What LEM is not

[Skepdick]

On top of making too many mistakes when it comes to very basic things, you also happen to be quite arrogant. That makes it rather difficult to have a fruitful conversation with you. And that is why I asked you to leave this thread. Yet, here you are, complaining about other people not thinking like you, presupposing that you're the one who knows it the best.

I have absolutely no idea what is "best". But I know what isn't even in the running for "best" - self-contradictory principles.

At this point, you're doing nothing but repeating yourself, i.e. restating your disagreements, without adding anything of substance.

Your inability to digest the substance doesn't mean there isn't any.

That's like saying that, if "x" is "2", then "x" is ONLY "2" and nothing else.

No, It's like saying "2 is either 1 or 2". It's not either 1 or 2. It's 2.

Note the term "even number" is synonymous with "either 2 or 4 or 8 and so on". In fact, all other terms have this "either/or" form.

You don't even understand what forms are. Forms contain free variables. There are no relevant free variables in tautologies.

It's exactly the same thing as Skepdick being a being, a living being, a human being, a male, a forum member and so on.

You really are trying too hard.

Nah. It's a definition. It presupposes nothing.

And your definition is self-contradictory. Which makes it a silly definition.

These are some circular definitions.

They aren't even definitions. They are pointing out the the boundaries between conceptual distinctions.

[Magnus Anderson]

Your inability to digest the substance doesn't mean there isn't any.

You're fortunate that I currently have patience to deal with your stubbornness. In any other situation, I'd simply ask you to leave ( or report you to moderators, assuming they are doing their job. )

Simply reasserting your conviction is NOT substance. A substance would entail an actual explanation as to why you're right and / or why the other person's argument is flawed. You haven't done any such thing in your previous post and it's an objective thing that anyone can see for themselves.

No, It's like saying "2 is either 1 or 2". It's not either 1 or 2. It's 2.

See? You're just repeating yourself, forcing me to do the same myself.

If you have nothing to add, go away.

[Skepdick]

Simply reasserting your conviction is NOT substance. A substance would entail an actual explanation as to why you're right and / or why the other person's argument is flawed. You haven't done any such thing in your previous post and it's an objective thing that anyone can see for themselves.

Sure... Here is the substance.

To deny this would be to say that P is BOTH not true AND not not true. And that is a contradiction.

I am not denying LEM. I am provisionally accepting it AND .... applying it to itself.

Therefore either LEM is true or it is false.

If you are insisting that LEM is ALWAYS true; then you are contradicting "For every proposition P, either P is true or it is false.".
A statement that is ALWAYS true is never "either true or false".

LEM with unary truth-value contradicts LEM with a binary truth-value.
If LEM asserts that ANY proposition P, P is either true or false; THEN LEM is false. Because LEM itself fails to satisfy "either true or false"
If LEM asserts that for SOME (but not ANY; and not ALL) propositions P, P is either true or false; THEN LEM is true.

If LEM is not true; then LEM is false (by LEM itself).
Therefore LEM is false.

Proof of negation Q.E.D

It's probably fair to say you are incapable of recognizing substance.

[Magnus Anderson]

Here is the substance.

And I responded to that post of yours.

The entire post is based on the mistaken notion that if a proposition is "true" then it is necessarily not "either true or false".

And I explained why it's mistaken. I explained what the term "either true or false" actually means thereby making it apparent that it is not incompatible with "true" and "false".

LEM is both "true" and "either true or false".

In the same exact way that if "x" is "2" then "x" is both "2" and "an even number".

There is nothing contradictory about these two statements.

[godelian]

This is only possible if the well-formed sentence has unique readability, which allows us to syntactically determine from its parse tree if this sentence is a legitimate proposition. We do not need to know what the symbols refer to.

So if I say "Mxcvn is prlsz", you do not have to understand the meaning that I assign to the symbols "mxcvn" and "prlsz" in order to evaluate the truth value of that statement?

You don't have to understand it in order verify that it is a legitimate proposition or not.You do need to understand it to evaluate its truth value.

Similarly, it is enough to compile a program to verify that it is a legitimate program. You do not need to run the program for that.

Example:

Code: Select all

var a=5
var b=0
var c=a/b

This is a legitimate JavaScript program. You don't need to run this program to determine that.

When you run it, it will yield a "division by zero" error. However, the fact that running this program will lead to runtime errors does not make it an non-program.

Similarly, the fact that a proposition is undecidable does not turn it into a non-proposition

[Magnus Anderson]

You don't have to understand it in order verify that it is a legitimate proposition or not.You do need to understand it to evaluate its truth value.

Similarly, it is enough to compile a program to verify that it is a legitimate program. You do not need to run the program for that.

Example:

Code: Select all

var a=5
var b=0
var c=a/b

This is a legitimate JavaScript program. You don't need to run this program to determine that.

When you run it, it will yield a "division by zero" error. However, the fact that running this program will lead to runtime errors does not make it an non-program.

Similarly, the fact that a proposition is undecidable does not turn it into a non-proposition

That depends on the definition of the word "proposition". And as I said previously, the only definition that matters is the one used by the author of LEM ( since we're talking about LEM here. ) As such, how mathematicians define the term is irrelevant.

In the context of LEM, a proposition is an idea that a portion of reality is such and such. It must consist of the following two components: the subject and the predicate. If at least one of the two components is missing, it's not a proposition.

[godelian]

That depends on the definition of the word "proposition". And as I said previously, the only definition that matters is the one used by the author of LEM ( since we're talking about LEM here. ) As such, how mathematicians define the term is irrelevant.
In the context of LEM, a proposition is an idea that a portion of reality is such and such. It must consist of the following two components: the subject and the predicate. If at least one of the two components is missing, it's not a proposition.

Your view on the matter is incompatible with modern logic:

https://en.wikipedia.org/wiki/Proposition

In modern logic, the term "proposition" is often used for sentences of a formal language. In this usage, propositions are formal syntactic objects which can be studied independently of the meaning they would receive from a semantics. Propositions are also called sentences, statements, statement forms, formulas, and well-formed formulas, though these terms are usually not synonymous within a single text.

A formal language begins with different types of symbols. These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants.(Grouping symbols such as delimiters are often added for convenience in using the language, but do not play a logical role.) Symbols are concatenated together according to recursive rules, in order to construct strings to which truth-values will be assigned. The rules specify how the operators, function and predicate symbols, and quantifiers are to be concatenated with other strings. A proposition is then a string with a specific form. The form that a proposition takes depends on the type of logic.

The reason why modern logic rejects your view, is because it is simply unsustainable. No formal system can function in the way that you propose. Such system would be utterly unusable if it tried. That is why a proposition is defined in modern logic as a "formal syntactic object", while every syntactically valid sentence of the designated form is a proposition in the formal language.

You can try to overrule the conclusions that necessarily follow from mathematics, but you will inevitably fail. There is no academic discipline that tries to do that, because doing so is a hopeless endeavor.

[Skepdick]

Here is the substance.

And I responded to that post of yours.

The entire post is based on the mistaken notion that if a proposition is "true" then it is necessarily not "either true or false".

And your entire post is based on the mistaken notion that if the value of a number is 2 then it's also either 1 or 2.

And I explained why it's mistaken. I explained what the term "either true or false" actually means thereby making it apparent that it is not incompatible with "true" and "false".

And I explained why it's mistaken. I explained that the value of number 2 is incompatible with being either 1 or 2.

LEM is both "true" and "either true or false".

Truth is both true and either true or false.
The number 2 is both 2 and either 1 or 2.

In the same exact way that if "x" is "2" then "x" is both "2" and "an even number".

There's your confusion. You are conflating the various types of number 2 with the value of number 2.

The VALUE of 2 is 2.
The TYPE of of the VALUE 2 is a number; and an even number; and a number greater than 1; and a number smaller than 3...

There is nothing contradictory about these two statements.

The contradiction is precisely in insisting that the VALUE of 2 is either 1 or 2. It's VALUE is only 2. Always.

Your idiocy amounts to claiming that Truth is either true or false. Truth is true.
The TYPE of a truth-value is Boolean truth.

[Magnus Anderson]

The VALUE of 2 is 2.
The TYPE of of the VALUE 2 is a number; and an even number; and a number greater than 1; and a number smaller than 3...

You probably meant to say that the value of "x" is "2" and that the type of "x" is "an even number".

That's all true but it's irrelevant as it does not contradict anything that I'm saying.

The contradiction is merely asserted by you. So far, it hasn't been proven at all.

You just have to understand how language in general works and forget about programming for a second ( you do seem quite obsessed with it, making it difficult for you to think outside of that narrow subject. )

In general, when we say "X is Y" we're saying that whatever is represented by X can also be represented by the symbol Y; or in other words, that it belongs to the class denoted by the symbol Y.

That's why it's true that Skepdick is a man even though the word "man" is denoting a class rather than a specific instance of that class.

That's why it's true that the number 2 is an even number even though the term "even number" is denoting a class rather than a specfic instance of that class.

That's also why it's true that a proposition that is true ( "truth" ) is either true or false even though the term "true or false" is denoting a class, a set of consisting of two elements, true and false, rather than a specific instance of that class, a member of that set, a value such as "true" and "false".

It seems like your obsession with programming has corrupted your mind.

[Skepdick]

You probably meant to say that the value of "x" is "2" and that the type of "x" is "an even number".

No. The TYPE of "x" is a variable. The VALUE assigned to "x" is 2. The TYPE of the VALUE assigned to "x" is "an integer"; and an "even number" and a "number greater than 1" and "a number less than 3".

That's all true but it's irrelevant as it does not contradict anything that I'm saying.

You are literally equivocating. The TYPE of LEM is a proposition.
The VALUE of LEM is false, because NOT ALL Propositions are either true or false.
SOME Propositions are JUST True. e.g LEM is JUST True.
SOME Propositions are JUST False. e.g 1+1=3 is JUST False.

The contradiction is merely asserted by you. So far, it hasn't been proven at all.

P1. ALL propositions are eIther True or False
P2. LEM is a proposition.
P3. LEM is JUST True - LEM is not True; OR False.
C. Contradiction

You just have to understand how language in general works and forget about programming for a second ( you do seem quite obsessed with it, making it difficult for you to think outside of that narrow subject. )

You just have to understand how thinking in general works and forget about language for a second (you do seem quite obsessd with it, making it difficult for you to think outside of that narrow subject.)

In general, when we say...

I don't care what you SAY. I am talking about thinking not speaking.

"X is Y" we're saying that whatever is represented by X can also be represented by the symbol Y; or in other words, that it belongs to the class denoted by the symbol Y.

1000 points for irony. If you are talking about denotation and symbols representing things - you are talking about programming. That's a very narrow subject.

That's why it's true that Skepdick is a man even though the word "man" is denoting a class rather than a specific instance of that class.

You are perpetually confused between the abstract classes and the concrete inhabitants of abstract classes.

Is Magnus Anderson either a man or a woman; or is Magnus Anderson just Magnus Anderson?
Is Magnus Anderson either a human or an animal; or is Magnus Anderson just Magnus Anderson?

You are also perpetually confused about identity.

Is Magnus Anderson either Magnus Anderson or Skepdick; or is Magnus Anderson just Magnus Anderson?

That's why it's true that the number 2 is an even number even though the term "even number" is denoting a class rather than a specfic instance of that class.

Q.E.D You are perpetually confused between identity (2 is 2 is 2); and 2's membership in the abstract class of "even numbers".

That's also why it's true that a proposition that is true ( "truth" ) is either true or false.

So it's true that Magnus Anderson either Magnus Anderson or Skepdick

It seems like your obsession with programming has corrupted your mind.

Irony level - infinite.

ALL Programming languages (modern Mathematics included) are founded on LEM.

I am human, not a machine.

[Magnus Anderson]

No. The TYPE of "x" is a variable. The VALUE assigned to "x" is 2. The TYPE of the VALUE assigned to "x" is "an integer"; and an "even number" and a "number greater than 1" and "a number less than 3".

That seems to be correct. In my own language, we use the terms "variable type" and "data type" interchangeably. Unfortunately, that led to a confusion.

You are literally equivocating. The TYPE of LEM is a proposition.
The VALUE of LEM is false, because NOT ALL Propositions are either true or false.
SOME Propositions are JUST True. e.g LEM is JUST True.
SOME Propositions are JUST False. e.g 1+1=3 is JUST False.

As I said, your obsession with programming languages is blinding you.

Try to understand how natural languages work for once.

Let me show you.

Since you're fanatical about programming, let's take this piece of code.

Code: Select all

uint32 x = 100;

Consider the following statements about the above and check which ones are true and which ones are false.

1. The data type of "x" is "uint32".

2. The type of value stored by "x" is a number.

3. The type of value stored by "x" is an even number.

4. The type of value stored by "x" is a power of 10.

5. The value of "x" is "100".

6. The value of "x" is a number.

7. The value of "x" is an even number.

8. The value of "x" is a number that is a power of 10.

Are you going to deny 6, 7 and 8?

If so, that would indicate that you have serious issues with natural languages ( as I've been suspecting for a very long time. )

Make sure you do not equivocate between the two different senses of the word "value", the programming sense and the everyday sense. Focusing too much of one's attention on programming can do that to one's brain.

P1. ALL propositions are eIther True or False
P2. LEM is a proposition.
P3. LEM is JUST True - LEM is not True; OR False.
C. Contradiction

You're pointlessly repeating yourself.

You just have to understand how thinking in general works and forget about language for a second (you do seem quite obsessd with it, making it difficult for you to think outside of that narrow subject.)

Language is the foundation of thinking. No language, no thinking.

But not programming language.

1000 points for irony. If you are talking about denotation and symbols representing things - you are talking about programming. That's a very narrow subject.

Not true at all.

[Magnus Anderson]

Me playing Skepdick's advocate with Chat GPT.

Consider this piece of code:

Code: Select all

uint32 x = 100;

Is the following statement about it true?

The value of "x" is an even number.

Yes, the value of x is 100, which is an even number. So, the statement is true.

Isn't that a contradiction? How can the value of "x" be both "100" and "an even number"?

There is no contradiction here because the value "100" is being described in two different ways:

1) "100" is the specific numeric value assigned to x.
2) "Even number" is a property of the value 100, meaning it is divisible by 2 with no remainder.

So, the value of x is 100, and 100 happens to be an even number. These are just two ways of characterizing the same quantity.

But the value of "x" isn't "even number"! That's not a legitimate uint32 value!

You're right! The value of x is specifically the number 100, and not the phrase "even number." The phrase "even number" is merely a description of a property of the value 100, not the value itself.

In a uint32 variable, the value must always be an actual number, not a descriptive label like "even number." The statement "the value of x is an even number" just means that the specific value 100 has the mathematical property of being even.

So, to clarify:

The value of x is 100 (a legitimate uint32 value).
100 is an even number, which is a true fact about that value, but not the value itself.
No contradiction exists, since "even number" is just a description of the value's properties.

Idiot!

I apologize if my response wasn't clear enough. Let me know how I can better explain it!

[Skepdick]

As I said, your obsession with programming languages is blinding you.

Try to understand how natural languages work for once.

Extra points for irony!

Let me show you.

Since you're fanatical about programming, let's take this piece of code.

Code: Select all

uint32 x = 100;

Now do

Code: Select all

bool x = false

Is false either true or false?

Consider the following statements about the above and check which ones are true and which ones are false.

1. The data type of "x" is "uint32".

2. The type of value stored by "x" is a number.

Contradiction. The VALUE stored by "x" (100) is a uint32.

A uint32 can be used to represent SOME numbers.
A uint32 can't be used to represent ALL numbers.

3. The type of value stored by "x" is an even number.

The TYPE of value stored by "x" is a uint32. The PARITY of the VALUE (100) stored in the VARIABLE "x" of TYPE uint32.
When the uint32 is interpreted as an number - the parity of that number is "even".

4. The type of value stored by "x" is a power of 10.

The TYPE of value stored by "x" is uint32. The VALUE (100) stored in the VARIABLE "x" of TYPE uint32.

When the uint32 is interpreted as an number - that number is a power of 10.

5. The value of "x" is "100".

Wow! One correct statement!

6. The value of "x" is a number.

No, it's not. The value of "x" is uint32. It can be interpreted as a number.

7. The value of "x" is an even number.

The value of the uint32 100 (when interpreted as a number) is even.

8. The value of "x" is a number that is a power of 10.

The value of the uint32 100 (when interpreted as a number) is a power of 10.

Are you going to deny 6, 7 and 8?

You are denying 2's identity by insisting 2 is either 1 or 2.

Make sure you do not equivocate between the two different senses of the word "value"

The "two senses" are the exact same sense. The Axiological sense. Values are valuable.

Language is the foundation of thinking. No language, no thinking.

That's not true. Language is just an expression of thought. Language is not thought. Language proceeds from thoght.

No thinking - no languguage

But not programming language.

In ANY language. Including programming language.

1000 points for irony. If you are talking about denotation and symbols representing things - you are talking about programming. That's a very narrow subject.

Not true at all.

The irony continues.

[Magnus Anderson]

That's not true. Language is just an expression of thought. Language is not thought. Language proceeds from thoght.

And that's the crux of your problem -- a lack of appreciation for the fact that language is at the foundation of all thought, i.e. that there can be no thought without language.

You constantly misinterpret.

[Magnus Anderson]

Contradiction. The VALUE stored by "x" (100) is a uint32.

That's what was said. The value assigned to the variable "x" is of data type "uint32". So you actually agree and are merely looking for reasons to disagree.

A uint32 can be used to represent SOME numbers.
A uint32 can't be used to represent ALL numbers.

True but irrelevant. The claim is that the value assigned to the variable "x" is an even number. The assigned value is 100. 100 is an even number. Therefore, it is true.

6. The value of "x" is a number.

No, it's not. The value of "x" is uint32. It can be interpreted as a number.

The value of "x" is 100. 100 is a number. Therefore, the value of "x" is a number.

You are denying 2's identity by insisting 2 is either 1 or 2.

I am not.

The fact that you're a memeber of a group such as the set of all human beings that are currently alive or the set of all human beings that can be conceived does not deny your individuality.

The "two senses" are the exact same sense. The Axiological sense. Values are valuable.

You're missing the point ( as you usually do in your efforts to disagree at all costs. )

The point is that when we say that the value of the variable "x" that I previously declared is "either 100 or 1000", we're not saying that its value is a category that is "either 100 or 1000". We're merely saying that its value, which is 100, belongs to the category that is "either 100 or 1000", i.e. it's one of the elements of that set.

How many more silly objections do I have to address before you finally decide that this is leading nowhere and that you should leave this thread alone ( since you won't do it on your own after being asked so many times )?