Well, your question was:

what is goal of life that is better than all other goals ?

A goal that is perfect in sense ......
A goal that in sense , is all good ......

now .... What would be that goal?.. — No One

... And I gave an answer to it: happiness

“How to achieve happiness?” is a different and more difficult question.

I think it's a personal matter though, so I don't see what interest there could be in me telling you what makes me happy.

My preferred view on this matter is that of Aristotle: the ultimate goal of life is happiness, and all the other goals only have value in so far as they help us get closer to happiness.

So the answer to ‘why is there something rather than nothing?’ is ‘no reason’ — Devans99

Or the question itself is meaningless (a pseudo-question).

One problem of many philosophical questions is that they are often admited as legitimate questions, when very often they are not.

Just because something has the form of an interrogative sentence, that does not mean it is a question (or at least it doesn't mean that it is a meaningful question). I think Chomsky made that point once.

There is no reason to assume that all “questions” we pose must have an answer.

Well, there's not much to say, is there?

A fallacious argument doesn't necessarily have a false conclusion, but it gives no good reason to believe its conclusion, even if it were true, because it's fallacious.

The way I see the matter: There are some people who claim that God exists, and believe that God exists, and then there are other people who simply don't believe in that claim which the others make.
Not believing X≠ Believing ¬X

And it is not the case that one must either believe X or ¬X, for instance: just because I don't believe that the exact number of stars in the milky way is even, that does not mean I believe that it is odd. In this case, I believe neither claim and suspend judgement, since I have no way of knowing one way or the other.

Atheism is not a belief, anymore than baldness is a hair style, in my opinion.

Inductive arguments can not show their conclusion to be true, they can at best raise suspicion about the truth of some claim. — forrest-sounds

They show that their conclusion is probably true (for practical purposes). Of course one may doubt that through sceptical arguments like the problem of induction, but nobody can go through their normal everyday life without acting as if some beliefs were more likely to be true than others, using induction.
This does not apply to most other beliefs “justified” by circular reasoning or some fallacy such as appeal to authority, or ad populum.

Also, please make no mention of deductive arguments since these can only be made in theory with each premise of a deductive argument ultimately being justified through induction for all practical examples. — forrest-sounds

I'm not sure about that. It's possible that mathematical knowledge, for instance, doesn't need to be justified by induction. The same seems also to apply to the truths of logic.

Like everyone, the skeptic does not "adopt the custom and conventions of the country where he lives" any more than she "adopts" her parents or mother tongue. — 180 Proof

Like I answered to j0e, I agree when it comes to trivial and uncontroversial customs and conventions, but not as regards controversial/ important ones (such as slavery for example).

Non sequitur. Firstly, Protagoras was a relativist and not a skeptic. — 180 Proof

I would say he was both, take for instance his doctrine that “man is the measure of all things”:

He (Protagoras) is chiefly noted for his doctrine that "Man is the
measure of all things, of things that are that they are, and of things that are not that they are not."
This is interpreted as meaning that each man is the measure of all things, and that, when men differ, there is no objective truth in virtue of which one is right and the other wrong. The doctrine is essentially sceptical, and is presumably based on the "deceitfulness" of the senses. — Bertrand Russell

Also, what Russell says after that shows the connection between scepticism and pragmatism:

One of the three founders of pragmatism, F.C.S. Schiller, was in the habit of calling himself a
disciple of Protagoras. This was, I think, because Plato, in the Theaetetus, suggests, as an interpretation of Protagoras, that one opinion can be better than another, though it cannot be truer.
For example, when a man has jaundice everything looks yellow. There is no sense in saying that things are really not yellow, but the colour they look to a man in health; we can say, however, that,
since health is better than sickness, the opinion of the man in health is better than that of the man who has jaundice. This point of view, obviously, is akin to pragmatism.

It is true that Sextus says that some aspects of the philosophy of Protagoras differ from Pyrrhonism, but he also says that his main doctrine is akin to Pyrrhonism:

Protagoras thinks that man is the measure of all things; of things that are, that 216 they are; and of things that are not, that they are not. And by "measure" he means the criterion, and by "things" he means objects or facts. So in effect he says that man is the criterion of all objects or facts; of those that are, that they are; and of those that are not, that they are not. And for this reason he posits only what appears to each person, and thus he introduces relativity. Wherefore he too
seems to have something in common with the Pyrrhoneans.

Sextus often holds tenets which are more or less those of Protagoras, for example the mode of relativity:

The eighth mode is the one based on relativity, where we conclude that, 135 since everything is in relation to something, we shall suspend judgment as to what things are in themselves and in their nature. But it must be noticed that here, as elsewhere, we use "are" for "appear to be," saying in effect "everything appears in relation to something." But this statement has two senses: first, as implying
relation to what does the judging, for the object that exists externally and is judged appears in relation to what does the judging, and second, as implying relation to the things observed together with it, as, for example, what is on the right is in relation to what is on the left. And, indeed, we have taken 136 into account earlier that everything is in relation to something: for example, as regards what does the judging, that each thing appears in relation to this or that animal or person or sense and in relation to such and such a circumstance; and as regards the
things observed together with it, that each thing appears in relation to this or that admixture or manner or combination or quantity or position.

Of course not. Sophists, like Gorgias, use rhetoric to pursuade instead of evidentiary or logical grounds to warrant their claims. Also, he wasn't a Pyrrhonian ... IMO not relevant to the discussion. — 180 Proof

1.Tell that to Sextus then, since he presented the argument of Gorgias in a way that makes it clear that he thought Gorgias had grounds for the claim that “nothing exists” (if you read Adversus Mathematicos you'll see that that is so).

