And of course this goes for other mathematical entities, too. They are things we do, not things we find. — Banno

Baloney. Are not ideas things we "find?" Whenever we discover a concept, is that not a "find?" Is a Hilbert space something we "do?" So there. :nerd:

Watching philosophers talk is sort of like watching a bird with a broken wing keep flapping it, and trying to readjust, not understanding what's wrong — Snakes Alive

:cool:

No deductive argument will settle any of these issues: it simply pushes the problem back by introducing new premisses subject to the same issues. Still, the same structure is found in other disciplines. For instance, in mathematics, chains of reasoning ultimately run back to axioms, and the question of their justification eventually arises (Maddy 2011).

This is true of mathematics. However, the vast and productive bulk of non-pathological mathematical results, particularly those that describe nature, do not involve critical analysis of axioms ultimately underlying them. The mathematical snowball was well on its way before substantial efforts to establish foundations occurred.

Nevertheless, by altering basic assumptions new perspectives arise, sometimes contradicting previously held notions. For example, https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis

Once adopted by a clique of mathematicians, the game of logical development and creativity proceeds as a kind of social effort. How does this compare with philosophical arguments? You tell me.

Pure philosophy hasn't made a dent in unraveling the mysteries of mind. Classical philosophy is a dead end here. One needs to move into a mix of neuroscience and modern philosophy to make any progress. Chalmers, with his Hard Problem, is a leader in these efforts. Also, Zen practice leads to experiential knowledge of the subject.

https://en.wikipedia.org/wiki/David_Chalmers

Although there is nothing in the mathematical world, there is no nothing in nature. If you propose pure emptiness, you haven't looked hard enough. :cool:

http://www.supertopo.com/climbers-forum/1593650/What-is-Mind

Been there. Done that. No conclusion in 22K posts. :worry:

I was tempted to ask if anyone still reads Being and Nothingness. But of course no one ever actually read Being and Nothingness. — Banno

I did, back in the late 1950s. Existentialism and the Look made an impression and influenced my attitude toward solo climbing. The simple presence of another living soul alters experience.

Sometimes superior articulation conceals faulty arguments.

. . . questions like "what are these possible paths that Langragians integrate over?" seem to make sense — jkg20

Amazing how cancellation reduces an infinite set to a finite one. I still puzzle over the measure employed in those functional integrals. :nerd:

I would love to see all medical training, for doctors, dentists, nurses, aides, and all other healthcare workers to be 100% paid for by the government...with a healthy stipend for people entering the field. — Frank Apisa

As a young USAF officer, I was sent to the U of Chicago to qualify me as a meteorologist. All expenses paid plus a decent salary at the time. I knew of MDs and one lawyer who had been entirely supported as I had been. The lawyer remained in the Air Force and retired a Colonel - he's now the district attorney where I live. The others put in a few years and left the service, as I did.

That was in the 1950s. I assume such programs still exist. Actually, I'm in favor of free education all the way, provided the recipient is serious and studious and not simply sponging off the US government. As a former professor I have unfortunately seen that happen.

Glad you got that off your chest. Here's good wishes for a quick recovery! :smile:

Perhaps nothingness is unattainable, like infinity. In math we routinely set x=0 in formulae, but math is an intellectual exercise and doesn't necessarily describe nature precisely. Even in math there are little number critters just to the right of zero on a scale, but to the left of any positive real number. These infinitesimals arose from the minds of Leibnitz and others long ago. Maybe in some crazy way they connect with the virtual particles of physics (although I have my doubts). So, entities below the Planck scale may surround a hypothetical nothing, which doesn't really exist.

Hey, just babble in the time of the Plague. :cool:

People get nervous during the pandemic, and talking on the net helps relieve the tension. It also produces even more nonsense babble than usual. :nerd:

Haha, Balloon Calculus — bongo fury

Lot of UFOs there! :gasp:

So how is starting with preliminary definitions a weakness? — tim wood

The old computer science observation: "Garbage in = garbage out"

But I realize I am guilty of judging philosophical arguments from the perspective of a (once) active, non-set theorist, mathematician. Philosophy is a much fuzzier discipline and what I perceive as a "weakness" is merely part of the game. For instance, some time back there was a discussion involving the notion of "metaphysical actuality", and I kept trying to get the person using the expression to define it. He never could, or lost interest. However, I did come across one reference in a letter to Leibniz, and from that an example was cited that made some sort of sense, at least to me. :smile:

In terms of the mean doctrine, I would say that the two vices in opposition are:
- ‘impatience’: one interacts only with the imagined reality; and
- ‘apathy’: one interacts only with the actual, observed reality. — Possibility

Apathy is a lack of interest, whereas being overly patient demonstrates a lack or suspension of judgement regarding an anticipated action or outcome. How long should a teacher wait for a student to answer a question?

Definitions are the Achilles' heel of philosophy. :confused: — jgill

How so? And keeping in mind that Achilleus's heel itself as a heel worked just fine, no complaints. — tim wood

Wiki: "An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common."

Definitions are the Achilles' heel of philosophy. :confused:

but what would you call the excess of patience? — Lecimetiere

To measure the degree of patience is subjective, although at extremes there might be consensus. Most would consider it "overpatient" to wait for a reply to a simple question in normal conversation for ten minutes, let's say. But "overpatient" would probably not be interpreted as a pejorative, like "impatient" could be. Just comments.

I can imagine the arrow has its momentum during any duration of time however short, but at the point where no time passes? — tim wood

The key word is "viewing." Zeno's condition doesn't actually stop the arrow, it observes the arrow at an instant. But the idea I advanced is not original. Some time back a well-known physicist I know dismissed the whole nonsense thing with this observation. :cool:

From a mathematician's perspective, many, if not most, philosophical issues lack closure and are endlessly debated - sometimes with very fuzzy definitions to begin with - and thus not really satisfying. However, philosophers seem to be very intelligent and, from many posts on this thread, usually impressively literate and knowledgeable. Especially those engaged in discussions about set theory and its parallel universe in computer science. I continue to learn things about these subjects by trying to follow discussions.

Definitely not insane.

Theoretically viewing a frozen instant of the arrow in flight does not destroy the momentum the arrow possesses at that instant.

Not insane. Just very talkative. :smile:

https://www.history.com/news/women-leaders-elected

And it almost happened here in the US. :smile:

and math crumbles before philosophy. Wouldn't it result in there being only one number? — Gregory

Yes! And I alone know what it is. :nerd:

My dog will not tolerate closed doors. I question her consciousness. :smirk:

From Einstein's Autobiographical Notes, a thought experiment he had at age 16:


"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."

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

Sorry, guys. My point is that an assumption of nominalism in physical nature is not required if one speculates about nominalism of numbers and other math concepts. Go directly to the question of whether nominalism exists in math. :cool:

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

Your hypothesis is nominalism. From which you draw a conclusion: nominalism.

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

"In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one" — jgill

Well, your wiki reference gives rather more succinct definitions, though they may require some unpacking. — SophistiCat

I don't wish to belabor the point, and, to keep it elementary and overly simplistic, avoiding the unpacking, the example

${{F}_{n}}(z)=f\left( {{F}_{n-1}}(z) \right),\text{ }{{F}_{1}}(z)=f(z)$,
$f(z)={{z}^{2}}+1$

shows the difficulty in reversing steps in a dynamical system, an expansion, this one very well behaved. The paper in question is far more sophisticated and I can't argue in that advanced physics environment. Although it makes more sense to deal with system reversibility than pointwise reversibility.

This would actually be a weaker version of absolute normality - the property of containing every finite sequence of digits in every base with "equal frequency" (scare quotes because this is more complicated than it sounds). — SophistiCat

Interesting. Thanks.

QM effects are already non-reversible... — VagabondSpectre

From Physics StackExchange: Reversibility in Physics

" The point is that you can't focus on the particle alone and have reversibility. If you focus on the particle alone in a measure process, then the process is irreversible. On the contrary, if you consider the whole system "particle + measure instrument", the dynamics is reversible. If after the measurement the whole system is described by the product of a state for the particle and one for the instrument (unentangled), using the reversible evolution of the whole system backwards you get the original complete state before measurement. Of course such state is usually entangled."

This topic is becoming increasingly complicated. And there are various definitions of chaotic behavior. Plus there are differences between physics and mathematics. :roll:

Find a critique of the philosopher's ideas, written by another philosopher who can explain them.

This is distinct from chaotic behavior (which is, in a technical sense, reversible) — SophistiCat

Explain what you mean by "which is, in a technical sense, reversible". Please provide a reference.

"In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one"

From Wiki:

"In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one"

(most of the functions I've used fail to be univalent, so irreversible)

"[In physics] T-symmetry implies the conservation of entropy. Since the second law of thermodynamics means that entropy increases as time flows toward the future, the macroscopic universe does not in general show symmetry under time reversal."

There could be a thread on the concept of time-reversibility. There seems to be a slight conflation here between forward and backward dynamics.

From: https://royalsocietypublishing.org/doi/full/10.1098/rsta.2015.0161

"This fact leads to a paradox if one ponders the reversibility and predictability properties of quantum and classical mechanics. They behave very differently relative to each other, with classical dynamics being essentially irreversible/unpredictable, whereas quantum dynamics is reversible/stable."

"Although, the dynamics are predictable and reversible with an exact representation of the state of the system and an exact implementation with a perfectly precise set of equations of motion, any deviation of either leads to exponential instability in the predictability of the reversed dynamics."

Chaotic systems can arise from SDIC: sensitive dependence on initial conditions. Reversibility seems far-fetched to me even though it can be theoretically possible, having worked with deterministic systems in the complex plane. But I lack the credentials to speculate about the physical world.

In fact, one of the protocols of math is never read mathematics without a paper and pencil nearby. And an anecdote I've mentioned before: The maid of a famous mathematician was once asked what her employer did for a living. She replied, "He scribbles on paper, then wads it up and throws it in the trash."

:cool:

I'm not clear about this. I've always assumed (and I could be very mistaken) that "time reversibility" is just a quirk arising when describing a physical process using mathematics. The two are not the same.

"And they have shown that the problem is not with the simulations after all."

Well, they're doing computer simulations in an environment of exceptional chaotic behavior. So I don't know what to think about reversing the actions.

Time for a real physicist to chime in with their opinions. Beyond me. :chin:

There is a vast universe of mathematics that has existence as potential. All the logical derivations that lie in wait to be discovered, accompanied by acts of creativity yet to appear - like works of art. :cool: