also doesn't refer to WHAT symbols symbolise, nor does it refer to HOW symbols should be manipulated.

You are confusing logical and nomological necessity!

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am And you are 'reifying' the abstraction of NATURE as due to humans in an anthropomorphic interpretation that ALL 'logic' is just some featureless game to which we'd have to include chaotic behavior, like a child scribbling on paper.
That is precisely what it is! Logic is instrumental to humans.

It doesn't say fuckall about reality. It's just a self-imposed game of rule-following, where we are the ones interpreting the rules.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am "Logic" (intentional) is the particular models about reality to which we substitute symbols to reference things, use the system to draw conclusions, and then replace the symbols in those conclusions to be about the world.
There you go! Making the error I warned you about :lol: :lol: :lol: :lol:

Confusing the world of logic with the real world.

You mind is trapped in a cage of your own making.

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am The minimal 'logic' has to be about some intent to symbolize reality in a ONE-TO-ONE correspondence of which the Law of Identity is a minimal rule in ANY system that says
Not SOME intent. ANY intent. My one-to-one correspondence needs not be your ONE-TO-ONE correspondence.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am , WE AGREE TO THESE RULES. That 'agreement' of asserting IDENTITY is AT LEAST to say you have SOME RULE or even if you assumed it to BE just a 'game', it would have no referent.
I didn't agree to shit! The rules were here when I arrived.

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am The identity relation here is like assigning the memory space NAMED, "X", to contain "!X" in its memory as data
It's not an assignment, idiot. It's an assertion

X == X is ASSERTED as being false. That's called a decision.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am You are interpreting identity as an assignment to some variable content.
Leave me out of this. Talk about yourself. Tell me how YOU would falsify the identity axiom for yourself.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am IF you are referring to say, an actual hardware example
I am not referring to any hardware examples. A symbolic model of computation has infinite physical forms - you can build a computer purely out of children's toys. you can build a computer with water, you can build a computer with chemical reactions.

All of this is implementation detail - I am talking about design.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am , you can treat a flip-flop memory gate as ACTING like this. when electricity is limited IN TIME to flow through some circuit AND it gets fed back to itself as an input, Input-y as initially zero CAN output an Output-Y that feeds back to ALTER the function of the circuit. In this way, you may think this is a system DEFINED inconsistently, right? The reality tells us that given this IS a contradiction, it is not necessarily paradoxical because TIME itself resolves this in a way that permits this to be non-contradictory: Input-y(t=0) differs from Input-y(t=1). The whole label including its content are themselves distinct variables, "Input-y(t=0)" != "Input-y(t=1)" even while the partial label, "Input-y" they share is fixed.
Dumb electrical engineer.

Go ahead and make your analogy about a Turing tumble.

It's still a computer, just not made of electric circuits.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am PROVE that you understand me correctly before you impose your internal impression of what you believe I mean maps to your meaning. Unfortunately, you'd be just PROVING that the 'law of identity' applies because then we'd have ...
That's a stupid request. The notion of "PROOF" is meaningless outside of symbolic logic. HOW would I prove to you that I understand you? What could I possibly say to you to convince you that you are wrong? Absolutely nothing!

That's why I insist that you prove yourself wrong.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am The value in each of these named variables as labels have to be what is called, 'identical', not the labels of the variable. But when we do, we'd state the labels as 'identical' when we have
But it's precisely the values which are NOT identical, even though the labels are.

NOW is always labeled as NOW.
The value of NOW is not the same as the value of NOW.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am You're best 'proof' [to convince me sufficiently] would simply be to disagree with me perpetually until the end of infinite time. As you do this well here in finite means, there is likely no way...and that is why the law of Identity is itself a perpetual law BY MEANING!
This is precisely the reason I refuse to engage in philosophical debate.

Arguing is about defending your position - becoming further and further entrenched in your religion.

Science is about counter-examples. If that's not sufficient for you, then you have to tell me what is.

What experiment would you perform, what observation about reality would convince you of the error in your semantics?
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am "Turing completeness" is NOT relevent and actually undoes what you appear to be asserting and favors my position
How is it not relevant when I have shown you a Turing machine which ASSERTS A = A as being false??!?!?!

Do you even give a shit about empirical evidence?
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am I stick with using "universal machine" given this definition is very specific to Turings literal expression in his paper on that. I have it, read it many times, compared it to other versions or expressions and it reduces in meaning you are implying as simply "universally complete", which happens to mean that those "universal laws" of logic necesarily apply or they cannot be proven 'complete'.
Good for you! So when you read Turing's paper did you also read that the universality of Turing machines is only about transformations from Nat -> Nat.

So are you then aware, that at higher types (such as the ones I am designing) your understanding of Turing's paper doesn't matter.

http://math.andrej.com/2006/03/27/somet ... ontinuous/
The lesson is for those “experts” who “know” that all reasonable models of computation are equivalent to Turing machines. This is true if one looks just at functions from N to N. However, at higher types, such as the type of our function m, questions of representation become important, and it does matter which model of computation is used.
So, I am in fact referring to a notion of computation that's not constrained to the specific model of Turing machines. Because you do know that there are other models, right?

P.S make sure you understand the implications of the Löwenheim–Skolem theorem.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am I have advanced computer logic under my belt.
I have practical experience under mine.

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am Dito. But unlike you, I actually think you have a likely understanding under the surface but misappropriate the meaning of those universal laws with a bias that is unwarranted.
:lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol:

In a society that's dominated by people who think like me I could say the exact same thing about you!

Universal laws. :lol: :lol: :lol: :lol: :lol: :lol: :lol:

Scott Mayers wrote: Tue Jan 26, 2021 8:56 am Although others HAVE argued this within their own proposed alternatives, ...like how some who dismiss traditional logic as FALSE rather than INCOMPLETE as they attempt to upsell their presumed superior idea as a complete replacement that undoes the old.
There's nothing to be argued about. There's a principle in Mathematics: no self-defeating objects.

This principle is a self-imposed RESTRICTION on symbolic logic. Without this restriction the language is "too powerful".

Which is a stupid, stupid principle to embrace for people who WANT powerful languages.
I WANT a language that can make A become not-A. I WANT a language that can mutate the state of the world, not merely describe it.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am I am hoping that you eat these words after reading the above. But I'm certain you'll come back with something else. If you presume me 'incorrect' (ie, 'false' by our some universal meaning), you have yet to prove you understand the meaning of the universal laws that reference 'identity' and 'contradiction'.
They aren't universal laws, you moron. You can VIOLATE them AT WILL.

They are just social norms.
Scott Mayers wrote: Tue Jan 26, 2021 8:56 am They are the essential mechanisms of nature......
The "universal" laws of thought are an "essential mechanism of nature"?

:lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol:

Fuck. You are dumb.
Scott Mayers
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Re: What is P and -P?

Post by Scott Mayers »

Skepdick wrote: Tue Jan 26, 2021 9:52 am
I read only the first part of your response and was sufficiently insulted. Furthermore, a quick scroll only proves worse.

I'll leave you alone. You have issues that I can't unmask given your anonymity. I gave you charity and you shit on it. Thanks.
Skepdick
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Re: What is P and -P?

Post by Skepdick »

Scott Mayers wrote: Wed Jan 27, 2021 12:57 am You have issues that I can't unmask given your anonymity.
What a peculiar thing to say!

Almost as if you are focusing on me, and not on my argument.
Scott Mayers wrote: Wed Jan 27, 2021 12:57 am I gave you charity and you shit on it. Thanks.
That wasn't charity - it was left overs. I didn't ask for it - I asked you to negate your axiom.
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Re: What is P and -P?

Post by Skepdick »

Scott Mayers wrote: Wed Jan 27, 2021 12:57 am I read only the first part of your response and was sufficiently insulted. Furthermore, a quick scroll only proves worse.