2. You are mistaken: Gorgias (and other sophists like Protagoras) did have logical grounds to support their claims. For instance, for the claim that “nothing exists”:

Gorgias of Leontini belonged to the same party as those who abolish the criterion, although he did not adopt the same line of attack as Protagoras. For in his book entitled Concerning the Non-existent or Concerning Nature he tries to establish successively three main points — firstly, that nothing exists; secondly, that even if anything exists it is inapprehensible by man; thirdly, that even if anything is apprehensible, yet of a surety it is inexpressible and incommunicable to one’s neighbor. 66. Now that nothing exists, he argues in the following fashion: If anything exists, either it is the existent that exists or the non-existent, or both the existent and the non-existent exist. But neither does the existent exist, as he will establish, nor the non-existent, as he will demonstrate, nor both the existent and the non-existent, as he will also make plain. Nothing, therefore, exists. 57. Now the non-existent does not exist. For if the non-existent exists, it will at one and the same time exist and not exist; for in so far as it is conceived as non-existent it will not exist, but in so far as it is nonexistent it will again exist. But it is wholly absurd that a thing should both exist and exist not at one and the same time.
Therefore the non-existent does not exist. Moreover, if the non-existent exists, the existent will not exist; for these are contrary the one to the other, and if existence is a property of the non-existent, non-existence will be a property of the existent. But it is not the fact that the existent does not exist; neither, then, will the non-existent exist.
68. Furthermore, the existent does not exist either. For if the existent exists, it is either eternal or created or at once both eternal and created; but, as we shall prove, it is neither eternal nor created nor both; therefore the existent does not exist.
For if the existent is eternal (the hypothesis we must take first), it has no beginning; 69. for everything created has some beginning, but the eternal being uncreated had no beginning. And having no beginning it is infinite. And if it is infinite, it is nowhere. For if it is anywhere, that wherein it is is different from it, and thus the existent, being encompassed by something, will no longer be infinite; for that which encompasses is larger than that which is encompassed, whereas nothing is larger than the infinite; so that the infinite is not anywhere. 70. Nor, again, is it encompassed by itself. For, if so, that wherein it is will be identical with that which is therein, and the existent will become two things, place and body (for that wherein it is is place, and that which is therein is body). But this is absurd; so that the existent is not in itself either. (...)

...and he goes on like that, concluding at the end:

Such, then, being the difficulties raised by Gorgias, if we go by them the criterion of truth is swept away; for there can be no criterion of that which neither exists nor can be known nor is naturally capable of being explained to another person.

I think the sophists (who are also sceptics in my opinion) tried to show by these arguments what David Hume called the “imbecility of reason”.

All in all, I quite agree with what Russell says here with regards to Pyrrhonism:

There was not much that was new in his (Pyrrho's) doctrine, beyond a certain systematizing and formalizing of older doubts. Scepticism with regard to the senses had
troubled Greek philosophers from a very early stage; the only exceptions were those who, like
Parmenides and Plato, denied the cognitive value of perception, and made their denial into an
opportunity for an intellectual dogmatism. The Sophists, notably Protagoras and Gorgias, had
been led by the ambiguities and apparent contradictions of sense-perception to a subjectivism not unlike Hume's.

Again you're mistaken, Amalac, and have these positions reversed.

https://thephilosophyforum.com/discussion/comment/524556 — 180 Proof

Well, let's make things clear: when speaking about pyrrhonism I'm refering to the doctrines set forth by Sextus Empiricus in Outlines of Pyrrhonism and in Adversus Mathematicos.

As for the support of the claim to which this particular quoted statement of yours responds to:

As I said above, there have been not a few who have asserted that Metrodorus and Anaxarchus, and also Monimus, abolished the criterion — 88. Metrodorus because he said “We know nothing, nor do we even know the very fact that we know nothing” — Sextus Empiricus

He (the sceptic) considers that, just as the "All things are false" slogan says that together with the other things it is itself false, as does the slogan "Nothing is true," so also the “Nothing more” slogan says that it itself is no more the case than its opposite, and thus it applies to itself along with the rest. — Sextus Empiricus

(...)even if it does banish itself (here he is talking about the argument which deduces that proof does not exist) the existence of proof is not thereby confirmed. For there are many things which produce the same effect on themselves as they produce on other things. Just as, for example, fire after consuming the fuel destroys also itself, and like as purgatives after driving the fluids out of the bodies expel themselves as well, so too the argument against proof, after abolishing every proof, can cancel itself also. 481. And again, just as it is not impossible for the man who has ascended to a high place by a ladder to overturn the ladder with his foot after his ascent(...) — Sextus Empiricus

I don't know. (It's been decades since I'd read Sextus.) — 180 Proof

I'd suggest you re-read both Adversus Mathematicos and Outlines of Pyrrhonism then.

Apologies. Trivial difference, however. — 180 Proof

It seems for some reason you are ommiting what I said right after what you quote, so I'll put it here:

If the sceptic doesn't know if it is better to not believe anything dogmatically rather than to believe some things dogmatically, then why does he talk about dogmatists (like Sextus does) as if it were better to be a sceptic than to be a dogmatist? — Amalac

Talking about X (dogmatism) as if it were worse than not-X ≠ Talking about X.

Interesting, I confess that I unfortunately haven't had the time to read Hegel's works in order to make a proper judgement of them, but those passages that you mention are indeed quite interesting and give a good picture of the philosophy of Stirner/Nietzsche, as well as good criticism of them. Guess I should add it to my list of books to study now.

I think it's better to not view (most of) custom & convention as a conscious choice. — j0e

I agree that many of our actions are determined by custom and habit, but I was hinting rather at other customs and conventions, such as religious beliefs,customs and conventions, and some other (more controversial) principles derived from the traditional morality of their culture.

For example: I don't think a sceptic should have defended the slavery of ancient Greece on the grounds that his scepticism leads him to do so because it is conventional and traditional. I also don't agree with Protagoras' choice of being sure that the gods of his time ought to be worshipped, specially considering the influence that such teachings would have on the people to whom he taught as a sophist, which could have been quite bad if it led them, paradoxically, to fanaticism.

And also, though it may be hard to act contrary to custom and habit, it's not impossible if one has the will to put in a lot of effort, and sometimes one may argue that it is better to fight against conventions and traditions rather than not to, even if it's hard.

If a sceptic insists that one should never do that, then it could be argued that they are no different from any ordinary citizen who never thinks about philosophy, since they behave in a very similar way in practice. What good was his scepticism then? It just lead him right back to where he started.

It depends on how narrowly you want to define "action". Whether you limit it only to (some) bodily actions, or whether you include the mental and the verbal (when you think or speak, this is doing, it's action). — baker

Agreed. I think we can infer that Hume uses a sense limited to bodily actions that depend upon one's will, and thus draws the conclusion that if a pyrrhonian tried to make his practice conform to his theory, he would be led to complete silence and to wait for his death by starvation:

(...) a Pyrrhonian cannot expect, that his philosophy will have any constant influence on the mind: or if it had, that its influence would be beneficial to society. On the contrary, he must acknowledge, if he will acknowledge anything, that all human life must perish, were his principles universally and steadily to prevail. All discourse, all action would immediately cease; and men remain in a total lethargy, till the necessities of nature, unsatisfied, put an end to their miserable existence. — Enquiry Concerning Human Understanding

There aren't usually any grounds to doubt (or disbelieve) most customs & conventions (i.e. social norms, ritual observances) — 180 Proof

But there are no grounds to believe them either, according to the theoretical philosophy of the pyrrhonian, that's why the choice is still arbitrary.

Why, for instance, does the pyrrhonian adopt the customs and conventions of the country were he lives, and not those of some other country? He has no rational justification for choosing any of them.

I suppose one possible answer is a kind of pragmatism: they would do that in order to avoid unnecessary conflict and hostility from the people of their community. But that brings the further question: If the pyrrhonian tries to doubt everything, why doesn't he doubt that pragmatism as well? After all, customs, conventions and traditional morality and beliefs are sometimes quite deplorable, and it may therefore be better to oppose them (at least sometimes). For instance, religious beliefs that were customary and traditional that some people in the past used to justify the crusades or the inquisition, were such that a person with a decent morality would vehemently oppose them. So I wonder: If Protagoras lived in the times of the inquisition, could he still say that God ought to be worshipped and that we ought to defend those religious beliefs on the ground that they are conventional and traditional? In theory, and from a purely logical point of view, he might be justified to think that in such a scenario, but if he then talked and acted accordingly I would find him contemptible.

which makes them, for ataraxia-seeking Pyrrhonians, more preferable in everyday practice to abide by than undecidable beliefs such a religious or philosophical ideas. — 180 Proof

Protagoras defended the religion and the customary philosophy of his time, and so he abided by them (to some extent, at least). They are included in “customs and conventions”.

And why "create his or her own new philosophy" when philosophy is (mostly) what a Pyrrhonian is skeptical of? — 180 Proof

Pyrrhonism is a philosophy too (as Sextus acknowledges), so if a pyrrhonian is sceptical of most philosophy, then he should also be sceptical of pyrrhonism itself. If he is not, then one wonders whether that's a case of special pleading. Why then is he sceptical of some philosophies but not others?

if there aren't grounds to doubt, then believing is not at issue. — 180 Proof

The pyrrhonian claims to know nothing, not even that very thing, (that is: he says he doesn't even know that he knows nothing) unlike the academic sceptic. If so, he has no way to know when there are grounds for doubt and when there are not (as Sextus himself points out: he has no criterion of truth to distinguish the two).

I mean, did Gorgias have grounds for doubting whether something exists or not? Did Sextus have grounds to doubt the logic proposed by the stoics or whether or not addition and substraction are possible, as he did in his Outlines?

Besides, Sextus "talks to dogmatists" because there's more to learn from those with whom a skeptic disagrees than from other skeptics. — 180 Proof

Here you are putting words in my mouth, I never criticised Sextus for “talking to dogmatists” (he can talk to whoever he wants of course), but rather for talking about dogmatists...

...as if it were better to be a sceptic than to be a dogmatist — Amalac

Where one lacks grounds to disbelieve (from sufficient evidence to the contrary) AND lacks grounds to doubt (from undecidability), one believes by default out of custom, convention or habit (re: Witty's, On Certainty). — 180 Proof

Supposing a sceptic claimed this, he has no way to know what the default position is nor, supposing that were the default position, to know that it is preferable (not even in practice) to adopt a default position rather than a non-default one. That is why I think their choice is arbitrary, their belief that some doctrine X “works better for him or her than other reflective ways of life” is also arbitrary, from a logical standpoint, as well as the belief or disbelief in the pragmatic criterion they use to choose, since they can't even know that it is more likely to be a better course of action than not.

I suppose you may disagree with this principle though: If I do not know X is a better/ more rational way of acting than not-X, and I also do not even know if X is more likely to be a better/more rational way of acting than not-X, then the choice between X and not-X is arbitrary.

Such believing is not "dogmatic" in so far as a skeptic's beliefs are open to being reconsidered in the light of new evidence. — 180 Proof

That's true for more moderate forms of scepticism, but the pyrrhonian's scepticism is radical, they doubt even whether or not it is reasonable to conclude that belief X is more likely to be true than other beliefs even if the evidence seems to suggest that (assuming they even grant that the evidence exists and is not merely an illusion). They can use things like Agrippa's trilemma, the problem of the criterion, Hume's problem of induction, and/or Descartes's evil demon to doubt that.

So in a sense, there is always grounds for doubting anything (even in practice), however obvious/ self-evident it may seem.

That way, the sceptics can never be convinced that their position is mistaken, or even more likely to be mistaken:

If we adopt the attitude of the complete sceptic, placing ourselves wholly outside all knowledge, and asking, from this outside position, to be compelled to return within the circle of knowledge, we are demanding what is impossible, and our scepticism can never be refuted. For all refutation must begin with some piece of knowledge which the disputants share; from blank doubt, no argument can begin. Hence the criticism of knowledge which philosophy employs must not be of this destructive kind, if any result is to be achieved. Against this absolute scepticism, no logical argument can be advanced. — Bertrand Russell

However, it would seem also that nothing the sceptic says can convince those who think that asserting X is equivalent to asserting “I know that X” or “X is true” and that the sceptic contradicts himself, that they are wrong, because they can always retort that those who reject that are claiming that they know that X is not always equivalent to “I know X” or “X is true”, so that in the end they claim to know something, no matter how many times they deny it. It always goes something like this:

Sceptic: I don't know anything/ nothing is true

Dogmatist: So you know that you don't know anything/ you think it's true that nothing is true, and therefore your position self-destructs.

Sceptic: No, I don't know that either, and I don't claim that it's true that nothing is true.

Dogmatist: So you know that you don't know that you don't know anything, and you claim that it is true that you don't claim that it is true that nothing is true, and therefore your position self-destructs.

Sceptic: No, I'm not saying that.

Dogmatist: Oh, but then you are claiming to know what you just said/ that what you just said is true...

... And the cycle repeats forever and ever, leading absolutely nowhere.

Here I ask: Is it not obvious that neither party can ever convince the other, no matter what they say?

Doesn't this show that it is futile to even pick a side and to try and discuss anything related to (radical) scepticism (even with regards to their practice) pretending to try and solve the problems raised by scepticism, as some philosophers still do at the present day?

At any rate, there seems to be no way out of Kolakowski's maxim:

We can never escape the infernal circle of epistemology: whatever we say, even negatively, about knowledge implies a knowledge we boast of having discovered; the saying “I know that I know nothing”, taken literally, is self-contradictory

It is impossible not to act. Even plumping oneself down at a crossroads is an action. — baker

In a sense, it is impossible not to make any choices, that does seem correct.

If I remained sitting in a chair without moving an inch and not saying anything until I starve to death, then one could say I chose to not do anything. But we would not say that I'm “acting” right? Because I would not be doing anything besides what does not depend upon my will (i.e breathing, seeing, ...)

A Pyrrhonian, it seems, aspires to live simply (i.e. ataraxia), and by custom, convention and some sort of (e.g. Deweyan) pragmatics. — 180 Proof

Ok, but I guess that's what strikes non-sceptics as suspicious, because the pyrrhonian cannot know that living by custom and convention is better than not to, so why does he decide to abide by them rather than not to?

Once again, it seems the choice is arbitrary: why does he decide to remain a pyrrhonian instead of becoming a stoic or an epicurean, for example (or just create his own new philosophy)? If the sceptic doesn't know if it is better to not believe anything dogmatically rather than to believe some things dogmatically, then why does he talk about dogmatists (like Sextus does) as if it were better to be a sceptic than to be a dogmatist?

Furthermore, why does he act as if he did believe some things dogmatically if he claims that he doesn't believe anything dogmatically?

So if you keep skepticism, you are forced to be arbitrary in your world view. If you throw away skepticism, then you are automatically arbitrary (from a skeptic's viewpoint). — god must be atheist

I guess so, but maybe even this claim of yours is arbitrary (as well as my own claim just now). It seems in the end to boil down to this statement of Kolakowski:

We can never escape the infernal circle of epistemology: whatever we say, even negatively, about knowledge implies a knowledge we boast of having discovered; the saying “I know that I know nothing”, taken literally, is self-contradictory

I refrain from ever insulting people during discussion because I find insults unnecessary, but I don't mind if people insult me.

My view would be that insults are fine as long as the person insulting also answers the objections against their position, and doesn't merely insult while ignoring the arguments of the other party.

I'd say one can just ignore the insults.

Modal realism is the view propounded by David Kellogg Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours."[1] It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now". — fishfry

I agree with you in this point, that sounds insane.

There are things that are logically possible yet still not possible. I'm not sure if there's a name for that position but if there is, that's what I am. I'm curious about that now. Maybe I'll google around. — fishfry

Good! If I got you curious about something, then our exchange about possible worlds wasn't entirely fruitless.

We can have no possible information about the part of the universe we can't observe. For all we know, in the unobservable universe, bowling balls fall up. There, I just contradicted my own position on this matter. — fishfry

I mean the part of the universe we can't observe at present, but may be able to observe in the future. We may never see those parts, but it's not logically impossible to see them. But then we're back to modal logic, and there we disagree.

If we could see them, then eventually (if space has some ultimate limit, even if we could never see it) we would have to reach something that is not transparent and not translucent by logical necessity.

I'll answer a few of your other points later, right now I've some work to do.

David Lewis claims possible worlds are real. That, I find clinically insane. — fishfry

I already told you I'm talking about Leibniz's doctrine of possible worlds, not Lewis' strange claims (if he does in fact claim what you say he does, which I don't know). I don't agree with Lewis, I don't believe “possible worlds” (other than the actual world) exist.

But you didn't address my question about non-Euclidean geometry. Is there a world where Euclidean geometry holds (Newton) and one where it doesn't (Einstein)? There are a lot of technical problems with that belief. — fishfry

I did address it, I said if there is nothing logically contradictory about a world where Euclidean geometry holds or one where it doesn't, then by definition they are both possible worlds. If you are going to say that there is no possible world in which Euclidian geometry and newtonian physics are wholly true, then that must mean that their truth implies a logical contradiction, in which case you just have to tell me what that logical contradiction is.

Perhaps you could say that Euclidian geometry contradicts some basic axiom of mathematics or logic, in which case there are no possible worlds in which that's the case. If you are asking: Assuming that the current laws of physics don't change in the future, is there any possible world in which the whole of newtonian physics is true? Then the answer is no, since as you pointed out newtonian physics were, at least partially, falsified by observation.

But the thing is, logic is not limited by the laws of physics. When saying that there is some possible world in which newtonian physics is the case, what one means is that we can conceive of a world where newtonian physics wasn't ever falsified, and in which the behavior observed that falsified newtonian physics simply didn't happen. That's possible, since there is nothing logically selfcontradictory about such a state of affairs. But then you may still go back to determinism and deny this.

You say I'm just making you repeat yourself, yet you have asked me the same thing again about newtonian physics.

I'm saying the whole idea is incoherent to me, notwithstanding all the smart people to whom it's coherent. I'm just not one of those smart people. — Amalac

Well, I simply don't agree with you in the least about what you say here, so there's no point in discussing the matter of possible worlds further. There's no common ground. Perhaps the Stanford Enciclopedia of Philosophy can do a better job than I did: https://plato.stanford.edu/entries/possible-worlds/

Those are of course physically made, imperfect window. I have for several posts already stipulated to a PERFECT window. You could have one ten miles thick and it would be perfectly transparent to visible light. — fishfry

Ok then, if that's what you meant by “perfect window” then there are no problems. I accept that definition.

You're going quite far afield now. What the average person would see of the real world is irrelevant to your point. — fishfry

It's not irrelevant, I was trying to clarify what I meant by “transparent”: When the average person speaks about X object being transparent, they probably have in mind something very different from what physicists have in mind. When saying «a window is transparent», they usually don't mean that it lets X,Y or Z amount of light to pass through, they mean simply: you can see through a window.

To quote Wittgenstein again: The meaning of a word is its use in a particular language game. The language game of describing things in daily ordinary life is not the same as the language game that results from doing physics.

Humans or bats? Human eyes or radio telescopes? Cameras or sonar? Cameras or radar? You haven't defined transparency at all. — fishfry

Human eyes. Have I defined it well enough for you now?

There is no Newtonian possible world, except in our imagination. It would make a fun science fiction story, but NOT serious philosophy. — fishfry

So modal logic is not serious philosophy according to you? I disagree

I don't think I agree. The edge of the observable universe is as far as we can see. It doesn't matter what's beyond it. We can't see it in any event. It would appear black I assume. — fishfry

Ok, but I'm not talking merely about the observable universe, I'm talking about both the observable universe and the parts of the universe we have not observed yet (that's why I said I meant “universe” in an all-encompassing sense).

I use the term in the same sense as the one suggested by Bertrand Russell in this passage:

Space and time appear to be infinite in extent, and infinitely divisible. If we travel along a straight line in either direction, it is difficult to believe that we shall finally reach a last point, beyond which there is nothing, not even empty space.

But as TheMadFool notes, it's not transparent to heat, sound, etc. What exactly do you mean by transparent? Bats can detect windows by echolocation. To a bat, a window is not transparent. So you need to "define your terms" as they say. — fishfry

Again, I don't use the word “transparent” as it is used by physicists, but rather in the sense Wittgenstein uses it in my OP. You can substitute “see through” (meaning: such that you can see through it) every time I say “transparent” if you like. I guess it's a sense more akin to phenomenology than to physics.

At any rate, what is wrong with this definition of transparent object?:

An object such that when a human sees it, through it some other object that is both not transparent and not translucent can be seen with clarity.

There's no way we can answer the question without being dishonest.

I would've liked to say that I know nothing but then I know that I know nothing and that's self-refuting.

I would've liked to take Agrippa's route and bring up the Munchhausen trilemma but that to is self-refuting to a certain extent and it's no longer as satisfying as it would be were that not the case.

I guess, given these two limitations, I should simply shut up and not say a word.

Perhaps, instead of all that I wrote above I should post this: :zip: The less said, the better :smile:

Those who speak don't know. Those who know don't speak
— Laozi — TheMadFool

That's pretty much my answer too, couldn't have said it better.

But if the point is that a perfect window has no color, I suppose I can agree with that. — fishfry

My point was more like: If the universe has an edge, then such an edge must not be transparent by logical necessity (not merely physical necessity), because otherwise we would be able to see what is beyond the universe.

The argument would be: anything we see is part of the universe. Therefore, if we could see something through it, that thing would be both in the universe and beyond the universe, which is absurd. Therefore, it's impossible for there to be anything beyond the edge of the universe (in an all-encompassing sense, not in the sense some physicists speak of “multiverses”).

And yet, if nothing could be seen through the transparent object, then the transparent object would not have any color when we looked at it. But that's also absurd: since we impose color onto all that we perceive, it's impossible for us to see something that has no color.

Therefore, in view of the 2 previous conclusions, we conclude that it is logically necessary that such an edge is not transparent/translucent.

As someone who finds the doctrine of possible worlds incoherent, I don't see why logic and math couldn't be different in some alternate world, just as physics is. I agree I can't conceive of it, but who made me the authority on such things? — fishfry

Well, the doctrine of many possible worlds is just taken for granted in modal logic, for example. When saying X is logically possible, all one means is that the existence of X does not violate any of the laws of logic. That's just the definition of a “possible world”, there's nothing incoherent about it. When asserting that there is some possible world in which X exists, one does not assert that such a world literally exists in some alternate reality (at least most people don't), rather one merely asserts that reality could have been that way, or could be that way, depending on what the assertion is.

I could say, if the CMB is the remnant of the big bang, how could it be transparent? But we'd be arguing nonsense. — fishfry

But then you are doing physics again, while I'm trying to do logic. This seems to me like a case where you are confusing one language game with another.

For example, Wittgenstein said this in his Remarks on Colour:

We are not doing physics here(...)

(...)The question is: how does our visual image have to be, if it is to show us a transparent medium? How, e.g., does the medium's color have to appear? Speaking in physical terms - although we are not directly concerned with the laws of physics here - everything seen through pure green glass should look more or less dark green.

(...) That is not a proposition of physics, but rather a rule for the spatial interpretation of our visual experience.

As you yourself pointed out before, a universe where the CMB were transparent would have different laws of physics, and there is at first no logical impossibility in it having laws which would allow it to be transparent, not until you start considering what that logically entails.

But if the CMB is leftover radiation by definition, how can it be transparent? It always has some small but nonzero color temperature. — fishfry

Again, is there some possible world in which the CMB had the necessary physical properties to be transparent, or were the Big Bang happened differently? Yes, so long as that does not involve a logical contradiction. That's all the doctrine of many possible worlds asserts. It does not claim that there are in fact alternate realities or multiverses, one in which that's the case (at least most interpreters of the doctrine don't, it seems to me).

But I am not convinced that physics is contingent either. I wonder if anything is contingent. In some logically possible other world, Socrates was a bricklayer and not a philosopher. But what other things would have had to change? You'd have to drill that down to his ancestry and environment and life experiences. I don't think I have enough imagination to believe in contingency at all. Today I'm wearing my determinist hat. Socrates was destined to be a philosopher from the moment of the big bang. — fishfry

I mean, it's quite simple in a sense: I can imagine/conceive that if I jumped of the roof of my house I started floating upwards instead of falling. I can imagine/ conceive of the sun not rising tomorrow, and these events imply that physics is contingent. And since I can conceive of them, they are possible, they involve no contradiction.

On the other hand, I can't conceive of me counting one orange, and then only another orange, and then somehow having altogether 50 oranges (1+1=50), because that contradicts the most fundamental and most self-evident axioms of mathematics. I can't conceive of seeing something that both was and was not a tree (at the same time and in the same sense), because that would violate the Law of Contradiction.

3.0321 We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry. — Ludwig Wittgenstein

However, supposing one takes the route of determinism, then I ask: Do you agree with Leibniz's Principle of Sufficient reason as interpreted in his esoteric system, according to which every true proposition is analytic, including empirical truths? If so, I suppose there's no sense in arguing with you about possible worlds in which the laws of physics were different.

Do you believe there's a possible world in which Einstein's famous prediction failed and Newtonian physics reigns supreme? — fishfry

To answer that we need to answer the question: Does such a state of affairs (a possible world in which Einstein's famous prediction failed and Newtonian physics reigns supreme) involve a logical contradiction? If it does, then there is no possible world in which that's the case. If it does not, then there is such a possible world.

It seems clear to me that such a scenario does not involve or imply a logical contradiction, but if you think otherwise, then tell me what the logical (not physical) contradiction that such a scenario implies would be.

No amount of philosophical theorizing could possibly give us knowledge of the actual world. — fishfry

Would you say this proposition does not give us knowledge about the world then?:

If the universe has a boundary, then such a boundary must not be transparent when seen by a human by logical necessity, since it is impossible for a human to see anything that does not have any color, in the sense in which black and white are also colors.

Notice that assuming that the universe were in fact finite with regards space, then we could have knowledge about the boundary from the truth of the proposition above, without the need of experience (such as the experience of observing the boundary), merely by logically analyzing the meanings of words. And although in that case it would be perhaps considered an analytic proposition, nonetheless it seems to gives us knowledge about the world.

Is a perfect window colorless? — fishfry

Well, that's not the question but it is related to it somewhat. I would like to confirm: if a clear glass window (which according to physics apparently does have a color: blue) was in a world were the only other objects in it were other transparent objects, then is it correct to say that they would all look monochromatically blue?

Some reddit user answered the question about what color is a window:

if you stack up enough windows you'll see that window glass is actually usually a blue/green color. It's just so translucent that with only one pane it's pretty much impossible to see

http://www.tucsontabletops.com/Images/seamed-v-polished/edge-color.png

And apparently the same is true for clear water:
https://www.usgs.gov/special-topic/water-science-school/science/water-color?qt-science_center_objects=0#qt-science_center_objects.

But that is relevant for the physics definition of transparent. I am using a different sense of that word, the one most commonly used in ordinary life by ordinary people.

So you have to say what you mean by transparent — fishfry

I did in my OP: such that through it some other object (at least one object) that is both not transparent (not transparent= such that you cannot see through it with clarity) and not translucent can be seen through it.

The important aspect of that definition is that it is not a physics definition of «transparent», but rather one which defines the word according to our visual experience.

If a window would indeed look monochromatically blue/green if it was surrounded only by other windows, then the average person who is not knowledgeable about physics would not call it transparent in the sense I gave in the OP.

They would not be wrong, they would in that case only use the word with a sense that is not the physicists' sense (the meaning of a word depends upon its context, and the way it's used in a particular language game, as Wittgenstein would put it).

If 2 + 2 = 5
— fishfry

There is no possible world in which 2+2=5
— Amalac

How do you know? — fishfry

Technically I don't, but I thought you would just take this for granted. I mean, you can take the extreme sceptic route of doubting that 2+2=4 is true in all possible worlds, but that would just dispose of mathematics and logic altogether, and I doubt that's your aim.

A world where 2+2=5 is inconceivable. If you have 2 oranges and 2 other oranges, how could you possibly not altogether have 4 oranges? 2+2=4 is analytically true, just as “a bachelor is an unmarried man” is: it follows from the definition of 2+2. Perhaps you could doubt this, as Kant did, by saying that 2+2=4 is in fact synthetic. But even Kant did not doubt that 2+2=4 is a priori true.

But I would like to ask you, besides mathematics, can you name a necessary truth? I mean one that's not trivial, such as that "if all men are mortal and Socrates is a man then Socrates is mortal." Can you name a meaningful proposition that is logically true, necessarily true in "all possible worlds," that doesn't rely on math? — fishfry

All analytic propositions are necessarily true, because the predicate is contained in the notion of the subject. All analytic propositions are trivial because of that (and yet they are still meaningful).

Then there is of course the famous debate between empiricists and rationalists, as to whether we can have knowledge about the world that can be obtained by mere reasoning, without the aid of experience.

What I asked in the OP was if there could be statements which are true about the world, but which are known a priori (Such as: If the universe has a boundary, then such a boundary must not be transparent when seen by a human by logical necessity, since it is impossible for a human to see anything that does not have any color, in the sense in which black and white are also colors).

Immanuel Kant, for instance, held that the Law of causality was synthetic (not analytic), but known a priori. And the Law of Causality, if true, would give us knowledge about states of affairs that we have not yet experienced (a priori knowledge about the world).

The claim that "the CMB is transparent" is factually false, so anything at all follows from it. That's my reasoning. — fishfry

This here is maybe where you are going off the rails: I'm not claiming that this is the case, I'm asking if it is even possible for the boundary of the universe to be transparent, as in: could this be known by mere analysis of the concepts of “transparent”, “seeing”, “universe”,etc? Or is it a synthetic proposition that is nevertheless still a priori true, just as Kant held the Law of Causality to be?

Now about these other worlds. For one thing, the CMB is the boundary of the observable universe. I imagine you might be inclined to grant that this is a necessary truth. In which case, if it's transparent, we still can't see past it. So we'd see black. Necessarily, because by definition we can't possibly see past the CMB. — fishfry

In that case either: it looks black because there is something black beyond it, which contradicts the idea that nothing could be beyond that, or it looks black because it is black. But then it's no longer transparent (in the sense I gave in the OP), since as Wittgenstein pointed out something transparent cannot look monochromatic. This contradicts the definition of that possible world (as in: we would in that case no longer be talking about that possible world, but rather about some other possible world), so it too can't be the case.

It may in that case still be transparent as the word is used by physicists (in the sense that it let's X kinds of light to pass through, despite looking as if it were opaque), but not in the sense that you can see through it.

But even ignoring that, if by definition that is so, could we then say: “The CMB (or the boundary of the world) is not transparent (in Wittgenstein's sense)” is an analytically true proposition that nonetheless gives us knowledge about the world?

But if the CMB is transparent, then we're in a world with different laws if physics. In which case, why might there not be different laws of mathematics or logic? — fishfry

Because then we would not be talking about possible worlds, since a possible world in Leibniz's sense is one which does not contradict the Laws of logic. So, if that world is a possible world, then it can't possibly have different laws of logic, since otherwise it would not be a possible world. And if you accept that mathematics is a prolongation of logic, then the truths of mathematics also cannot be different (although this second claim about math being an extension of logic is far more controversial):

6.375 As there is only a logical necessity, so there is only a logical
impossibility — Ludwig Wittgenstein

If 2 + 2 = 5 — fishfry

There is no possible world in which 2+2=5

then I am the Pope — fishfry

p→q is equivalent to: not p or q, so “If 2+2=5 then I am the Pope” means: Either 2+2≠5 or I am the Pope, which is true because 2+2≠5. The paradoxes of material implication only arise because they contradict the way we use them in ordinary life, to logicians they don't pose any problems if we interpret them as not p or q. But at any rate, material implication has nothing to do with my question.

And what if I say that rainbows and unicorns are logically necessary? — fishfry

If rainbows and unicorns were logically necessary, then their non-existence would imply a logical contradiction. But obviously that's false: no logical contradiction arises from denying their existence, since they are, in that sense, contingent (as Leibniz would put it: it would be logically possible for them not to exist).

When asking: Was it logically necessary that not everything in the world was transparent? I ask: Does the existence of such a world involve a logical (not physical) contradiction? If so, what is the contradiction?

Possible worlds (you mean David Lewis or physics multiverse?) — fishfry

No, I mean Gottfried Leibniz's doctrine of many possible worlds, the one used in modal logic:

One of the most characteristic features of that (Leibniz's) philosophy is the doctrine of many possible worlds. A world is "possible" if it does not contradict the laws of logic. — Bertrand Russell

Like I say, what color would you like it to be? If you're talking possible worlds, I suppose there's a world where there's a transparent CMB and behind it a background of rainbows and unicorns. Who can say otherwise? — fishfry

It seems to me that you are missing the point of the experiment. In that possible world, absolutely everything would have to be transparent, and if there were something behind the CMB, then whatever was behind it, being a part of the world, would also be transparent, and if there were something beyond even that, it would also be transparent and so on ad infinitum.

Let's suppose that there some ultimate boundary of the universe, beyond which there is nothing, not even empty space (i.e. the universe is finite with regards space). Then I ask: Is it logically necessary that this boundary is not transparent? (Otherwise we would see “nothing” if we looked at it, no colors at all)

And let's suppose that the universe were infinite with regards space, how would it look like if absolutely everything was transparent?

It's not logically possible for the CMB to be transparent, because its existence is a consequence of our best theories of physics AND it's been seen by experiment. — fishfry

Ok, but we're talking about possible worlds. It may be physically impossible for the CMB to have been transparent, but if we say that it is logically impossible for it to have been transparent, that means that the idea of a transparent CMB would have to entail a logical contradiction (as in: there is no possible world in which the CMB is transparent). In that case, what is the contradiction?

As Wittgenstein pointed out in his “Remarks on color”, in the context of philosophy he doesn't use terms like “transparency” in the sense in which they are used by physicists, rather in the sense we use those terms in ordinary life. He adds later that he is not looking for a physical theory of color, but rather for the logic of color, or the logic of color concepts. And here I'm looking for the same thing.

If everything in the world was transparent, you'd see the CMB. — fishfry

But the CMB is part of the world/universe (in the widest, most all-encompassing sense), right? If so, when asking how it would look like if everything were transparent, that includes how it would look if the CMB were transparent.

The CMB is not transparent, but would you agree that it was logically possible for it to have been transparent?

Everything is pretty much transparent. — fishfry

Not in the sense I am speaking of. That's why I gave this definition:

Let's use this definition of “transparent”: such that through it some other object that is both not transparent and not translucent can be seen with clarity. — Amalac

And Wittgenstein's:

Transparency and reflection exist only in the depth of the dimension of a visual image.

The impression of the transparent medium is that something lies behind the medium. A completely monochromatic visual image cannot be transparent. — Ludwig Wittgenstein

But anyway, let me phrase it in another way: The window of your house looks like what can be seen through it, right? So then, how would it look like if the only objects that were in the world were other windows just like it (and where spaces were also transparent in the sense I described)?

If all skepticism is
wrong, then anything goes.
Since that's not the case, some skepticism is right. — jorndoe

I see, in that case which parts of scepticism do you think are right? For example, how far are things like Agrippa's Trilemma or the problem of the criterion problematic according to you?

If all skepticism is right, then doubt about skepticism is also right.
Hence, unjustified belief can be right. — jorndoe

Yes, a statement can be true despite being unjustified. The problem is, we need justification in order to avoid having to randomly guess which beliefs are true and which beliefs are false (and which are neither true nor false).

However, many of the anticipated objections have not actually been made by anyone. — Bartricks

This I take to be the true state of the question, and cannot approve of that expeditious way, which some take with the sceptics, to reject at once all their arguments without enquiry or examination. If the sceptical reasonings be strong, say they, ’tis a proof, that reason may have some force and authority: if weak, they can never be sufficient to invalidate all the conclusions of our understanding. — David Hume

It seems clear to me that the “they” he mentions is not merely a rhetorical device, but maybe I'm wrong. It really sounds like he's adressing an argument he read or heard about from other philosophers.

I think the same about Sextus.

What is the Phyrronian thesis, though? That there is as much reason to believe any given proposition as disbelieve it? — Bartricks

I guess the phyrronian could say:

a) That they don't present any thesis

Or

b) Suspend judgement when you can't find out whether some belief is more likely to be true than its negation (which for them is always). This sounds similar to what you say.

In practice, however, the phyrronian can't suspend action and hope to survive at the same time.

Phyrrho held that no line of action could be more rational than any other.

If so, the choice of any action and the choice of any belief would be based on taste, sentiment and custom, as Hume would put it.

(I mean, Sextus and Hume are sceptics, right? So they are not the ones making the argument, they are simply addressing it - but that's not evidence that anyone has actually made it). — Bartricks

I suppose you are technically right. I can't (at present) tell you who exactly put forward the arguments mentioned by Sextus and Hume. The fact that they don't give the names of the proponents is also unhelpful.

Maybe they were lying and fabricated the arguments. Personally, I don't see any reason for them to lie about that, but I'm open to that possibility.

Later with more time I'll investigate to see if I can find who advanced the arguments that scepticism is selfcontradictory in antiquity.

I do not really follow your meaning here. You accept, I take it, that the thesis that there are no reasons to do or believe anything is self-refuting? — Bartricks

Self refuting in the sense you have described, yes. But I meant rather “self-contradictory”. Perhaps I should correct the title.

What I mean is that the academic sceptic makes negatively dogmatic claims such as “No belief can be justified”, “We know nothing”, etc. whereas the phyrronian suspends judgement and doesn't make any claims, neither affirmative nor negative.

So I do not believe that there are many philosophers who would claim otherwise. — Bartricks

I have given a quote by Sextus Empiricus (the one Banno wrote), as well as the Hume quote in the OP, that show that a significant number of philosophers in the past did claim that, and at present you may find that many people do claim that scepticism is selfcontradictory (not merely impossible to believe). If you don't believe me:

lookup videos on that subject and what many philosophers have said about scepticism, and I'm sure you'll find many people using it. — Amalac

The claim, rather, is that it is 'self refuting'. "It is raining, but nobody believes it is raining" is one such thesis. It contains no contradiction. But it is self-refuting, for to believe it is to render it false. — Bartricks

I get your point here, but some kinds of sceptics (phyrronian sceptics, as opposed to academic sceptics for example) would not put forward the argument as a proof that no argument can be proved, or claiming that we should believe that “there is no reason to believe anything”, rather they would mention it so that they could pit the arguments against the claim “there is reason to believe something” against those in favor of it, and then suggest that we should suspend judgement as to whether or not there is reason to believe anything, since we seemingly have no way of knowing one way or the other in view of the apparent equipollence of each opposing arguments. The practical choice between the two would then be a matter of taste, they may say.

It seems to me that you are arguing that there is no contradiction involved in the sceptical thesis and thus that the sceptical thesis is not self-refuting. (Unless I have misunderstood). — Bartricks

You have not misunderstood.

I take it that a theory is 'self-refuting' when there would be a practical contradiction involved in believing it. — Bartricks

I sort of agree in a sense. As Noam Chomsky pointed out, there are no sceptics (in practice).

However, I take one of Descartes' lessons to be that self-refuting positions are more certainly false than those that contain contradictions. For I know more certainly that I exist, than that the law of non-contradiction is true. — Bartricks

Hmm, I'm not sure if I agree with that. Bertrand Russell describes the status of our knowledge with regards to Descartes's cogito quite well in my opinion:

Descartes's indubitable facts are his own thoughts--using "thought" in the widest possible sense. "I think" is his ultimate premiss. Here the word "I" is really illegitimate; he ought to state his  ultimate premiss in the form "there are thoughts." The word "I" is grammatically convenient, but does not describe a datum. When he goes on to say "I am a thing which thinks," he is already using uncritically the apparatus of categories handed down by scholasticism. He nowhere proves that thoughts need a thinker, nor is there reason to believe this except in a grammatical sense. 

Fernando Savater gives an illustration of this: If you translate the statement “It rains” to spanish, you get “llueve” (the subject dissappears completely). And so, just as we would not argue that there must be something that “rains”, (an “it” in the same sense as an “I”) it may also be argued that it is not necessary for there to be some subject who “thinks”, and that maybe the right way of saying of describing the occurance is: “thinking is happening”, just as we would say “raining is happening”.

There is also the view that the self is merely a bundle or collection of perceptions, since we have no impression of self, and therefore no idea of self (this would be David Hume's criticism). Unless we say that we have an innate idea of the self.

And "It is raining, but no one believes it is raining" would be another, as although it is possibly true - there seems nothing impossible about the scenario described - to believe it is to render it false. — Bartricks

Well let's start by clarifying: If it is raining and I say “it is raining” , does that imply that I implicitly believe that it is raining? It would seem that way, for otherwise I would not claim it (unless I wanted to tell a lie, if it wasn't raining, and so “I believe it is raining” would be false, and “no one believes it is raining” could still be true).

It is not self-contradictory however, since if the human race perished tomorrow, and it was still raining on earth, then the proposition “It is raining, but nobody believes it is raining” would be true (and not even self-defeating, since it need not be uttered by someone in order for it to be true). But anyway, this is not the right thread to discuss the transcendental notion of truth.

All those points you mention will surely get us off topic, so I won't respond to them further, unless they are more directly related to the OP.

The second premiss is surely a contradiction, no? — Banno

Well, ¬p→p is equivalent to: ¬¬p v p, which is just p (Proof exists), according to the rules of material Implication, double negation and the idempotent law. So in that sense, I suppose it's not a contradiction.

SO yes, it is a bad argument. But it's far from the only argument against scepticism. — Banno

I didn't say it's the only one, but it's one very commonly used in the internet and by many philosophers. If you don't believe me, lookup videos on that subject and what philosophers have said about scepticism, and I'm sure you'll find many people using it.

Pages 88-89 (185) in the pdf you linked, it starts saying: It will suffice to have said this much... — Amalac

That's where it starts I mean, Sextus finishes talking about it in page 90.

Where? — Banno

Pages 88-89 (185) in the pdf you linked, it starts saying: It will suffice to have said this much...at the end of page 88

[

Wouldn't it have been simpler to point out that this leads directly to a contradiction, and hence is invalid? — Banno

Their argument is that the argument the sceptic uses proves the sceptic's conclusion “therefore, there are no proofs”, and therefore refutes itself, because if there is no proof, then the sceptic's argument is not a proof either. They then conclude that it's impossible for the statement “No statement can be proven” to be true, since if it were, then that would imply a logical contradiction.

More interestingly, who are the Greeks and others who used such a silly argument? — Banno

They are refered to as “the dogmatists” by Sextus Empiricus. I assume he means, based on the people he references in “Outlines of Pyrrhonism”, philosophers from the school of Plato, Aristotle, and/or stoic philosophers, of his time and of earlier times.

At face value, no. I would say it needs another element to make it properly analyzable, though. — Zophie

Ok, what is wrong with the argument that has the horns of the Trilemma as its premises and “Therefore no claim is justified” as its conclusion? According to those systems of logic, it must be either invalid or unsound (either at least one of the premises is false, or the conclusion does not follow from the premises). There is no third option.

I didn't. It's set by the definitions of every well-defined system. — Zophie

Really now, which set of definitions are you refering to? Why should one accept the implicit premises in those definitions, such as those which already assume, right off the bat, that nothing can ever disprove logic, not even logic itself? Such definitions would in that case just assume that the sceptic can't refute logic using logic, but why should the sceptic accept them then?

I think the arguments of skeptics -- using those systems at least -- give trivial subjections to those systems that resolve to the thesis that not even logic can disprove logic, and that this is expected because it's a sign that the logic is true. — Zophie

Ok, let's try this approach instead: Surely you'd say that sceptical arguments such as the argument that uses Agrippa's Trilemma to conclude “therefore there are no proofs” are invalid/unsound.

But why is it invalid/unsound? Is one of the premises false? Does the conclusion not follow from the premises? At least one of those must surely be true according to those systems. If not, then according to logic it must be valid and sound, and therefore its conclusion “Therefore there are no proofs” must be true (since otherwise it would not be valid and sound). According to logic, we should be able to pinpoint the error in that argument, and also in the argument which concludes that if not p (p= There is at least one proof), then it's not the case that not p implies p.

You say the sceptical arguments resolve to the thesis that not even logic can disprove logic, but how do you know this? How did you come to that conclusion? How do you know that it is not instead how Sextus or Hume say it is?:

(...) just as it is not impossible for the man who has ascended to a high place by a ladder to overturn the ladder with his foot after his ascent, so also it is not unlikely that the Sceptic after he has arrived at the demonstration of his thesis by means of the argument proving the non-existence of proof, as it were by a step-ladder, should then abolish this very argument.