Mathematics for the sciences? — keystone

Yes, from the axioms of set theory, we derive the theorems of calculus.

I'm working in Hilbert's fictional realm. — keystone

Set theory is abstract. It doesn't have hotels. To be more exact, I should say that from an imaginary analogy to set theory, you impose an incoherent interpretation. It's incoherent because you start out by describing a program to output values (presumably in a certain order) but it's not a program.

I exhausted loads of my time and patience with Thomson's lamp with you. You're making a variation of the same mistake here.

Printing it early is no trick.

the program has value even though we cannot literally go the limit. — keystone

".89[...]" is notation for a limit. And that limit is .9. And ".9[...]' is also notation for a limit. .9[...] = 1.

You don't like that mathematics for the sciences doesn't comport with your understanding of impossible fictional realms. Yeah, that's a real dagger in the heart of the mathematics for the sciences.

eventually output a 1 — keystone

Then it will miss outputting one of the 9s.

You can't have cake and eat it too.

If it runs only finitely many steps but outputs the 1, then it skips an infinite number of the 9s.

If it runs without end, then it outputs each of the 9s, but never outputs the 1.

it will never print a 1, but I can still write the program — keystone

You can write whatever you like, but my point, as seen in context, is that it's not a program to print all the entries in the sequence.

Consider the ascending sequence of members of w+1 (omega plus one). That is a denumerable sequence with a last entry. But there is no program to write all the entries in that ascending order. On the other hand, it's trivial to have a program write:

1, 1/2, 1/4 ...

while 0 is not an output.

That's just a starker example of what you're doing. Yes, it's a program, and it outputs every successive halving. But 1 is not an output of the program.

He’s referring to the halting problem in relation to turings complete machine — Deus

No he's not. The halting problem is not that there are programs that don't halt. But rather that there is no program to decide whether any given program and input will halt.

You don't know what you're talking about. You're just throwing out red herrings. A form of trolling.

a teetotaller abstains from drinking on all occasions apart from when he unknowingly drinks alcohol because his wife can’t be trusted. — Deus

Depends on the exact interpretation of a given definition. If taken literally in the sense of 'practices complete abstinence' then drinking alcohol even inadvertently makes one no longer a teetotaler at that moment. But I grant that ordinarily, probably most people wouldn't regard that as failure to maintain being a teetotaler; and I overlooked that possible situation. So, I'll give you not a full point for that one, but at least most of a point.

I can certainly write a program to output digits corresponding to 0.89[...]1. It's just that that program can never be executed to completion so it would never reach a moment where it would output a 1 digit. — keystone

Whatever you have in mind, it's not a program. If P is a program to print the entries in a denumerable sequence, then for each entry, there is step at which that entry is printed.

As in other threads, you're using technical sounding verbiage without regard for making sense with it.

Do you claim that teatotallers are not drunktrollers ? — Deus

The word is 'teetotaler'. No teetotaler is drunk, therefore no teetotaler is both drunk and a troller.

I didn't assume anyone is drunk.

Refer to the subject of non-standard analysis in mathematical logic (starting with Abraham Robinson), or, with a different method, internal set theory. You may consult many a book or article. Probably many articles on online.

You think it is incorrect to say that no teetotaler is drunk?

A teatotaller <> drunktroller — Deus

I don't know what '<>' is meant to symbolize. If it is for some form of equivalence, it's the opposite of what I said. No teetotaler is drunk.

nor am I interested in debating the validity of non-standard analysis — keystone

Infinitesimals are rigorously handled in non-standard analysis. It's not a question of validity.

I didn't know whether you're talking about yourself or about me. (And I couldn't resist the wordplay.) In any case, if your point is that you're better at least for not being drunk, then congrats.

First you called me a crank troll but in the above statement I’m only referred to as troll. — Deus

Both.

drunk troller — Deus

A teetotaler can't be a drunktroller.

a logician yourself — Deus

I'm not.

The point is not to insult, but rather to flag the situation. Usually cranks are not trolls, since they are sincere, though horribly self-misguided. But I take you as a troll since you don't even offer arguments but just simple flippant nonsense.

'flexible enough', 'deal with operations', 'render useless'.

Not even philosophical, let alone mathematical.

Deus is a crank troller.

Define 'self-limiting theory'.

Okay, I get it. You're trolling.

Proof that 0.89'1 = 0.9 — Real Gone Cat

(Using the apostrophe for '...')

for any x an y,

x'y

doesn't stand for an real number expansion.

In ordinary set theoretic context, there is no object called 'infinity' that is an operand in an addition operation.

♾ — Deus

Is that supposed to be the leminscate?

the countable infinity problem that was proved by Cantor — Deus

What specifically do you refer to ?

guys like Tones — Deus

There's only one.

I noted the first place in your original post that you spouted nonsense. Now you've revised. If I'm in the mood, I'll give you a second chance.

my notation of putting a digit after the repeating term is an interesting way of potentially representing an infinitesimal — keystone

That is more nonsense.

I don't know what that emoji means. I take it though that it doesn't indicate anything substantive.

Just trying to make sense of RAA. — Agent Smith

Just look at the truth table.

Anyway, you didn't use RAA.

Pretty much, you proved P from the premise ~~P. Congratulations. And your point is?

I'll use '*' instead of the overbar.

0.89*1

is not defined.

There is no real number that has an infinite decimal expansion but with a final entry.

Your imaginistic scenario, not even itself approaching a mathematical argument, not even of alternative mathematics, is done. Argument by undefined symbolism is a non-starter.

You are typical of cranks who argue with undefined terminology and symbolisms. Using terminology and symbolisms in merely impressionistic ways.

/

continuously growing but always finite — keystone

On your own finitistic terms, at any point, the sequence is finite. 'continuously growing' is never witnessed. Only finitely many individual finite sequences.

I'm just unsure why you're characterizing modal logic as ones that deal with existence predicates — Kuro

I agreed that existence predicates are handled in systems other than modal logic. And I'm not claiming that every version of modal logic in basic forms includes the advanced subject of an existence predicate.

most modal logics are standardly extensions of FOL with K and some of the additional modal axioms, and therefore do not express nontrivial existence predicates. — Kuro

But in the overall subject of modal logic, we do find a definition an existence predicate. We find that in textbooks such as Hughes & Cresswell (among the preeminent introductions to modal logic) and L.T.F. Gamut. I'm highlighting modal logic for this subject only because one is more likely to encounter a course in, or textbook on, modal logic before some of the other advanced alternative logics.

I have no interest in convincing you or anyone else not to investigate existence predicates in whatever logic systems you or anyone else wishes to study them in whatever order you or anyone else wishes to study them.

/

It's been a while since I studied this, but, if I recall correctly, Hughes & Cresswell and L.T.F. Gamut do define an existence predicate in modal logic that is an extension of classical FOL=. (I'll happily stand corrected though if I my memory is incorrect.)

most logics with existence predicates are not modal — Kuro

But modal logic is the more common one to study than all the others combined. (That's not an argument that modal logic is "better" or anything like that, just that it's natural enough to first turn to modal logic, as a common subject, to see what it offers, while not precluding that the number of other approaches is potentially inexhaustible too.)

Yes, for any rational being it is not plausible that for all q we have Pq -> ~q.

But — Srap Tasmaner

And that 'but' is not going refute that it is not the case that for all q we have Pq -> ~q.

it is also the case that "It might be in the car" implicates (but does not entail) "I don't know for sure where it is" — Srap Tasmaner

No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the car". If I was looking for the book, then I would not appreciate my friend being coy that way, but he would not be logically incorrect.

Or, let 'Kq' stand for 'q is known'. Let 'L' stand for '~K~q'.

For any rational being it is not plausible that for all q we have Lq -> ~q.

Or, let 'Bq' stand for 'q is believed'. Let 'Cq' stand for '~B~q'.

For any rational being it is not plausible that for all q we have Cq -> ~q.

Anyway, the point stands, only a nutcase says that "Possibly the book is in the car" implies that the book is not in the car.

Let's make it a life and death situation:

A young boy is lost in treacherous terrain. The county sheriff's search and rescue expert tells the parents, "Possibly he's in the canyon. So he's not in the canyon." I don't think there is any parent in the world who would say, "Okay, I understand your logic perfectly. Let's not waste time looking in the canyon."

/

Unrelated but poignant is Sartre's "The Wall". SPOILER ALERT. In the Spanish Civil war, Pablo is a prisoner of the fascists. His imprisoners will execute him if he doesn't give up the hiding place of his comrade Ramon. Pablo believes Ramon is not hiding in the nearby graveyard. As a joke on his imprisoners, Pablo lies to them that Ramon is hiding in the graveyard. But Ramon is hiding in the graveyard. And later Pablo learns that Ramon was caught in the graveyard and killed.

"I'm the only one here who is right. Everyone else is wrong. I have an open mind. They don't". Thus spake the crank.

"Possibly P" implies "Not P" — TonesInDeepFreeze

Just to be clear, I don't propose that.

It's not that simple. — Srap Tasmaner

It's simple that the poster is nuts to think that "Possibly P" implies "Not P".

I'm not clear on what you expect to achieve by posting it — Srap Tasmaner

I don't expect to achieve anything other than giving a simple starting point, since there had been confusion in the thread.

You're surely not arguing that someone's intuitions can be refuted by the definitions and axioms we've chosen — Srap Tasmaner

Of course not.

What models? — Srap Tasmaner

Whatever models one likes.

How do you construct them? — Srap Tasmaner

Most formally in the usual methods of mathematical logic and/or formal modal logic. Less formally, in whatever informal way one likes.

I don't think we get to assume this is all settled for natural languages. — Srap Tasmaner

Of course not.

Are you referring to the E formula from FOL= (and similar systems), such that Exists(x) =df ∃y y=x? — Kuro

Of course not. (1) AxEy y=x is a theorem, but I have never seen Ey y=x in FOL= as a definiens for Exists(x). It would be pointless. (2) My point is the opposite: FOL= does not have an existence predicate. (3) Indeed, the "existence predicate" I mean is Exists(x) as in modal logic.

You are talking with a poster not capable of making sense.