This is simply not true. Numbers are defined by quantity, not order. — Metaphysician Undercover

You're failing to distinguish between cardinals and ordinals. — fishfry

MU knows so little of mathematics and yet is so confident. It's almost an admirable trait . . . but not quite.

The point I'm trying to make "when the car is in the garage" the space occupied by the car (while in the garage) - that space is still part of the garage (even though it has a car also in that same space). To me, that means, at that time, both the car and the garage are (in fact) occupying the same space - Not all of the space - just the space where the car is parked — Don Wade

The garage defines the space within it, that space is not part of the garage. The garage door is part of the garage, the cement floor is part of the garage, etc. ff is correct: you are playing a word game.

As has been noted, there are various ways of opening the doors of perception that, once experienced, render philosophy inconsequential. My initial exposure occurred nearly a half century ago, and my first thought was Now I understand the ancient origins of religion. Experience triumphs over reason.

I did some Venn diagrams on a drawing program but haven't worked out how to post it here. — Mark Nyquist

If you become a subscriber ($/month) you can upload images. Otherwise to link them it seems you need a source that is secure.

Encyclopedia Britannica is simplifying and reifying the model more than is necessary. — Enrique

And they should know better! :gasp:

(The good and bad threads should be combined under the rubric, Physics Jabber.)

Is "pure" mathematics, meaning, mathematics that does not apply to the world (via physics, for example), something invented or discovered? — Manuel

Most practicing mathematicians at one time or another spend a short period contemplating this question. Then they move on and do mathematics. My thoughts are that some is invented and some is discovered. For example, I recently "invented" an attractor transform for certain functions. Then I set about trying to discover its features. (of course, it may have been invented before - that happens not infrequently in math)

Some philosophers like to ponder the question you posed. Most math people don't care. :cool:

As usually propositions do not change with layers,
we do not notice this change of layers in our surroundings.

But the layers could be there all the time ... — Trestone

You have developed a personal philosophy based on LL. Congratulations.

The sequence a,b,c,d,e is a sequence of five letters. e is letter five. — jgill

That's an arbitrary designation, dependent on a stipulation that there is a left to right order to the sequence. "a" could just as easily be letter five, or we could assume an ordering which makes any of the letters number five — Metaphysician Undercover

No. I have implied the order of the sequence. It's not arbitrary. A more mathematical format would be
(a,b,c,d,e). This omission may have confused you. :roll:

A physical observer is an objective instrumental observer not a person — magritte

Bingo!

As the article says, "the absolute square of the wave function is interpreted as an actual matter density" — Enrique

Really?

"The square of the wave function, Ψ^2, however, does have physical significance: the probability of finding the particle described by a specific wave function Ψ at a given point and time is proportional to the value of Ψ^2." (Britannica)

mathematics is called the "Queen of the Sciences" — jgill

The 'queen of sciences' used to be theology. — Wayfarer

I was unaware of that, thanks. It was Gauss who coined the phrase I quoted and he is a mathematical deity! :cool:

He also claimed number theory to be the Queen of Mathematics. :roll:

From the Stanford entry: "One way to distinguish between science and religion is the claim that science concerns the natural world, whereas religion concerns both the natural and the supernatural."

That pretty much does it for me. But then I'm not a scientist (although mathematics is called the "Queen of the Sciences", it's not one itself.)

On one day we get for a number n the prime decomposition P1.
One week later we get on the same computer with the same program for n
another prime decomposition P2 (and similar disturbing results with other computers). — Trestone

Why would another prime decomposition, P2, arise if not for a computer implementing this layer logic? Thus, avoid disturbing results by ignoring layer logic.

Sorry. I see things from weary old eyes. :roll:

The sequence a,b,c,d,e is a sequence of five letters. e is letter five.

Imagine not having the pressure of trying to figure everything out, instead, just going with the flow of ideas, allowing them to come and go as do all things — synthesis

Like a leaf in a stream, floating quietly in sluggish waters, but skimming past whirlpools to be on its way, frivolous and ethereal. :cool:

With a closed mind, you will always be wasting your time — synthesis

Good troll thread, eh doctor? :cool:

Possibly because simple ideas like "and" and "or" are defined as type, whereas set theory is not so bizarre. Maybe not.

If you would accept the notion that each object in The Universe occupies unique coordinates and is subject to unique Universal forces, then one might conclude that each object in The Universe is "one of a kind," that is, unique in and of itself. If this is indeed the case, then what exactly does "2" mean? — synthesis

There are unique coordinates? I take it you mean two objects don't occupy the same space at the same time. What does "one of a kind" have to do with counting two apples, one red and one green?

You have to accept the fact that mathematics sort of avoids this reality and "pretends" that 2 or 3 (or whatever number you choose) exists because it works (until it does not). — synthesis

No I don't. Nor should you. But we each choose our paths. You might consider joining forces with Metaphysician Undercover. His concern is the supposed equality between 2+2 and 4. :roll:

Explanation #3 - People just get really excited about waves. They think they explain everything. Fields too. They just sound all sciencey and stuff. — T Clark

To say nothing of the nature of the waves, ocean waves vs probability waves - all the same stuff apparently. The more esoteric ones travel through the absence of the aether, as well! Spooky action, truly. :rofl:

And then, there are all those infinities . . . :scream:

My own thread may be far too obscure to be taken seriously on a philosophy forum — Jack Cummins

Actually, it's a refreshing departure from the babbling brook. :cool:

"I think, therefore I am" — Qmeri

I've always considered this nonsense. But his mathematical ideas had great merit. :cool:

But the situation for mathematics is not all good:
As the proof for the uniqueness of the prime factorization is no more valid,
there might be different factorizations in different layers. — Trestone

At first glance I might think, How absurd. But these days there are lots of things in highly abstract mathematics that are beyond my pale, so maybe there is something to your ideas. I'm curious what fishfry and fdrake might think of it. In a faint way it resembles Schrödinger's cat. Nice article on Blau.

I think it might actually be a particle that we can't see because it goes away too fast and gets here too soon. — James Riley

So, a particle of time has speed, which is defined by the particle of time?

Time, like space, simply is. How we perceive time can vary dramatically, however. And what of time dilation in special relativity? That goes beyond perception and is registered by clocks or machinery.

The greatest minds have pondered this question.

There's too much here for a professional physicist to deal with. No wonder they have left the premises. :sad:

Well, I gather you've had your three cups of coffee, Tim!

Thanks for explicating what should be axiomatic on a philosophy forum. :cool:

How ought a community deal with such a neighbor? — BitconnectCarlos

Ignore them. Yes, this is easy to say, but could be difficult to do. It depends on how attenuated the community is regarding ethnic issues. Remember, "Why can't we all just get along?"

Suggestion: Put a click link to the paper on researchgate to facilitate reading it. Use the little handcuffs above the message space.

Conversations between those having interests in physics but not deep knowledge go on and on, and can be entertaining. Even arguments between actual scientists on interpretations. But I wonder if Feynman wasn't onto something when he argued to do the calculating, focus on the math and stop speculating.

When he introduced his Integral of all Paths concept to a room full of professional physicists most were taken aback and some startled by his explanations and were prone to discard his discovery. But as time went on and experimental evidence mounted his approach was adopted to a large extent. Even today, as a mathematician, I'm not sure of the nature or underlying soul of the functional-type integral he described. And I use the word "soul" in a context that only mathematicians can understand. It means not only superficial comprehension but deeper context, what lies beneath even the proof of the theory, a feeling of the actual substance of the concept.

I would not be surprised if future development of quantum theory might arise from going to the soul of the math that seems to predict so well. If so, philosophers may be chipping away at pretty hard marble.

Don't ask me to describe "soul". After many years of thinking about a particular aspect of dynamical systems in the complex plane I can "see" processes as they act to some extent, and this enables a glimpse into the undiscovered.

Or, ignore my nonsense entirely! :cool:

What does it mean to say a bat has an identity? That the bat knows who it is? That Baker knows it is a bat? What is it you think is taken for granted? — Banno

Salient points, and look how long this conversation has gone on. On the other hand, knowing what it is like to be be another human is another matter. We can imagine ourselves being someone else, at least to a certain degree. As we read along a first person narrative in a novel we do just that if the author is skilled enough. But to come awake as another is a different ball game entirely.

I get the impression that many if not most posters on this forum have little to say of their own experiences apart from those arising from studying philosophy. I've wondered, Do the philosophically inclined have fewer dimensions to their lives than normal? I would enjoy reading of interests that are either separate from or overlap philosophy that have meanings to posters lives. Maybe another topic, one that might go to Lounge.

