It's like rain on your wedding day. This should be the first post in a new sub;

/selfindulgentsophistry

One might even say that it > lay beyond the framework of signification

A squared circle is a terrible example of a paradox. There's much more going in with the phrase than one would interpret in a geometric sense.

The circle in question is not a prototypical circle, they are referring colloquially to a circle on the ground where it is customary to engage in hand to hand combat. Squared is altering that meaning, not the meaning of a prototypical circle.

Squared circle means we have an area meant for combat (just like it's round counterparts that tradition cemented into our language), except this one is square.

It sort of fits into a pattern of "isn't it crazy we drive on the parkway and park in the driveway." Yea.. that's what we call it.. crazy huh.

Well, yes and no...

It would be interesting to know when 'paradox' got twisted by logicians and mathematicians to mean seems true but is false instead of seems false but is true.

It's the latter that is genuinely useful and the original meaning. Trust logicians to fuck it all up.

I studied logic and my mentor was a logician. He had a lecture in his back pocket for this.

In short, no, paradoxes are a first-class entity in metamathematics/model theory. A “real” mathematical paradox is a statement that is provably neither provable nor disprovable. Such paradoxes include the continuum hypothesis.

I meant it tongue in cheek.

But still, in real life a paradox is something true but appears false. The multiple meanings (with Websters even condescending to a straight 'contradiction' as a final definition of about 5, in contradiction of it's meaningfulness of existence) makes use of the word quite tricky in public debate.

If a word having multiple meanings bothers you I have some bad news about nearly all words for you.

LOl, sure :)

But so many parallel and orthogonal meanings and one that just outright defeats the purpose of its existence makes it difficult to use even with context, right?

(I actually very much enjoy the multiple meanings of the word; I wouldn't change the situation.)

The only "truth inherent to language" is that it is language, and so is the word "truth". Modern philosophers who were ignorant of physics, and postmodern (or neopostmodern) philosophers who wish to ignore physics, try valiantly to formalize some metaphysical mechanism or method which would allow language to ascertain truth rather than simply enmatter truth, and continue to fail in that regard.

Paradox remains suspect by those philosophers because they desire truth (and metaphysics) to be bound by logic, which provides a precision and consistency of computational validity, and this seems, to them, the only reasonable meaning for truth. But being need not be described to be, and remains ineffable for that reason. The truth is that paradox (logically irresolvable conundrums) are far more meaningful than any tautology (which can be defined as anything which is not a teleology or a paradox), and understanding them, not resolving them, is the proper approach to reasoning. There is an unavoidable paradox intrinsic to the ineffability of being, which is indistinguishable from any other properly formed paradox in reasoning, and identical to metaphysical uncertainty: the unknown is just as unknown as the unknowable.

I read the article and I'm disappointed by how abstruse the whole thing is. I don't mean that paradoxes are difficult to contend with, more that the authors seem to do their best to muddy the waters of what's being discussed in the first place. After the first few paragraphs they seem to be engaging in an exercise that's all together different from explaining the topic. I'm of the opinion that a convoluted explanation is worth less than a straight forward one.

Lets talk about category theory, lets talk about nested statements. Hell, I'm game to play games. But to obscure what you mean in an exposition that amounts to plate of spilled spaghetti is just a pet peeve of mine.

https://youtu.be/vxhTDIUCPMM

I think that a "paradox" is how we describe the impossibility of two contradictory, albeit unassailably true (whether in reality or arguendo), facts. Oftentimes, a paradox describes an inconsistency between logical and experiential truth. Those are my favorite kinds because it pits sensory experience against logic.