1 = 1 is true from the definition of equality

1 + 1 = 2 is true from the definition of 2

@JohnDvorak 1=0 is true in Z/Z the fields of one element

so?

challenge this idea, propose a theory which for you it don't have a model

1 = 1 is true in every field, and 1 != 1 is false in every field

Z/Z is generally considered not a field, because all sorts of things break in it

the symbole 1 in the first place in the line is 1, and second is for 2,

so 1!=1

like 1!=2

got to go, sorry, I have to walk my fish

This statement is undecided, if not false.

@Dattier Well, if you change what symbols mean, of course you can make any statement true or false.

@Deusovi 1=1, 1!=1

@JohnDvorak I mean, if you change "!=" to mean "is the same thing as", then it's going to be true, no?

He have give a symbol and don't say how interpret it, so I propose in the model an interpretion,

oh.

What I was trying to say was that changing what symbols mean changes the statement.

A statement is not a set of symbols. That's just how we represent a statement.

^

If you can make things mean whatever you want, then of course anything can be true or false. But that's not useful.

Well, what is the mean of 1!=1 ?

in english

without symbole

One factorial equals one.

what's a factorial ?

Do you agree with this sentence (flase without model for you) : one stone in bag don't stay one stone in bag ?

for positive integers, it's the product of all integers from one to that number

for zero, it is defined as 1

Walking fishes it is

do you agree with this sentence :

this sentence (flase without model for you) : one stone in bag don't stay one stone in bag

a stone is a stone, a bag stay a bag

I don't understand what you're trying to say.

if you put one stone in a bag, the same bag Which you do not remove, remains with one stone

Are you agree ?

@Deusovi @JohnDvorak

I don't understand how this is relevant or why you're asking it here.

so the negation have no model, for you

yes ?

It depends on what you mean by "model". (For example, what if there's a hole in the bag?)

still walking fishes

If you allow reinterpretation like this:

then you can make any statement true or false.

How is this relevant, though? And why are you asking it here?

No, the bag is without hole

because it's like an enigma

when you have a theory, which seems without explanation

solve the enigma is give a model

If you define "give a model" as "reinterpret the sentence however you want", I fail to see the purpose.

Not exactly, give a context where the sentence is true

like the enigma

Your "context" seems to be a "reinterpretation" in the message above.

@Deusovi a context, when you give only symbol, the context is an interpretation of this symbol

Words are just a sequence of symbols, too.

yes, but there have an interpretation a meaning

And so do the symbols used in mathematics.

so what's the meaning of 1!=1 ?

in mathematics

It means "the factorial of the number 1 is equal to the number 1 itself".

(Or, if you're using "!=" as a replacement for the ≠ symbol, it means "1 is not equal to 1", a false statement.)

I don't is not my challenge, @JohnDvorak what's the meaning ?

I don't understand what you mean.

Still walking my fishes, sorry

so choose @Deusovi

The original statement was that the statement "1 is not equal to 1" is false in every field.

The schyzo-field between Z/Z={0,1} and Z/2Z={0,1}

in the first 0=1 (Z/Z), in the second 1!=0 (Z/2Z)

when the second is even Z/2Z

In the meantime, here is some nightmare fuel for those who want to learn about a really creepy mushroom: en.wikipedia.org/wiki/Clathrus_archeri and commons.wikimedia.org/wiki/Clathrus_archeri

but it's a model

@Dattier That's not a field.

why ?

It's not even consistent with itself.

It doesn't follow the field axioms.

Equality is reflexive by definition: that is, x=x. There is no equality in that "schizo-field".

is not an axiome of fields

what have I walked in on

No, equality needs to be established before you can even define a field.

@Rubio Me trying to explain that "1=1 can be false because you interpret the second 1 as a 2" is ridiculous.

we have the instantaneous egality

I propose that this discussion be moved to a separate room.

If that happens, feel free to trash my mushroom.

@Dattier You have to rigorously define that. That's not a concept that makes sense. Mathematics has no idea of "time" other than as a variable used to parametrize something.

find a context, is explain an enigma

I propose that this discussion be moved to a room under a different stack where it's, perhaps, "on topic".

Philosophy?

@Rubio I mean, this is just "general discussion", so pretty much anything is on topic. But I don't think this conversation is getting anywhere, nor is it useful.

I propose that @Dattier implements his ... mathematical structure ... in Haskell. Then we can talk about its properties.

What are you even talking about?

It feels more meta than actual rigorous logic. There may be a place where the denizens are able and interested in discussing ... unusual ... premises in propositional logic, but I don't think P.SE is going to be that place.

@Deusovi what do you want rigoursly define ?

the instantaneous egality ?

← 99 messages moved from The Sphinx's Lair

@Dattier Yes, along with the "schizo-field" and everything you've made up so far.

I don't think "instantaneous egality" obeys the axioms of equality.

in the first time I propose to challenge this affirmation, all theory have a model

so @John propose a field where "1 not equal to 1"

@Dattier ...What?

sorry, I rember the context

of my intervention

"I don't think "instantaneous egality" obeys the axioms of equality."

yes, the hipothesis is necessary, unless the identity is not true

fo exemple "Felix is ​​a live cat so felix is ​​a live cat" is not true

because if when I read the "so" Felix dead (I d'on't suppose the instantaneaous

Why not?

So the logic is not valid

You need A imply A

But "Felix is a live cat" is not a proposition. "Felix was a live cat at 1:00 PM, Sunday, August 27, 2017" is a proposition. But things that change over time are not propositions (unless you include an implied "at the time of this statement").

I have to go prune and water my cat

But in the logic you want do that with all sentence with not auto-refrence

A imply A

When I give an theorem, I don't say, it's true for the 27 August 2017

Mathematical theorems are abstract statements and don't depend on time.

But if a statement does depend on time, you need to specify the time.

Yes the logic too

why you don't give the position gps, the pressure, the temperature...

that's depend of that too

No, it doesn't. You can't be "alive at one temperature and dead at the same time, but at a different temperature".

If a statement depends on something, then you need to give that for it to be 100% true or 100% false.

For example, if you say "it is day outside", you have to give a location for the statement to be true or false.

I am persuaded that it is only a matter of imagination

Have enough imagination

That's only true if you think words and symbols don't have any meaning. But if you do think that, there is no point discussing this further.

formal logic, by definition, requires formality, not unspecified information left to subjective interpretation (let alone imagination)

for prove that I want to prove

all theory have a model

if you want to discuss this, you can't call it what you're calling it. the words you're using have an established meaning that you're intentionally not using, making this not a meaningful conversation; there's no common language and framework when you're using the same terms others use to mean specific things, but using them in novel and unexplained ways. this is a recipe for frustration and confusion on everyone's part, not the reasoned discourse I certainly hope you were seeking.

I have re-find a reasoning without rules, axioms or principle

The empirsm reasoning

If you have no rules, principles, or axioms, then you have no meaning. If you have no meaning, then conversation cannot happen.

then don't couch it in the vocabulary and framework of a system that not only has, but is intrinsically built on, rules, axioms, and principles.

I'm not interested in discussing this further if you do not want to talk about things with actual meaning.

no, there are meaning, the reasoning is build on definition

The universal affirmation A is conjecturally correct (EC) if A admits at least 10 examples and no known counterexamples.

well, thanks and bye

the title makes this sound like a talk show i would actually watch. xD

and now, reading through it, it probably is