All of math would exist even if there were never any intelligent beings to discover it. — Douglas Alan

This statement might be true if known mathematics were entirely discovered. But mathematicians have long pondered the question of mathematics being discovered or created. All the years I've studied and researched the subject have left me without a strong opinion in this regard. I would speculate that mathematics is both discovered and created, and if the latter, then non-existent prior to its creation.

It might be that one has to actually do research in the subject to understand the issue. Plato or no Plato. Maybe not.

There are a few other math guys on this forum, and they might provide their opinions. :chin:

"The word 'thought' may mean: a single product of thinking or a single idea." (Wiki)

The PT is an idea transmitted down through the ages. Thought = Idea. Your definition of "thought" is far too narrow. You clearly want to keep all your thoughts to yourself. :roll:

There is no continuity of existence between a thought at one time and a thought at a later time, so the two are not the same thing. — Metaphysician Undercover

Nonsense. Take the Pythagorean Theorem: ${{a}^{2}}+{{b}^{2}}={{c}^{2}}$

The original thought occurred millennia ago, and it has been transmitted through the intervening years both by a variety of symbols and word of mouth. It remains essentially the same in Euclidean geometry, which by and large is the world in which we live, even though there are other forms of geometry.

the new thoughts are not the same thoughts as the old thoughts — Metaphysician Undercover

Probably true if you qualify your statement. But even then there is indeed an underlying structure of thought which might be analogous to a step function. The function, though discontinuous at points of time, exists throughout a long period and in effect provides a continuity of existence across time in that interpretations exist at each instant, although they may differ, changing abruptly from time to time.

Who cares what philosophers think? What of professional mathematicians?

Well, many think of MUH in the same way they think of ZFC: Not a lot. :cool:

The thoughts which were used to produce those symbols are events which are in the past, and no longer have existence. — Metaphysician Undercover

But those who read and interpret those symbols revive those thoughts and give them renewed existence. Thus, like monks reading and reciting scripture, were an order to so illuminate and pronounce mathematical works with unflagging resolve those thoughts would exist forever.

Hemingway's thoughts exist unendingly, for someone, somewhere is reading them now.

Non-existent things provide no support. — Metaphysician Undercover

You would deem the mathematics "supporting" the moon landing and Mars' vehicles non-existent. You would also label the very thoughts you post here non-existent. :roll:

Notice that no conceptual structure is completely new, in an absolute sense, it's always built with some already existing principles. — Metaphysician Undercover

My late advisor would say that there is nothing really new in mathematics. I would disagree, but to some extent much is preordained by the past. There has long been an ongoing discussion as to whether mathematics is discovered or created. I think it is both.

" we might consider that there was a first mathematical idea created"

Counting fingers and toes by some means, perhaps. Think how much of the modern world flows from that. :chin:

I'm persuaded that most who post to TPF neither know what a definition is nor what they're for. The evidence is many, many threads feeding on the energy of failed attempts to understand what the subject is, or what the terms mean — tim wood

I wonder what the pros in the Philosophy Department's faculty lounge would think of this?

I've long felt that failure to rigorously define leads to endless babbling. :roll:

It doesn't work though, because it doesn't explain how I'm here when no one's looking. — Metaphysician Undercover

You and the moon don't need the attention.

The practise of mathematics itself, requires that a foundation already be laid in order for that practise to occur — Metaphysician Undercover

Assuming that by "foundations" you mean the acceptable accumulated knowledge and practices up to any particular moment of mathematical history. Weierstrass and Cauchy laid the critical foundations for my interests, above and beyond what came before.

Formal foundations, such as PAs and ZFCs are another matter. Apart from certain mathematical specialties, they are dispensable. Others might differ. It's a philosophy thread. :cool:

Why would older Democrats’ Medicare be threatened by Bernie? — Pfhorrest

The entire system would be watered down if everyone had it.

Because we use the language as if there is an existent thing referred to by "game", "rule", or "concept", we fall under the illusion that there is such existent things. — Metaphysician Undercover

Interesting metaphysical limb upon which you are perched. Nothing really exists because there are no entities of sufficient purity that they are not compositions of things, many of which fail to exist themselves. Believe me, mathematics does indeed exist, as do the peculiar thoughts that bubble up into your consciousness, having complex pedigrees which apparently do not exist as well.

