A photon is an object defined as a particular quantity of energy. If any energy of equal quantity can be said to be "the same" photon, because the law of identity is violated in the way that it is in mathematical axioms, then it's very obvious that temporal continuity of a photon, as an object cannot be maintained. — Metaphysician Undercover

Hmmm. :chin: Physicist around?

It's unfortunate that the law of identity uses the equation symbol, = , since in math the equality symbol has two meanings: (1) 2=2, identical, and (2) 2x=x+3, conditional. I would think philosophers would use the identity symbol, ≡, which means both sides are always equal in a particular discussion.

If people are playing the same game, then they hold the same goal as the object of that game. If all mathematicians do not have the same goal, then they are not playing the same game, and we cannot describe mathematics as "a game" — Metaphysician Undercover

How pleasantly wrong you are, MU. There are cliques within the broad structure of math in which participants work towards common goals. I was in such a clique.

Pure mathematics is more like an art. — Metaphysician Undercover

Since leaving my clique years ago, this is how I perceive math. I was never a good game player since I enjoyed going off in imaginative directions and doing my own thing.

I don't consider any such human activity as a game. Games are played for entertainment, and in general, the goal is to win. — Metaphysician Undercover

Sometimes games are played for money or prestige. The professional mathematician finds his activities entertaining, frequently fascinating, and he definitely likes to arrive at a result before others. He likes to win.

You must use a different definition of "game" — Metaphysician Undercover

Nope

Anyway, fishfry goes beyond your definition of "pure mathematics" to claim that "You can, if you like, view the entire enterprise as an exercise in formal symbol manipulation that could be carried out by computer, entirely devoid of meaning. It would not make any difference to the math." — Metaphysician Undercover

That's one way of looking at it. It's not the way I perceive the discipline.

1. x + 3 > 5. What is the solution set for equation 1? {3, 4, 5,...} — TheMadFool

It's not an equation. I know, nit-picking, But I am idle at the moment and feeling peevish! Nothing to do.

After almost ten years in a physics department, I haven't come across it — Kenosha Kid

I was thirty years in a math department, and I cannot recall any sort of serious discussion condemning philosophers for meddling in our subject. Occasionally someone might bring up intuitionism or Platonic ideals, but no one paid any attention to academic philosophers dissecting mathematics.

We must ensure that the mathematical axioms which we employ conform to reality or else they will lead us astray. Therefore it is actually necessary that we do change mathematical axioms as we try and test them — Metaphysician Undercover

You appear to suggest that mathematical axioms are similar to theory in physics. String theory, however, seems un-testable at present. Does it then lead us astray? If you were to say it does, how could you possibly know? How might you test the Axiom of Choice?

It's interesting to read perspectives of mathematics that I suppose could be called pre-foundational to distinguish them from formal foundation theory that fishfry is good at explaining. These are notions I never entertained while active as a mathematician. Of course, I didn't spend time looking into formal foundations either.

fishfry refers to math as a game, and it certainly is that. But a practicing mathematician may lose that perspective and math may assume a kind of non-physical solidity and seem "real", even when it's not obvious that it may be related to physical phenomena. Similarly chess probably seems "real" to serious devotees. Incidentally, MU, "pure mathematics" simply means not immediately applicable to the physical world. I've dabbled in this sort of math for decades.

And, I think jgill agreed with me on this point in that other thread as well. — Metaphysician Undercover

From the perspective of appearances of symbols you have a point. Clearly, 2+2=3+1 displays symbols on either side that are not the same as symbols on the other side. So the two sides are not "the same" in this sense. But this is a triviality among mathematicians - and the general public - who associate with each side a mathematical entity, the number 4. Likewise, Four=4 shows different symbols representing the same mathematical item. However, I believe your position exceeds these parameters and is somehow more "fundamental".

This seems like a silly game of distinction without a difference that could only appeal to intellectual descendants of medieval scholasticism. But I could be wrong.

Set theorists are morally bad people? Who need to be shown the error of their ways? — fishfry

Good one! :rofl:

This might be the key to their salvation: { } = {N} :cool:

I really hope a few people read this and become disabused of this notion that in an infinite sample space everything must happen infinitely often. It's not true. — fishfry

Repeating this for emphasis. But I fear it will be quickly forgotten. :cry:

For instance, a person untrained in singing, who has never heard an excellent singer, will be content to listen to even a bad singer. Thus, this person, and his friends, all equally ignorant, will happily sing to each other — Garth

This is hilarious. One of the reasons I enjoy this forum. :cool:

You are thinking too small. One mythical triangle, a hundred triangles, immaterial. Consider a structure akin the Tegmark's mathematical universe that interweaves and supports the entire universe. Call this MATH.

We mathematicians pull threads from the rich fabric, imagining ourselves creating mathematics, when in fact we only uncover wisps of a majestic and largely unknowable tapestry - a single entity beyond our wildest speculations.

H.P. Lovecraft (1890-1937) — 180 Proof

I've never thought of him as a philosopher, but I suppose he was in a way. Cthulhu and Great Old Ones diminish human existence.

However, don't be fooled by the word "simple" for it's only so by virtue of the wisdom gained from the collective effort of people actually philosophizing over many generations — TheMadFool

Does that mean that those people became simpletons? I'm confused. :chin:

By demanding and pursuing some perfect and excellent way of understanding the world, we really do nothing but discourage our ignorant friends from participating — Garth

Clearly you are not speaking of the social environment here at TPF. :wink:

Whoops! Misread this as "Quantum Immorality". Now there's a metaphysical topic worth pursuing! :nerd:

. . . that nothingness has a limit (a state of non-existence would be a state of non-existence and nothing else) requires that something exists; that is, nothingness can't never be [the "existence" of a state deprived of things that exist (nothingness) would necessarily induce a state populated by things that exist due to its limited nature]and it is this characteristic about nothingness which is responsible for the origin of the universe — Daniel

Well, that was easy enough. You might join TheMadFool in his investigations of nothing.

As I mentioned, professional philosophy appears to be much like professional mathematics. Even in youthful days it was not easy for me to keep abreast of progress in my area of expertise, much less so in other areas. Those times are long gone, so I toy with elementary concepts I find interesting merely as a hobby. Somewhat analogous to philosophy appearing in this relaxed forum. :cool:

thus, people cannot be held responsible for their actions if they did not make a choice to break any such laws — ToothyMaw

How does this accord with the judicial "Ignorance of the law is no excuse"?

I'm with Feynman on this, let's see some examples that unravel the word scramble. :chin:

I think it's really something that you are still in pursuit of nothing! Keep up the good work. To many this means nothing, but they are wrong, it is something! :cool:

Am I a seeker after the nature of viruses, or the man who tells you how best to arrange public policy to avoid its spread? — Todd Martin

Referring to the esteemed Marcus Gabriel: "In an April 2020 interview he called European measures against COVID 19 unjustified and a step towards cyber dictatorship, saying the use of health apps was a Chinese or North Korean strategy. He said the coronavirus crisis called into question the idea that only scientific and technical progress could lead to human and moral progress. He said there was a paradox of virocracy, to save lives one replaced democracy by virocracy." (Wiki)

The reasoning and wisdom of an accomplished philosopher. :roll:

He argues that the concept of existence is incompatible with the existence of the world and therefore proposes his innovative no-world-view. — Apparently Someone

MG: "I call metametaphysical nihilism the view that there is no such thing as the world such that questions regarding its ultimate nature, essence, structure, composition, categorical outlines etc. are devoid of the intended conceptual content. The idea that there is a big thing comprising absolutely everything is an illusion, albeit neither a natural one nor an inevitable feature of reason as such. Of course, there is an influential Neo-Carnapian strand in the contemporary debate which comes to similar conclusions. I agree with a lot of what is going on in this area of research and I try to combine it with the metaontological/metametaphysical tradition of Kantian and Post-Kantian philosophy." (Wiki)

Nice presentation, Todd. From Wiki "Contemporary Philosophy":

"The end result of professionalization for philosophy has meant that work being done in the field is now almost exclusively done by university professors holding a doctorate in the field publishing in highly technical, peer-reviewed journals. While it remains common among the population at large for a person to have a set of religious, political or philosophical views that they consider their "philosophy", these views are rarely informed or connected to the work being done in professional philosophy today."

Sounds a lot like the professional mathematics community. On the other hand, Nagel has much to say apart from the highly technical. Certainly philosophy has much to offer in ethics, morals, and judicial areas.

It takes a special person to explain an advanced concept to a layman. I had a friend, a physicist, who worked with high school students in an impoverished region in the deep south. He would carry an old cigar box full of coins stacked neatly, that he would show. Then he'd ask a student to shake it up and take a look inside. "That's entropy", he would explain.

He recruited several students to his college who went on the earn PhDs.

Am I the discoverer of the effects of greenhouse gases on the environment, or am I the one who best shapes public policy to curtail emissions? — Todd Martin

The former quite obviously needs an extensive science background, and the latter needs to be very conversant with politics, governmental processes, and social psychology. All above and beyond the abilities to reason and write well about past generations of philosophers.

I think it is a tough path to take these days, and I don't envy those professionals who do. It would be more than I could accomplish. Math, by itself, was hard enough.

Motion without time? Look at a photograph. Think of the universe as a dynamical system, forever changing. Time is a way of perceiving change. A tiny iteration of a process in space could be interpreted as a tiny step in time. No change = no time.

Just a thought. :roll: My attempts at philosophy are shallow.

Acolytes are expected to develop indifference to the discomforts of heat and cold . . . — Harold Stewart

I was once told by a practitioner that there were several dogs beneath the thin floor of their meditation building that kept up a racket. They were told to get used to it. :smile:

It's unfortunate there is no one on the forum who has had the Zen epiphany, described in various ways. I did Zen meditation for about a year sixty years ago, but dropped out of the practice. A friend has been doing Zen for over thirty years and he describes the sudden enlightenment as a very stunning, even jarring moment. He then describes his mental state as "empty awareness" - and I argue that since he is seemingly aware of the state it cannot be empty. He also argues it is not a "mental state".

I suspect an actual Zen practitioner would be chuckling at all the philosophical positions in this conversation.

BBC: "Zen is not a philosophy or a religion. Zen tries to free the mind from the slavery of words and the constriction of logic."

Think: Deep Sleep

There are a countably infinity of Turing machines hence a countable infinity of computable numbers, hence a bijection between the natural numbers and the noncomputable numbers. — fishfry

Sorry. Am I missing something here?

I think philosophers should talk about the "big stuff". But that stuff is prone to be very technical, requiring knowledge that takes patience and study to accrue. Of course philosophers should talk about the intricate issues of physics - provided they have deep understanding of the subject. Of course philosophers should address complicated issues in economics - provided they are economists. We don't live in the Athens of 500BC.

I think what I really like about the Dialogues of Plato is just that they take a bite at stuff that is NOT the kind of things like laws of physics, stuff like friendship, love, how to run a state — Ansiktsburk

A political philosopher needs a background in PolSci. Some denominational ministers are quite good at friendship and love - in that sense they are philosophers. And, of course, amateur philosophers can talk all they want about anything. Sometimes people listen.

One of the unsolved problems in science is the so-called Theory Of Everything (TOE). While I'm not clear on the details and hopefully that doesn't matter , , , — TheMadFool

I'm sure the details are insignificant, so proceed with your investigation of reality! Bully show! :smile:

If it is just drawing from things that already exist? — Darkneos

Can you identify Dora Maar from Picasso's portrait?

This is a painting (drawing) of a thing that already exists. Suppose that thing was a photo of Maar. Would Picasso's portrait be considered a copy then?

{ } is a subset of A, { } has N as an element. So A = {x, y, N} — TheMadFool

Since N is an element of A, it is something: an element of A. :worry:

Ergo, Nothing is impossible. That's why there's something. — TheMadFool

I'm so glad you have proven this to your satisfaction. It shows that something is nothing to worry about. Thank you. :up:

Nothing = The empty set = { } — TheMadFool

The empty set is not nothing. But it contains nothing. At least in naive set theory. :nerd:

It is nothing, but it can become everything. — leo

Very pleasing and Zen-like. A koan? :up:

In the pre-universe either something comes from nothing or there was an eternal and immaterial (no-thing) first existant. It is so simple. — val p miranda

You seem to be thinking of the hypothetical pre-universe as something that we can reason about, as if the logic of our world can be applied to what might be completely alien to us.

I don't see it as a valid question, more like a waste of time. — Darkneos

Ditto. Like discussing an afterlife.

For this theory of reality being a simulation to fly, it's necessary that the program that codes the simulation be finite for if not the program can't be completed/finished let alone executed on a computer. — TheMadFool

Why? You seem to assume that whatever meta-reality "programs" our reality is subject to the same laws and processes that occur in our world. Perhaps our notion of time does not exist there, nor the physical laws of our universe. In that case your argument concerning the irrationals is meaningless. Just a thought. :chin: