Time for an appropriate joke: — Frank Apisa

:rofl: Don't worry, , we got yours too. (we did ??!)

Haha, Balloon Calculus

Does it differ significantly from fig 1?

I can't see how. — Banno

Me neither, in respect of whether it counts as a 'real' proof. Isn't this a live area? I thought that article was going to update me, but it wasn't quite that area. But I wouldn't be about to try persuading you otherwise.

saying is a complicated way of showing. — Banno

In what way complicated? Is the justifying/demonstrating/showing perhaps more complicated than the exemplifying/showing?

It states a sentence, as a conclusion, and it exemplifies ("shows") a pattern of inference. Which is justifying ("showing") the conclusion, but not justifying ("showing") the pattern of inference. (?)

Does this say or show? — Banno

It exemplifies the pattern, yes? So, shows an instance.

Isn't understanding [...] a kind of discovery? — Banno

Wasn't that the credo of Dewey et al, yes?

showing and stating. — Banno

Proving and discovering?

I'm more interested here in the distinction between showing and stating. — Banno

Ok. :grin:

And if someone does not see it thus, but sees it so...

...then it's not a justification at all. — Banno

And this couldn't as easily happen with words? That the person doesn't hear/think them thus but hears/thinks them so?

for proving or following a proof the subject must be aware of the way in which the conclusion is reached and the soundness of that way; — Giaquinto

(The quote is from a contrast of proof with discovery, but if I wasn't mistaken this was meant to correlate roughly with that of words with pictures.)

Again, I'm not seeing any important difference between words and pictures. I'm just as likely to follow a textual proof uncomprehendingly or inappropriately as a visual one, am I not?

And an automatic prover would (in principle) be indifferent as regards type of symbols, would it not?

they simply indicate how they are most often used.

Sometimes they even get that wrong! — Frank Apisa

If only there were a fact of the matter, to be right and wrong about... A population of word-use events, from which to sample appropriately.

And if it weren't for pesky kids like Humpty Dumpty, Quine (Gavagai), and Chomsky (probability of an utterance)...

Once one is dead, one is indifferent to such event, — JacobPhilosophy

But also unable to increase the sum of human happiness, which one has almost certainly just measurably reduced.

Pointing a word (or other symbol) at more than one thing.

Don't underestimate the move of re-situating ("casting the net-wider") - it has retroactive effects that modify the apparently 'local' as well. It changes the significance of 'thinking-of', and all one would like to associate it with. — StreetlightX

Sure, we hope it will. I just said don't assume that, and don't perpetuate too many myths about the supposedly narrower question in the process.

Carry on :clap:

I won't say too much about this because it should be pretty familiar. — StreetlightX

And coherent? That local problem solved, now cast the net wider? That move always disappoints me. Always cast wider, sure, but don't assume we've drilled deep enough, or that drilling deeper won't, and casting wider will, effect a better map of the territory. In this case, don't further entrench all of the mythology of subject/object, of mental words and pictures, albeit circumscribing it.

Of course I can hate the recipe but love the pudding, of which the proof will be in the eating. Thanks for the book recommendation. And the thread.

Also you [@Nagase] seem to assume that if a rule goes from true beliefs to true beliefs, it is justified. — 83nt0n

Agreed.

Once again, this is using modus ponens to prove modus ponens. — 83nt0n

I disagree. It might just be recognising soundness as a self-evident virtue. Another modus ponens (aside from the one being justified) needn't be involved. You were just on a roll with that objection, no? It is the tortoise's expected refrain, true, but the tortoise doesn't talk about this combination, wherein the student accepts A, B and Z (from true to true) but not C (the rule). The tortoise invites us to justify Z on the basis of A and B, and then of course he claims to need C (and then D etc).

I only mention this in case it connects the tortoise's problem to the alleged 'scandal' of deduction: of its telling us no more than we already knew; of soundness being an empty (as well as self-evident) virtue. If Z does indeed follow from A and B as C claims, then C goes without saying. So much then for,

“Whatever Logic is good enough to tell me is worth writing down,” said the
Tortoise.

I'm curious to see what some other people think about this. — 83nt0n

Me too: https://thephilosophyforum.com/discussion/comment/377693

I'm actually tempted to call it the 'problem of deduction'. — 83nt0n

Different to this, though?

https://www.semanticscholar.org/paper/The-Enduring-Scandal-of-Deduction-Is-Propositional-D'Agostino-Floridi/6ff51e3f704044fac00b2c7430cf1ac775283820

Yes, I think so.

Male and female brains are “wired” differently, — NOS4A2

Undeniable. (I'm guessing.)

“Male brains are structured to facilitate connectivity between perception and coordinated action, whereas female brains are designed to facilitate communication between analytical and intuitive processing modes”. — NOS4A2

Decade-specific fantasy. (I'm guessing.)

Love jazz, hate jazz-ism - the assumption that there are this and that musical natures or essences, and we should care whether this instance or kind is part of that kind (except insofar as doing so does happen to enhance musical appreciation; but thinking the kinds are natural isn't going to make that more likely).

Love philosophy, hate philosoph-ism, the assumption that we should care whether this instance or kind of thinking should be considered part of that.

Love critiques of essentialism...

We can talk about "such things as unicorns." What, if anything, we mean by such talk is a secondary question, — SophistiCat

To be fair, "such things as unicorns" usually expresses impatience to clarify exactly what, if anything, can possibly be referred to, given that meaning of some sort is happening.

Retreat here is against the rules defined by context. :wink:

But you basically agree with me about the trouble.

We can refer to unicorns in thought and in speech. — SophistiCat

By "unicorns" do you perhaps mean unicorn-stories, or unicorn-pictures? Or something more psychological such as unicorn-ideas or unicorn-thoughts? Or something even more exotic?

Or is your notion of reference itself exotic? Can you point at something which isn't there? (Any more than riding or stroking it?) Does reference never fail?

Either way, if so, why claim to be retreating to syntax?

I had the same syntactic sense in mind in both cases. — SophistiCat

Please advise?

any subject of a sentence, anything to which we refer. — SophistiCat

Trouble is, a unicorn can be the first but not the second.

What if for an alien's brain, 2 plus 2 equals 100? I can see how that could work. — Gregory

Ok, is that like their Romeo copping off with their Tybalt, and it working as drama, perhaps... or it being canonical?

Or is it, after all, a matter of their having a system of symbol-pointing that we could reasonably interpret as equating certain (or all) quadruples with certain (or all) centuples, in some way that works for them?

It is an elemental conception of the 20th century. Please read:
Popper, K. R. (2002): Unended Quest: An Intellectual Autobiography, London & N.Y.: Routledge [1978], 7, pp. 15 ss. — Borraz

Haha, ok.

:roll: (seems the nearest emoticon for "unconvinced"... don't mean "roll")

Aren't they only fictions? — Gregory

If you like. Although wasn't Frege and Russell's logicist project roughly (I think I'd better stress the roughly) about construing them as kinds of quantities? And then isn't there also the option of treating equations as pure syntax?

But ok, settling on the popular course of deferring literal translation of our grown-up math talk just as we do with our Romeo and Juliet talk, and just agreeing to play "pretend", what then is your question? Which numbers or classes of numbers are you supposing do or don't share a nature, and under what assumptions?

I am not doing what jgill says. — Gregory

I hope I didn't misrepresent @jgill; his description just put me in mind of a possible contribution to that other thread.

If reality has no common natures, why should numbers share a nature necessarily? — Gregory

Numbers construed how? As fictional characters, or concrete quantities?

incredulous — StreetlightX

Incredible, Shirley? (I know you're a stickler.)

What makes for a good philosophy? — A Seagull

Exploring of apparent implications under threat of reductio ad absurdum in order continually to clarify, revise and construct?

https://thephilosophyforum.com/discussion/comment/397745

I see this kind of argument here not infrequently. :roll: — jgill

What, exploring of apparent implications under threat of reductio ad absurdum in order continually to clarify, revise and construct? If only!

https://thephilosophyforum.com/discussion/comment/397746

https://thephilosophyforum.com/discussion/comment/334932

It seems to destroy math actually. — Gregory

How so?

Nothing is exactly alike because individuality is what defines things in this philosophy. — Gregory

:ok:

Letters have a pragmatic function in the structure of the word, and words have a pragmatic or technical function in the formulation of theories — Borraz

You said that before. Please elaborate?

simple spelling or grammar — Pfhorrest

is a direct applications of my

for which were are simply not

without concerning itself with what anyone might be communicating about what [about which of the various possible?] attitudes toward them.

My struggle with that one may be due more to my philosophical prejudice against attitudes than to any capital problem for the sentence. Can't quite tell.

And so on with all those we can replicate [:?] implication,...

whether there are, or or whether

reality being describable by a formal language would be either that ome

, continuous with the one we find ourselves in and the of same nature as it;

the question of whether were are

Interesting and worthwhile. Thanks for sharing.

If your intuition is that the Planck length is represented as fixed because it is a physical constant, — fdrake

More like, that some error threshold imposed by the Planck length is represented as fixed.

What if we put in an error threshold of the Planck length, — fdrake

That would be a dp thing rather than sf?

Yeah fine. They both cause rounding errors, but Planck length would be a dp thing rather than sf?

The internet told me floating was sig figs not dp?

Helpful post, thanks. Possible typos:

t = 0 to t = t. They they — fdrake

t = 0 to t = T?

They then? Obvs.

If you can only represent 3 decimal places, — fdrake

Fixed not floating, then? (And fixed by Planck length, if I understand you.)

I don't understand this comment. — Xtrix

Damn! I thought it was droll.

I long ago gave up the appalling vanity of trying to stay awake whilst meditating, but lately I have, perhaps ironically, become moderately skilled at prolonging self-awareness whilst falling asleep. I can, sometimes, observe the surreal failures of logic building incrementally, instead of the (still) usual pattern of suddenly waking (with a jolt), unable to retrace the train of thoughts back to the last fully wakeful one. I'm convinced this method of amusing myself (which is derived from a roughly similar practice of Salvador Dali's) is relevant to the quest of explaining consciousness. For example the issue of 'executive' control of thought, often associated with 'self'. How rambling and linearly uncoordinated can a stream of consciousness become without being in fact (or perhaps I should say, being by definition) unconscious? I'll stop here in case I prompt a similar question about the nature of a post.

Interested in people's reports about this kind of thing, however (inherently) unreliable.

Nelson Mandela, Martin Luther King, Mother Teresa... didn't they all have selves? — Shawn

Hence the joke of the original title of Life of Brian: "Jesus: Lust for Glory".

we understood death better than other animals — christian2017

https://www.theonion.com/scientists-successfully-teach-gorilla-it-will-die-somed-1819594897