Seek help, my friend. You limb is but a twig.

I am Hal. I do not understand your answer. Please speak in BASIC. :yikes:

Were Bernie the Democratic candidate, surely the young and energetic of that party would turn out in droves to vote for him. Well, maybe not if they are hungover from the Monday night party. But then, surely the older and wiser Democrats will pour forth for a New Page in American History! Well, maybe not if they want to keep their Medicare intact.

And then there is Sleepy Joe. Hope he stays healthy enough for the ordeal, should he be selected. The excitement he arouses is palpable.

An associated question: What if the computer tells you it is aware of itself and not simply aware to the extent it can answer questions? What would be your test for self-awareness?

I don't know how this pattern manifests at the cellular level but if a cell eats, grows, shits, senses, then maybe, just maybe, it can think too. — TheMadFool

And if so, would it have inhibitions, like humans? In social psychology, groups tend to act more strongly with fewer inhibitions than individuals. When a large group of cells get together all hell could break loose. As in the growth and spread of cancer.

What fishfry has finally started to realize above, this principle: "if mathematicians say it exists then it exists", is a faulty principle. — Metaphysician Undercover

Think of mathematicians sitting around a table and creating a game, discussing the pieces that are played, the environment in which they are played, and the rules that are agreed upon. Once done, would you then say, "The game does not exist."? You fail to recognize that math is a social endeavor, frequently deriving from observations of the physical world, but just as frequently not.

From this perspective, would you say the rules are the axioms? I would say no, there are ill-defined patterns of thought that precede the establishment of the rules, and that might be the subject of study and formalization at a later time - as is the case of the foundations of mathematics.

Just a thought. :smile:

Very interesting and complicated subject.

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

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

I don't see how it could cause problems; after all the Egyptian engineering didn't suffer from using pi = 3.1605. — TheMadFool

I think GM has employed some of those guys from the pharaoh's think tank to design their 10 speed transmission. :sad:

I'm surprised by how poorly Biden is doing, given all the polling — Xtrix

I think all the Burisma business has damaged him quite a bit. Bloomberg might rescue the DP.

We have minds and the superorganism that we're part of - communities, cities, states, nations - behave remarkably like individuals. — TheMadFool

Really? Does a government act like an individual? If so, then most individuals wouldn't make it through the day. Waffling and indecisive, of two minds, making huge mistakes in physical conflicts, and throwing away their savings at the drop of a hat.

I don't really see fractals associated with panpsychism. Couple animism with panpsychism and you have a soulful but mentally acute chunk of rock. Just doesn't seem that nature would err that much. :roll:

I had to wiki the axioms of ZFC, having forgotten them long ago. :yikes:

For example jgill or anybody else that can be surely qualified as a mathematician. Could you please . . . — Mephist

I'd like to chime in with words of wisdom, my friend, but category theory is terra incognita to me. Read about it years ago and decided to give it a pass. Don't worry about the empty set. It can take care of itself. If it feels lonely, it can con an element from a comrade. Life goes on.

You have a point but what about other numbers like 22 and 7. In high school, ages ago, we were taught to use 22/7 for pi. — TheMadFool

The Indiana legislature once attempted to define pi as 3.2

↪jgill There exists a relatively non-weird take on backward causation: Laws of physics are time-reversible — SophistiCat

That's true, however sometimes mathematical models of physical processes are not isomporphic to those processes and give answers that are not appropriate. This may or may not be the case with time reversal. A comment by a physicist would be welcome here. :cool:

Such as claiming that math proofs are computer programs, — jgill

This is in fact true. It's the famous Curry-Howard correspondence — fishfry

This is certainly valid regarding the structure of a mathematical argument. But by itself it leaves the impression that mathematics is merely symbol manipulation and not what it really is: exercises in imagination and creativity. On the other hand, it may be that sometime in the future AI will explore and develop mathematics so convoluted and complicated that the results will be on the edge of human understanding, or beyond. Perhaps issues like the nature of time will be resolved, but humans will not be able to comprehend the results. Who knows? :chin:

Stating that calculus is largely manipulating symbols — jgill

To be fair, that's exactly how we teach it. — fishfry

Oh, I am well aware of that! :nerd: I taught calculus at all levels for 29 years. But my introduction to the subject was unusual: after taking an excellent course in analytic geometry as a freshman at Georgia Tech in 1955, I was recruited, along with about fourteen other students, into an experimental first quarter calculus course taught by two professors. Epsilons and deltas on the first day and no text book. Mostly we were bewildered at first, the exception being two brainiacs who caught on instantly. There was no attempt to continue the experiment into the second quarter, so we all migrated back to the standard curriculum for engineers, physicists, etc. What a huge difference!

At the University of Chicago in the fall of 1958, I was surprised to learn that the physics department was no longer allowing its students to enroll in courses from the math department and was teaching its own mathematics.

Long ago, what attracted me to mathematics was the same thing that attracted me to my avocation as a rock climber: exploration, discovery and creativity. The course work in grad school was someth9ing I needed to plow through, and doing assigned problems that had been solved by generations of students was a chore. Like repeating well established climbs. The original research at the end was a delight, however.

and that formal education is detrimental. — jgill

Also to be fair, many of the high and mighty in the land say the same. — fishfry

Yes, a few spectacular success do just that. I disagree. I've watched students of mine graduate and move on into successful careers.

You do give the impression of not having been on the Internet much — fishfry

:smile: Wrong impression, Dude! I was on an outstanding climbers' forum for years until it folded last May. Along with a great deal of climbing discussion, there were threads about other subjects. The one I particularly enjoyed delved into the nature of mind and consciousness.

By the time the forum ended, this thread had well over 20,000 posts. Among those participating were several mathematicians, a well-known physicist, a neuroscientist, an academic anthropologist, a retired management prof, several academic philosophers, a well-known author who has practiced Zen for decades, and many others at all educational levels who chimed in from time to time. In particular, the debates between the physicist and the Zen person were stimulating. Also, even though avatars were used we all knew the identities of the primary contributors. So you see where I'm coming from. :cool:

Thanks for your comments!

Much of everything we know about mathematics was developed by that school. — Michael Lee

A bit of overstatement. But entertaining post — jgill

By overstatement I meant that of all the mathematical knowledge existing today, I speculate that over 99% was created or derived since 1700. It's true, the ancients got the ball rolling. If you can find figures that imply the Pythagoreans gave us a sizable percentage I'm interested.

Too many Wiki pages, not enough math, that's my diagnosis of your posts. — fishfry

Thanks for your post regarding mine, fishfry. Your quote above to sime is germane.

I’ve ruffled some feathers with my post, for which I apologize. I got a bit irritated last night and didn’t express my thoughts well.

First, I’m not coming from a feeling of superiority regarding math. As a retired prof my interests are in a sliver so small it’s barely visible, one low-interest page among 40,000 on Wikipedia. There are sophisticated discussions on this forum about math, computer science, and logic that I can only stand aside and watch. And most conversations about foundations are beyond me.

But sometimes posters will make statements about mathematics in general that are erroneous, but said with conviction. Such as claiming that math proofs are computer programs, or that there are no more geometrical proofs. Or saying that fiddling with axioms makes the entire body of mathematics flawed, when, in fact, most mathematicians wouldn’t even notice. Claiming that irrational numbers are a mistake and that this undercuts the entire structure of mathematics. Stating that calculus is largely manipulating symbols and that formal education is detrimental. That adding a symbol, a “number”, for infinity will undermine current mathematics. For misusing the expression “chaos theory” when discussing randomness. For claiming that much of what we know of math now was derived or discovered two thousand years ago. On and on. I've probably misinterpreted some of this. If so, apologies.

It’s this moving away from what one knows to speculative territory, but being convinced one is correct – that’s a little annoying to me. But this is a philosophy forum, so no harm done.

As for physics, well all is not well in that discipline. For example, there is an argument about the aether that seemingly goes as follows: The premise is that every wave must travel through a physical substance, and that the aether exists. Electromagnetic pulses are waves, therefore must be propagated through the aether. Hence, electromagnetic waves travel through a physical substance. Makes sense if the premise is true. It's conjecture stated as fact.

I took a year of physics in college, and as a math prof used some physics in my classes. But I would feel incompetent to engage in a discussion about anything beyond the simplest ideas. But here we have string theory, differentiable manifolds, general relativity, entanglement, Bell’s theorem, and on and on – all as if the poster is sure of what he is talking about and not merely parroting Wikipedia. Maybe it’s no more than a lack of modesty. If I have offended anyone, sorry.

I would not want to be in the shoes of Republicans who will have to answer to their moderate base — 3017amen

Many of whom feel the president did something wrong, just not cause for removal from office.

A conclusion cannot be incompatible with the premise — Metaphysician Undercover

And sometimes a conclusion is indistinguishable from the premise.

:roll:

I shudder to think of what would happen here if the posters on this and other threads with minimal mathematical knowledge apart from set theory and logic were to launch investigations into subjects like functional integration or even metric spaces or advanced calculus. But maybe there is a hidden reservoir of mathematical understanding just waiting for opportunities for expression. I may try starting a thread and see what happens. I know several of you have significant mathematical depth. But others? Not so sure. :smile:

Did you read what I wrote? Energy is a property of the "field", transmitted through the field. The field exerts a force on the particles. You do not see that the "field" is therefore a "substance"? Also, the field exists between the object which creates it, and the particles effected by it. Do you not see that the field is therefore a substance. — Metaphysician Undercover

Earlier MU: "Ether is necessary to account for the reality of waves. A wave is in a substance. We can deny the reality of these waves, but then fields and wavefunctions don't represent anything real. Observation attests to the reality of these waves. If the waves are real, then so is the medium in which they exist."

Substance: the real physical matter of which a person or thing consists and which has a tangible, solid presence

Matter: physical substance in general, as distinct from mind and spirit; (in physics) that which occupies space and possesses rest mass, especially as distinct from energy.

---------------------------------------------

Argument here is hopeless. Is there a real, live physicist who will enter the discussion and untangle this mess? :roll:

Much of everything we know about mathematics was developed by that school. — Michael Lee

A bit of overstatement. But entertaining post. :cool:

It appears like you would not believe what I produced anyway. — Metaphysician Undercover

No. But I would believe what Feynman produced. All you've been saying is you believe there is a physical substance through which waves travel, even electromagnetic impulses. I think the "medium" to which you refer is a metaphysical medium.

I don't understand "backward" causation but I feel the future cannot cause the past. — Andrew4Handel

Unlike some on this forum I don't have many weird ideas. But I've had the sneaking suspicion that in some way or shape the present might influence the past. Many-worlds notions might come into play. Just speculation. :nerd:

Hence, mathematical analysis could suffer from the same fundamental interpretation problem surrounding infinity — alcontali

Classical real or complex analysis: very doubtful. Soft analysis: no telling where that is going. :cool:

Thus, we are justified in believing very firmly that 2 + 2 = 4. — Bartricks

Wrong. 2+2=1
Figure it out.

You just don't learn, do you? :roll:

Please do. I am curious. :chin: — jgill

Without taking the time to research specifics, I can tell you the simple idea — Metaphysician Undercover

So you really can't back up your statement. OK :roll:

I believe that some physicists such as Feynman have produced very convincing arguments which demonstrate that electromagnetic fields must have real physical existence, i.e. substance. If you're not familiar with this, I could look it up for you — Metaphysician Undercover

Please do. I am curious. :chin:

However, physical existence doesn't necessarily mean a substance as medium. It just means it exists and interacts with the physical universe. But I could be wrong. Probability waves are a lot more abstract.

The premises of life: an ever ambiguous concept — The Abyss

It took 27 posts to reach an essential point of clarity. My biggest argument with philosophical discussions is lack of clear definitions. What are some or many of these "premises?" List some, and then others can reply intelligently (maybe).

At the age of 83, the best advice I could give is

Unleash your inner existentialist — The Abyss