Returning to your example, (2,3) and (1,4) cannot both be elements of a continuous set so the set you are considering is not included in the enclosing set — keystone

I don't know what you are talking about. You and @fishfry can sort all of this out if he is willing. Good luck.

"In a metric, the distance between two distinct points as always positive."


d([2,3],[1,4])=0 ? [2,3] not equal to [1,4].

According to some interpretations of irrational Infinity though, an infinite-sided die is not impossible, only supernatural, in the sense that you can imagine it, as an ideal concept --- e.g. a perfect multidimensional sphere --- but never reach-out and grasp it, in the real world. In what sense does that set of one "imaginary die" exist? :joke: — Gnomon

What is "irrational infinity"? Infinite sided die seems like a sphere in 3D.

Mathematics has a similar structure to certain conceptions of magic. It requires years of studying something entirely incorporeal, it seems to exist independent of the physical realm, it’s very powerful and has the ability to predict and influence the world around us, and it’s practitioners are BIZARRE — Gnomon

Does magic influence the world around us? Wow, what bizarre powers I wield! :cool:

Since you're joining in on the conversation, can you tell me if anything I'm saying makes sense to you? — keystone

Not much, I fear. But I stand aside and try not to impede the ongoing discussion between you and @fishfry, who is more familiar with modern math topics that I am. I am curious about the role of elasticity you describe regarding one of Zeno's paradoxes. I assume this is somehow basic to where you are headed.

As I mentioned before, the metric between ordered pairs (x1,y1) and (x2,y2) is defined as follows: d((x1,y1),(x2,y2)) = | (x1+y1)/2 - (x2+y2)/2 | — keystone

Is (x1,y1) a point in the Euclidean plane? That's a standard designation. Then (x1+y1)/2 requires some kind of a projection of the y1 down upon the x-axis in order for this expression to represent a midpoint of a line segment. Or, is (x1,y1) an interval on the real line? Perhaps use (a1,b1) instead to keep the level of confusion minimized. Maybe my colleague sees something here I don't. Please carry on.

Not so sure philosopher and critical thinker are one and the same.

Step two entails describing these intervals within the framework of a topological metric space. — keystone

You have used this expression frequently. Do you know what you are talking about? Just curious.

More like a inspiration to get peoples own ideas going — Elnathan

Works sometimes. Not always. A brief, concise OP helps.

The math doesn't identify any particular stopping point, but it does imply there has to be one. — Relativist

An exercise in free will. At each n the cube changes from white to black or vice-versa for time = 1-1/2^n. The clock runs out so you are free to say the process has ended and the final color is black. Your friend can say, no it is white. But you will prevail.

However: the kinematic process never actually reaches time 1 — Relativist

That's no surprise. It is an imaginary contrivance impossible to physically fabricate. Just a thought.

From the bleachers: Hasn't MU spoken of the existence of continua prior to points? What of Bergson's notion of time being fundamentally duration? Perhaps not elastic. Is this where the discussion is going? Peter Lynds has written several papers on the non-existence of points in time, as well.

Back to the popcorn.

Non-understanding does not equal understanding. — Echogem222

No argument with that. :roll:

For those, like me, who didn't know: Fallacy of the undistributed middle

Pass the popcorn, please. I am sitting in the bleachers watching with interest. :chin:

By definition, a limit is not reached, — Relativist

$f(x)=3x+2$, $f(1)=5$

$\underset{x\to 1}{\mathop{\lim }}\,f(x)=f(1)$

However, the clock does reach 1. At time 1, the stairway descent must have ended — Relativist

Certainly the relationship between time (independent of human control) and physical steps taken over a period of time has ended.

I would say they were very intelligent. — isomorph

But

a thinking capacity equal to ours, maybe greater than ours

?

Welcome to the Forum. :cool:

Our prehistorical ancestors had thinking capacity equal to ours, maybe greater than ours, and this can be seen in prehistoric cave art created by intellectual masters. — isomorph

How do the drawings on cave walls imply intellectual capacities rather than simply artistic abilities?

So there's just no paradox. There is only taking perfectly well-understood mathematical facts and dressing them up with physics-contradicting staircases and lightbulbs so as to confuse people. — fishfry

:up: Amen :roll:

I decided that I will contact the philosophy professor at the local college and ask him if he can be my mentor. — Fermin

I hope that works for you. I was a math prof for many years, and at large universities senior faculty might simply give an unsolicited paper to a grad student as an assignment to critique. It may be the same in philosophy.

How might all these dynamics interact? — Benj96

I wonder how dynamic systems would function. At each step there would be many options.

Wonder what that 8,500 crossings/day means? Not enough energy to check it out.

I say yes. I predict that in my area, math, there will be computer devised concepts and results beyond human understanding. If simply the length of a particular discovery - only so much that can be kept in the mind and be instantly retrievable for comparison.

Maybe not.

While they may not regard him as The Messiah the do believe his is a messiah and like all messiahs persecuted by the enemies of God. — Fooloso4

Or perhaps the only apparent option to remove the Biden cabal. Don't forget, Joe told immigrants to "Surge the Border", and gave Afghanistan back to the Taliban - where recently the supreme Poohbah stated he is bringing back stoning certain women to death.

The only problem with this type of exercise is that the dog does a lot of sniffing and we don't move very fast — Agree-to-Disagree

Be tolerant and thankful for a furry companion. :cool:

**Description**: Apply ethical theories to real-world scenarios. Discuss topics like environmental ethics, personal and social justice, and personal and social responsibility.
- **Age Appropriateness**: Middle schoolers are forming their identities and need guidance on ethical decision-making. — Lif3r

Add The Philosophy of Taylor Swift to the middle school part.

Finally got it down to a decent routine. Here’s my current schedule (in case you want to doze off — Mikie

Good for you. Keep it up. When you are very old something may knock you down, then as you try to recover, doctors will find something else. A downward spiral difficult to pull out of.

But I have not found a single one who will even respond to any question as to anyone who should not have a gun. — tim wood

I tend to vote more conservative than liberal these days and I object to illegal immigrants having guns.

Can a brutha get an AMEN?! :sweat: :up: — 180 Proof

No amen yet. Still hoping for a different Dem ticket. "Surge the Border Biden" deserves defeat.

If most citizens have the right to gun ownership, what of illegal migrants?

I'm proceeding with the assumption A.I. will be overtaking the task of heavy lifting re: thought. I'm rooting for S.A.I. in our lifetimes to run up cognitive yardage pushing past what human can imagine. Wittgenstein has directed our attention towards "the silence," conjecture unimaginable. Its nigh time for The Oracle: SAI to start sending us revelations from Wittgenstein's principled imagination silenced. We won't understand but a fraction of the import of the messages, but we'll get pushed to our utter limitations before being back-numbered into the subordinate section of the evolution hierarchy. — ucarr

:up:

It won't be long before mathematical concepts and results stretch beyond our abilities to comprehend.

If you take pi or the golden ratio or eulers number for example, eventually it will detail your entire genetic sequence from start to finish — Benj96

Reference?

Do you condone dishonesty and pretension? — Corvus

When it amuses. Keep going. :cool:

Agreed. But that philosophy should be provided by the scientists. — jgill

Any bumper sticker you can provide for why? It seems odd to me. Like saying hydrologists need provide the engineering know-how for hydro-dams. — AmadeusD

I am speaking of the actual science, not peripheral sciences nor philosophy concerning the use of scientific discoveries. Also, I included other kinds of philosophers. I suppose it is possible for a pop philosopher to dream up a concept that clarifies an issue defying the best scientists in that area, but unlikely. On the other hand there is ample proof top scientists can produce whoppers, viz. Mathematical Universe and Multiverses.

As for hydrologists who are philosophers as well, go for it!

Anyway, this is just my opinion. When a non-scientist philosopher produces a breakthrough in quantum theory I will eat my beanie.

I can say anything I feel correct — Corvus

Says it all :roll:

Useful for those who are not too lazy to be staring at Truth tables — Banno

So, this entire discussion devolves to something I used to teach freshmen.

I would like to have a discussion with Corvus about if the logic used here is actually logical, or if it is perhaps fallacious — flannel jesus

You guys need to find a bedroom. I'm surprised we others are allowed to witness the proceedings.

:roll: .

Royal Robbins, The American Climber
by David Smart (2023)

I do not think the complete scientific method can exist without philosophy — Philosophim

Agreed. But that philosophy should be provided by the scientists.

Maybe it's a stretch, but I think metaphysics as the grammar or rules of procedure offers suggestions as to how methodology might evolve. — ucarr

I don't see how philosophers looking over scientists' shoulders does any good. The various sciences have their own procedures, with the exception of quantum theory where there are questions.

In the modern era the philosophy of science is largely done by scientists who work on the cutting edge of science. Their speculations are the creative philosophical gems that propel discoveries.

There are some philosophers who are versed in contemporary knowledge who might qualify as well.

JMHO