I'll leave you alone. You have issues that I can't unmask given your anonymity. I gave you charity and you shit on it. Thanks.
To wrap up your mis-understanding I have just one reference: https://en.wikipedia.org/wiki/Kochen%E2 ... er_theorem
The theorem proves that there is a contradiction between two basic assumptions of the hidden-variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum-mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and independent of the device used to measure them. The contradiction is caused by the fact that quantum-mechanical observables need not be commutative. It turns out to be impossible to simultaneously embed all the commuting subalgebras of the algebra of these observables in one commutative algebra, assumed to represent the classical structure of the hidden-variables theory, if the Hilbert space dimension is at least three.
In trivial English: you can't have X as a variable, while also knowing the definite value of the variable at any given time.
Eodnhoj7
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Re: What is P and -P?

Post by Eodnhoj7 »

Scott Mayers wrote: Tue Jan 26, 2021 5:32 am
Eodnhoj7 wrote: Sun Jan 24, 2021 2:03 am
Scott Mayers wrote: Thu Jan 21, 2021 7:06 pm
This HAS been tried but 'equally' fails (mind the pun). The use of it CAN be done if one uses 'absolutes' but people interpret this concept in worse defiance than your point. That is, you CAN define everything as 'absolutely unique', but as soon as I use any language, like English here, to set up the colloquial part of explaining the theory/system, you are forced to use the 26 letters of the alphabet in which the argument could only use each letter once. That would be 26 letters maximum to explain the whole system!

Those main 'laws of logic' are about the language we use to express the meaning of identity only. Otherwise you can only mention the term exactly once (as an 'absolute' instance) and just PRAY that others could somehow intuit what you mean by mere chance.

The better way is to permit a class of 'variables' that have NO direct meaning as containers of particular concepts to refer to WHAT the variables MEAN, not their literal symbols. As such, a set theory type of expression of identity is their, "Postulate of 'extenstion'" ["extension" referring to the nature of the symbols to EXTEND to the meaning, beyond the symbol, just as our senses act as symbols of reality EXTERNAL to ourselves.] Here is an example of their first postulate (of most if not all systems of set theories):

(A = B) means identically that ((Given x is any element of A, that has the same element in B) AND [also that](Given y is any element of B, that has the same element in A))

This keeps the variable's distinct in a relatively 'absolute' way, that DEFINES the meaning of the equal sign, "=". But notice the repetition of the symbols cannot be avoided regardless. This particular set theory definition does this to clarify that the meanings of A and B refer to their contents or members, not the symbol as a whole class.

Now, if you still disagree, I can only ask if YOU can express any logical system that improves upon these. And, as I've asked before of others, can you define ANY system without reference to the postulated "laws of logic" referring to the meaning of "consistency, inconsistency, and contradiction"? All we need is one clear example that cannot be confusing.
1. False, one word can have a variety of meanings thus subjecting it to equivocation. Your answer of A=B shows the repetition of underlying sub variables which leaves "=" as undefined. "=" can only be defined through repetition where "= p =" is necessary for "=" to having any underlying identity.

2. As to the logical system: viewtopic.php?f=26&t=30276
Like I asked Skepdick, show me a system with postulates. But I see you attempt to at the above link but I cannot make sense of your own language or meaning in the OP to bother without alot more questions, like, for instance, what is 'context' to you? What does "all is context" mean when the term itself is specifically our word to mean something like, "the circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed."

You likely use context to mean, "the parts of something written or spoken that immediately precede and follow a word or passage and clarify its meaning." But this still is begging given such a definition is not an 'object'. You are likely referring to syntax, which still requires defining the MEANING of your symbols to MAP to defining symbols TO the basic universal logical laws.

Note that I understand the metaproof 'completeness of Propositional logic that begins first by describing HOW the system uses symbols to define what is 'well-formed'. This then gets mapped to truth tables that simply list all POSSIBLE sets of binary values of which 'true' and 'false' are applied. What it does NOT do is to interpret the propositions as these provide the literal meaning.

The question here is whether you can express a metalogic that can be 'complete' and 'consistent'. But, like me arguing with Skepdick, who assumes that ANYTHING goes, you are missing that the system has to at least have some meaning of 'identity', not that you CAN use arbitrary symbols and syntax to describe your system. That is, how can you have a system that has no meaning to 'identity' without losing sense to the meaning of even the user of your system to follow your expected rules 'consistently'? You would fail on your first 'rule' for the fact that rules are "a set of CONSISTENT behaviors expected of those agreeing to abide by them. What could be your 'first rule' to beg the system has no identity?

Rule 1 example: there is no such thing as 'consistency' ....no such thing as 'identity'. Then there should be no reason for anyone to play the game unless the game is merely be randomly do anything you want regardless of rules.
The identity of a context is that which points to phenomenon. As such a context such as (P) derives its identity by pointing to said phenomenon such as a "cat" or "house". Under these terms the variation of one context to another such as "blue house" as "((H)B)" is the direction of one context to another. A statement such as "The cat ate the bird" observes one context "cat" directed to another context "bird" through another context of "ate". One context is directed to another through a medial context which directs them: ((C)A-->)(B). It is through the directing of one context to another that contexts multiply, ie "cat" and "bird" (C)(B), allowing for a contrast to occur which allows for definition.
Scott Mayers
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Re: What is P and -P?

Post by Scott Mayers »

Eodnhoj7 wrote: Mon Feb 01, 2021 7:00 pm
The identity of a context is that which points to phenomenon. As such a context such as (P) derives its identity by pointing to said phenomenon such as a "cat" or "house". Under these terms the variation of one context to another such as "blue house" as "((H)B)" is the direction of one context to another. A statement such as "The cat ate the bird" observes one context "cat" directed to another context "bird" through another context of "ate". One context is directed to another through a medial context which directs them: ((C)A-->)(B). It is through the directing of one context to another that contexts multiply, ie "cat" and "bird" (C)(B), allowing for a contrast to occur which allows for definition.
You still use 'context' oddly for me. I understand you referencing what I learned as "denotation", the process of associating a symbol to something in reality by literally pointing to it as you present a coinciding word vocally, or written, or some other communication symbol, like how we learn this as a child.

Note that you appear to be setting up syntax/grammar rules or are assuming them understood. I don't know unless you explicitly spell out what is a 'well-formed' set of formulas based upon a step by step procedure that I can first learn to interpret your symbols. You need to first assert what is a minimal well formed literal/symbol, then express step-by-step how the other symbols in sequence are to be acceptable in a fixed way.

Example,

If we symbolize "wff" for "well-formed forumula", then here is the syntactical expression setting up Propositional Calculus (by E.J. Lemmon's text, "Begginning logic"):
(a) any propositional variable is a wff;
(b) any wff preceded by '-' is a wff;
(c) any wff followed by '→' followed by any wff, the whole enclosed in brackets, is a wff;
(d) like (c), with '&' replacing '→';
(e) like (c), with '∨' replacing '→';
(f) like (c), with '↔' replacing '→';
(g) if a formula is not a wff in virtue of clauses (a)-(f), then it is not a wff.
This example enables you to first spell out which symbols are allowed in the system and which, given ANY random ordering of your set of symbols defines a 'forumula', which ones are the fixed ones that define the syntax and grammar of a full statement.

Regardless, I have lost my appetite for debating on these issues because I don't believe others here share the same minimal background that I take for granted and spent a lot of energy learning. Your link appears to be intending to set up a syntax prior to postulates. This is fine but it is not clear enough for me. Then, you'd require setting up postulates of the system that interpret MEANING to the symbols that map to real life comparisons and operations. [I see you were sort of trying that above.]

Good luck. I can look at what you could present but am not going to promise feedback or debate. I am burnt out trying to speak of my own thinking that I cannot get agreement on of the basic foundations for the meaning of 'logic' rather than 'random' non-consistent forms of expressing thought that are unable to have any fixed meanings without. [not necessarily about you here if you know what I mean :wink: ]
Eodnhoj7
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Re: What is P and -P?

Post by Eodnhoj7 »

Scott Mayers wrote: Tue Feb 02, 2021 5:56 am
Eodnhoj7 wrote: Mon Feb 01, 2021 7:00 pm
The identity of a context is that which points to phenomenon. As such a context such as (P) derives its identity by pointing to said phenomenon such as a "cat" or "house". Under these terms the variation of one context to another such as "blue house" as "((H)B)" is the direction of one context to another. A statement such as "The cat ate the bird" observes one context "cat" directed to another context "bird" through another context of "ate". One context is directed to another through a medial context which directs them: ((C)A-->)(B). It is through the directing of one context to another that contexts multiply, ie "cat" and "bird" (C)(B), allowing for a contrast to occur which allows for definition.
You still use 'context' oddly for me. I understand you referencing what I learned as "denotation", the process of associating a symbol to something in reality by literally pointing to it as you present a coinciding word vocally, or written, or some other communication symbol, like how we learn this as a child.

Note that you appear to be setting up syntax/grammar rules or are assuming them understood. I don't know unless you explicitly spell out what is a 'well-formed' set of formulas based upon a step by step procedure that I can first learn to interpret your symbols. You need to first assert what is a minimal well formed literal/symbol, then express step-by-step how the other symbols in sequence are to be acceptable in a fixed way.

Example,

If we symbolize "wff" for "well-formed forumula", then here is the syntactical expression setting up Propositional Calculus (by E.J. Lemmon's text, "Begginning logic"):
(a) any propositional variable is a wff;
(b) any wff preceded by '-' is a wff;
(c) any wff followed by '→' followed by any wff, the whole enclosed in brackets, is a wff;
(d) like (c), with '&' replacing '→';
(e) like (c), with '∨' replacing '→';
(f) like (c), with '↔' replacing '→';
(g) if a formula is not a wff in virtue of clauses (a)-(f), then it is not a wff.
This example enables you to first spell out which symbols are allowed in the system and which, given ANY random ordering of your set of symbols defines a 'forumula', which ones are the fixed ones that define the syntax and grammar of a full statement.

Regardless, I have lost my appetite for debating on these issues because I don't believe others here share the same minimal background that I take for granted and spent a lot of energy learning. Your link appears to be intending to set up a syntax prior to postulates. This is fine but it is not clear enough for me. Then, you'd require setting up postulates of the system that interpret MEANING to the symbols that map to real life comparisons and operations. [I see you were sort of trying that above.]

Good luck. I can look at what you could present but am not going to promise feedback or debate. I am burnt out trying to speak of my own thinking that I cannot get agreement on of the basic foundations for the meaning of 'logic' rather than 'random' non-consistent forms of expressing thought that are unable to have any fixed meanings without. [not necessarily about you here if you know what I mean :wink: ]
There is no set agreement upon what logic is or is not, as best logic is descriptive thus any system of logic is descriptive by nature.

1. "(X)" represents any assertion such as "cat" or "dog", this assertion is a context.

2. ((X)Y) represents any context as defined by another context such that the context is a part of another context, this included modalities. A "blue house" would be described as ((H)B).

3. (X)(Y) represents the multiplication of one context to another where one context changes to another. "The cat ate the food" would be described as (C)(F).

4. ((X)Y-->) observes the transference of one context to another through a medial context of "Q". "The cat ate the food" would be described as ((C)A-->)(F).

5. (X,Y) observes the "and" function such as "The cat and dog ate the food" and would be described as ((C,D)A--->)(F). This "and" function applies to addition as well.

6. ((X))((Y)) observes the "or" function such as "The cat or the dog ate the food" and would be described as ((((C))((D)))A--->)(F)

7. (X)<-->(Y) observes "if" function such as "The cat ate the food if the cat is full" and would be described as (((C)A-->)(F))<-->((C)F)
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