I've mentioned an experience I had after several years of practicing Castaneda's Art of Dreaming in which I came partially awake as another person - someone living in a cottage in Ireland - with an entirely different feeling of personhood. Had the spell lasted more than scant seconds I've wondered if memories of that being would have come forth. What indeed does it mean to be who we are?

However we can say that ...."quantum mechanics exposed the subtle way in which the observer and [the] observed are interwoven"- Paul Davies. — 3017amen

Especially since the "observer" is a machine. :cool:

Traditional metaphysical problems have included the origin, nature and purpose of the universe, how the world of appearances presented to our senses relate to its underlying reality and order, the relationship between mind and matter, etc.. — 3017amen

nice summary. Thanks. Would you consider infinitesimals metaphysical?

. . . does much of science engage in some sort of metaphysical philosophy without actually knowing it (i.e. theoretical physics)? — 3017amen

When physicists speculate in the area of quantum mysticism, trying to find a real-world interpretation of what they observe rather than simply "doing the math", it seems to me they are engaging in metaphysics. But then again, I'm not clear on what the term even means. It would seem to go beyond reasoning. I think Leibniz was engaged in the practice when he postulated infinitesimals. .

The subject of this thread has an existential interpretation. If one creates meaning in their life by engaging in certain projects wholeheartedly, then, yes, to some degree you are what you do, and what you are transcends the biological creature accomplishing those functions.

. . . and in society generally. I think, ideally, it should make us better human beings. And if it isn't, then we're exactly like one of those mathematicians who, while perhaps brilliant in that domain, are otherwise not what one would aspire to be like. — Xtrix

You mean one-dimensional? You might be surprised. :cool:

I'll have to talk to jgill sometime. — Manuel

Don't expect much. :smile:

I retired over twenty years ago, but I still explore very limited and somewhat elementary areas of math and write notes as a hobby. fishfry and fdrake are modest, but they know a lot more about modern math than me, and express themselves well. As for Geometric Unity, I'm clueless.

Incidentally, you might think peer review certifies results that are published, but in math at least if what's being published is not of popular interest in mathematical circles you really can't be sure of complete accuracy. The other side of that coin is when a respected practitioner submits a paper, their colleagues who referee it might not look closely at every detail, assuming the author is quite competent.

A fellow mathematician from St Andrews U in Scotland and I created a minor journal thirty years ago for the purpose of quickly getting results to a limited community out - a little like arXiv.org now - calling it Communications . . .. We lightly refereed submissions. I'm sure some mistakes slipped by us, but we assumed legitimate journals would catch them when submitted. But even there you can't be certain.

Have a read of that first. — Banno

Is it worth the effort? :roll:

Bill Clinton clarified the Law of Identity in his unique way: "It depends on what the meaning of the word ‘is’ is. If the—if he—if ‘is’ means is and never has been, that is not—that is one thing. If it means there is none, that was a completely true statement. … Now, if someone had asked me on that day, are you having any kind of sexual relations with Ms. Lewinsky, that is, asked me a question in the present tense, I would have said no. And it would have been completely true."

That should put an end to the discussion.

After all, he only wanted the sciences to be treated democratically, completely without authorities, so that, for example, both evolution and intelligent design should be taught in school. — spirit-salamander

Intelligent design is a science?

To answer the question posed in the title of the thread . . . with utmost caution. If a philosopher wishes to engage in scientific speculation (philosophizing) they should learn the science. (Beware of quantum mysticism) :chin:

It's an inherently arcane field - it takes years of study. — csalisbury

Yep. I'll trust those reputable physicists who doubt his claims.

I suspect the official inflation rate will not gibe with my personal expenditures. Virtually everything I have bought recently has cost 15-30% more than a year or so ago. Could be it's just me. What has been your experience? :chin:

Edit: Whoops! My wife, who is almost a professional shopper, informs me many grocery items remain at pre-pandemic levels. :yikes:

This is probably as good as it gets: Problems with Geometric Unity.

I was a math prof, but not a physicist. I had not heard of GU, so thanks for the thread.

I think you are talking about Algorithmic Information Theory rather than mathematics in general, where your enquiry makes little sense.

If you shake both boxes continuously, the pattern of change of all marbles in a box will most likely be different from the pattern of change of all marbles in the other box. — Daniel

Not deep. :roll: