Relevant article https://www.jstor.org/stable/40694016?seq=4

I did post proof. But I used my unbounded powers to make Hanover erase my post. Don't ask him however, I erased his memories.

You are correct about his conclusion fitting the present. But this "I" which "is," is not the same "I" as the "I" which was nanoseconds ago thinking. The "I" is successive. Just as there isnt really a linear narrative, there are only successive nows. — ENOAH

For Descartes, ultimately, duration is an attribute of a substance, so it would remain through time; but for him, that is only possible because God allows it. It is a convoluted double cop-out, and the two parts don't seem like they fit here. Which is why I made this thread a while ago https://thephilosophyforum.com/discussion/14823/reasons-for-believing-in-the-permanence-of-the-soul/p1

Descarte's discovery was really "thinking therefore is-ing,." It does not rest thus no "am"; it does not rest thus no "I". — ENOAH

There are additional issues to that. When we conclude that that thought isn't ours and we only have a memory of it, we can no longer conclude that anything exists, as that memory is no proof of anything thinking; if anything, it is proof that I exist, because I am remembering it, and remembering is thinking. Furthermore, "someone thinks therefore something is" is a phrase, it is hard to articulate (and perhaps that is the issue) how that phrase translates to thoughts, ¿is it a single thought or 2+ thoughts one after the other? If the latter, perhaps the first "something" is not the same as the second "something".
If the former, when we say "I think" in "I think therefore I am", we can be talking about "I think therefore I am" itself, then it can be taken as self-fulfilling.


Sadly, this thread has reached 1.1 replies.

Please prove your claim with evidence. — Truth Seeker

Just did it.

A lot of their studies get discredited. Twins study for example. — Mark Nyquist

Was it? I have never heard of anything like that. And when I read the study, the methodology seemed solid.

So monism? Is non-dualism supposed to be a translation of advaita?

Once you have done the above tasks, I will be convinced that you have free will — Truth Seeker

I have done all those.

Here's a list of your replies to me. — Banno

Well, yes, in the first four I am defending skepticism.

SO, if we go back to the beginning, I gather you were being ironic. — Banno

No, I would still defend skepticism. The fact that I have to defend Descartes against improper criticism has nothing to do with that.

Is that it is an intuition enough for it to be 100% certain? Folk are 100% certain about all sorts of things. — Banno

If you mean it with "100% certain", Descartes' achievement is not immune to silly doubts like "Do I really know what 'is' means?". In any case, no one can convince oneself that one does not exist.
You may not remember, but some 15 pages ago, our roles were switched here, and I was defending skepticism.

Is it enough for it to be known with 100% certainty? Well, what justification is there for this intuition? — Banno

Using Bayes theorem, everything that relies on something else is already not 100%.

Thanks for your patience. — Banno

To be clear, I agree that the intuition is not logically valid just like p→q is not valid. Not that it is furphy, whatever that means.

Do you agree? — Banno

"Whatever thinks, exists" is not a tautology, yes.

You keep doing this. I ask for a demonstration that "Whatever thinks, exists", and you reply with a demonstration that if "Whatever thinks, exists" then I exist: — Banno

This is the first time you ask for a demonstration of that specific premise. The rest of the time you were asking for Descartes' argument as an inference. Even then, I preemptively addressed the first premise multiple times:

It relies on intuitions, like any argument does. An intuition is a belief that is not proven by inference or by experiment. Descartes is not worried to try to prove everything, he uses hyperbolic doubt, not unbounded doubt, so he does not doubt things that could not be otherwise (something thinking but not existing, or 2+2=4). — Lionino

As I said, Descartes uses hyperbolic doubt, not unbounded doubt — Lionino

The first premise is an intuition — Lionino

Is that enough for the first premise?

Don't you think he would want to know if he was or wasn't? — Beverley

No because that is not the point. Later in his metaphysics he refutes (or so he thinks) the existence of an evil demon.

The only thing that I can think of that would bridge such political divides effectively within a country is nationalism, or perhaps religion, those are usually universally inclusive, we the nation, we the Christians. Sometimes those two come in a package, in the case of Judaism.
But then again those two are also very traditional, even if not divisive.

I would say that Descartes wanted proof that the world, and he himself, were as he perceived them — Beverley

That is not what Descartes wanted. If you want to know "why" you have to read what he wrote.

And the more traditional political categories are?

So, this can create some ambiguity if one just focuses on the single sentence without the context — Bylaw

Which is the person's fault to try to interpret a view without having read at the very least the chapter in which the view is contained. Realistically, to really understand Cartesian epistemology you don't need much, perhaps the Discourse would be enough, but the metaphysics, which is relevant for the epistemology, can only be well understood after reading the Meditations, the Principles, and the Objections, at least.

I find it miraculous that this even needs to be said. — Bylaw

Pages 20 to 30 of this very thread would blow your mind.

You will tell me you don't know who the writer of The Lusíadas is? :sweat:

which includes what my room and I look like — Truth Seeker

And I know that.

An all-knowing being would be able to describe my room and what I look like even without teleporting into my room. Your lies are not even plausible. — Truth Seeker

What I know and what I wish to remember are different things. You said all-knowing, not all-remembering.

More traditional political categories — Pantagruel

Which are?

My sense is that the upper echelons benefit by playing groups off against one another in order to forestall their uniting against the common problem (the wealthy and privileged). — Pantagruel

Every Marxist has had the same "sense" and the result was more of the same problem.

I didn't pay attention, and nothing about it really stood out.

Well, for example, I just teleported exactly behind you.

Why would an all-loving, all-knowing, and all-powerful being as you claim you are, be afraid of exposing his or her identity? — Truth Seeker

I am not afraid, I just don't want to expose it.

What about doing something else from the list that doesn't expose your identity but still proves your claim that you have done all the tasks on the list? — Truth Seeker

As I have said, I have done all.

to effect a fundamental break from outmoded traditional political categories — Pantagruel

Most new ideas end up being bad ideas, especially in politics.

Again, as an ideological guide or norm, broad enough to bridge the traditionally divisive categories — Pantagruel

And by traditionally divisive categories do you mean things such owner/leaser, employer/employee, rich/poor, man/woman, student/teacher, or something else?

Showing a video of yourself changing your skin colour like a chameleon would prove that even though you don't have the genes of a chameleon you can do what a chameleon can do. — Truth Seeker

Well, I would rather not expose my identity here.

Sonetos by Camões, in both French and original Portuguese. Both are hard.
Then I will read Pero Vaz de Caminha's letter to King Manuel.

He agreed with A1? — flannel jesus

It seems like it:

But this just says that if some individual has a property, then there is an individual. It works not just for thinking but for being pink. For all x, if x is pink then there is something that is pink. — Banno

Very well put. Logic helps us clear ambiguities in our language, language being a vehicle for thought. I will say that language does not exhaust thought. Although we need language to express truth, language's failure to convey some thoughts does not mean that those thoughts are not important or perhaps fundational.

"I think therefore I am", if parsed as "p⊃q", is not a tautology, is invalid, and need not, at least on that account, be accepted as 100% certain — Banno

Because there is an unstated premise (many depending on how deep you wanna go). Not a big deal.

Now what I have asked is for someone to present the structure of the argument. If you have indeed done so, then I've missed it. — Banno

You have:

Whatever thinks, exists.
I think.
I exist.
The first premise is an intuition, the conclusion is not, because it very clearly derives from the premises (inference). We start with a universal, then to a particular, then the exclusion of the middle term. — Lionino

I will restate this syllogism at the end of the post to reply to something else.

To doubt some statement is to take other statements as undoubted — Banno

Like the law of non-contradiction. There was no such thing as dialetheias back in Descartes' times, and many would say that there is still no such thing as dialetheias. As I said, Descartes uses hyperbolic doubt, not unbounded doubt. He makes the point here:



Descartes was interested in proving whether something exists, not proving whether LEM comes from LNC or LNC comes from LEM.

Which is valid. But this just says that if some individual has a property, then there is an individual. It works not just for thinking but for being pink. For all x, if x is pink then there is something that is pink. This seems not to capture the quality of the Cogito. — Banno

Let's say pink then.
U(x)(Px ⊃ ∃(y)(x=y))
U(x)(Tx ⊃ ∃(y)(x=y))
These two arguments are identical in form but different in content, the difference in content being the statement that x instantiates the property of thinking or of being pink. The crux is that we may doubt that anything is pink, but we cannot doubt that we think, because when we doubt that we doubt, we are doubting, and doubting is a type of thinking — and that is self-evident aka clear and distinct.

P1 Everything that is pink exists.
P2 I am pink (whatever that means).
C I exist.

A1 Everything that thinks exists.
A2 I think.
B I exist.

P1 and A1 are evidently true, as you have agreed. C and B follow from their premises, however P2 may be objected, A2 may not, ever.

Pretty much. So mathematical expressions are true only if there is a proof-path that shows it to be true. There are, one concludes, mathematical expressions that are neither true nor false. — Banno

That is something that I tend to agree with.

This is opposed to Platonism — Banno

to platonism* :smile:

But then the claim "it is not the case that this proof-path pre-exists our construction of it", the syntax being the proof-path, and in our case being the FOL that we see in things such as ZFC, did we really construe relations such as ∧ and →? If so, it would then bring up "how did we"?

Great post.

Just as a photon is either a wave or particle depending on how it is measured, it seems like these difference in math philosophy may all be neither wrong nor right - it depends on how the topic is approached. — EricH

When it comes to the metaphysics of mathematics, it could very well be a matter of perspective, yes. But when it comes to the foundations of mathematics, there isn't much room for perspective I imagine.

Thanks for the links. From what I know, modern set theory's axioms are ZF(C). And from Ernst's article, ZF(C) axioms are expressed using a first-order logic/language whose only undefined term is ∈ (membership).

From a few different sources, it seems that second-order logic takes first-order logic and stacks upon it quantification of properties/functions/relations (whatever term the source chooses), which are sets of elements. Some sources seem to imply that SOL may have functions while FOL may not but others clarify that SOL's distinction is in fact that it quantifies over those relations, like ∃A(Xxy), there is a relation A that x bears with y.
I did study set theory throughout many years of school but not as deeply as a math grad would, naturally. What I gather from your link, however, is that what is called function in set theory (mapping) is a bit different from what a function is in SOL (or FOL), and a set theory function can also be represented as sets of sets, differently from FOL functions which are not but can be represented as sets in some contexts. That being, it is clear to see how set theory can be built off ZF(C) which is expressed with FOL, which (FOL) the SEP says is what is typically used for building set theory. If SOL is weaker than set theory as the SEP says and SOL applies to set theory as you say, I wonder how SOL is applied then. I am not a fan of ChatGPT, but it gave me this:

For example, certain principles or properties involving collections of sets may be more naturally expressed in SOL.

Second-order logic plays a significant role in model theory, which is the branch of mathematical logic that deals with the study of mathematical structures (such as sets) using formal languages.

After writing all this, I realised I made a mistake in my question, modal-structuralism does not reduce mathematics to a SOL but it is expressed instead in a SOL S5. So I guess I will edit the question later today.

For it could be that were I totally to cease from thinking, I should totally cease to exist.

That is because Descartes himself (or whoever is thinking about this) is a soul, a thinker, res cogitans. One of the modes of this substance res cogitans is thought. It could be that without thinking, a res cogitans does not exist, but that is because it could be that the existence of a res cogitans goes hand in hand with thought as an operation. That however does not apply to res extensa, whose attribute is being extended in space and modes are things such as colour, movement, and temperature. Res extensae do not cease to exist when they stop thinking because rocks don't think at all.
Even in the case of res cogitantes, it will depend on how broad your definition of "thought" is, as so that if there are other modes to the soul other than thought, which could be desire or memory, he would not cease to exist by just stopping to think. But when we pay attention to it, it feels as though our desires and memories are kind of thoughts themselves, which is why Descartes says that:

At last I have discovered it—thought; this alone is inseparable from me

In the same paragraph before he was talking about movement and physical feelings. Those things are separable from him, but not thought.
But that is not Corvus' argument, he did not bring substances, modes, or attributes a single time. His is the misunderstanding of the conjunction "therefore", which I cleared here.



I will reply to the preceding post later.

Plenty of time to think!

To start with, please post a video of yourself changing colour like chameleons. — Truth Seeker

I don't see how that proves my omnipotence, only that it proves I am a chameleon.

1 * 1 = 2 — flannel jesus

Speaking of.

the nail that sticks out gets hammered down — ToothyMaw

Denying the antecent has nothing to do with social pressure, now :roll:

Since you are an in-house mathematician, I will kindly ask you to take a look at question i. Of course a mathematician is not the same as a logicist, but it is as close as it gets.

Modal structuralism puts mathematics in terms of a second-order logic, while logicism seeks to prove that mathematics can reduce to statements that can be proven in first-order logic. Why is the distinction between first-order and second-order so important that these two schools are distinct? Is nominalism trying to explain what mathematics talks about and logicism what mathematics is based on? If so, how does that connect with one using first-order logic and the other second-order? If not, then what is the distinction? — Lionino

Logically, semantically, and metaphysically Cogito doesn't make sense at all — Corvus

With every page you switch your argument to new nonsense. Once debunked, you go on to make up more nonsense.

"I am thinking." loses its credibility and meaning, as soon as the utterer stopped thinking and the utterance "I think".  It is only valid when he is thinking.  When he ended the utterance, "therefore I am." has no ground or validity, because he is not thinking anymore. — Corvus

More nonsense. He is of course thinking when he states "I am". The closest thing to a rebuttal to Descartes in your argument is Russell's objection which is basically a one-liner version of Cardano's argument critiquing the idea that the human subject is both subject and object of the enquiry at the same time.

This is especially the case, if you accepted the nonsensical claim that "think" implies "existence". — Corvus

Four different people, including me, have completely eroded this claim of yours from multiple angles.

"Thinking" also doesn't exclude the possibility of being wrong.  How many times have you thought something was the case, but found out it wasn't later on? — Corvus

You have never read Descartes and whatever you have read about him you have not understood.

It could have been "I think that I don't exist, therefore I am." or I think I doubt that I am, therefore I am, ...etc etc. — Corvus

This is not even related to your previous paragraph. I have said before, I will spell it out again: the argument is about the ACT of thinking, NOT about what the thought is about.

It doesn't rule out these nonsense contradictory possibilities of implications in the expression. — Corvus

What?

Hence it appears that your claim has no logical or theoretical ground for validity.  There is no compelling arguments in your claims at all apart from the empty blind declarations that my points are wrong. — Corvus

Apart from the fact you refuse to understand what material implication is, what "therefore" means, and that you have basically zero knowledge of Descartes.

then why is it universally accepted that Jesus was baptized and crucified? — Brendan Golledge

It is not. It is not even universally accepted that Jesus existed.

If it's religious fiction, then why did the disciples die for it? — Brendan Golledge

I could easily find a news piece about someone who killed himself over some piece of fiction like Harry Potter.

many chronically and pharmaceutically-untreatable depressed people won’t miss this world. It’s not that they necessarily want to die per se; it’s that they want their pointless corporeal suffering to end. — FrankGSterleJr

That is somewhat the whole debate around euthanasia. And it is not only for depression but especially for horrible diseases that are incurable. But then the debate is whether they really are incurable. It is a bet of sorts.

Your mortal mind would not ever be able to grasp my omnipotence and omniscience. How could I ever provide you enough evidence?