And thus discovered/invented, together. What do you say, if you care to say? — tim wood

Creativity can enter when one speculates on new topics and definitions. If a flight of imagination leads to a new concept (if, in fact, there are any), then what flows from a logical analysis of this concept can be considered discovery. In other words, once the initiating concept is delineated, all that follows is in a sense immediately established - to be discovered. But the process of math research is almost always a sometimes convoluted combination.

Practicing mathematicians pay virtually no attention to this philosophical discussion.

Quantum computing has something contrary to say about the last part of your claim. — ucarr

Everything that quantum computing allegedly does is mathematical. If by physical you mean something more generic than existing at a point, then you'd have to mention what it is.

If mind emerges from brain — ucarr

I don't think it does.

Functional mind that has impact upon existentiality, meaning and usefulness is never uncoupled from the physicality of the natural world. — ucarr

An abstract mind could have an impact on the natural world without being identifiable in it, if abstracta are more generic than concreta.

What a priori reason is practiced by brain in a vat never in contact with the world? — ucarr

All of it? A priori reasoning doesn't come from sensory stimuli, by definition.

First off, I am lost in this entire conversation so this is just me clinging on to something I think may be worth mentioning, maybe.

The issue I see is that math is like physical law. We have a mental concept for it yes, but that concept was brought about from observing the physical world, which already operates on math. Any action we take, based on our concept of math or physical law, will still have its origin in physical reality. We observe -> we form concepts -> we let the concepts affect our physical actions.

"How can mental “objects” have causal effects upon the physics of the natural world? The answer is numbers." -- To me it seems incorrect, since our math is just us mimicking what is already there.

Pure math has connection to the natural world only as indecipherable signification representing thermodynamic equilibrium.

Since mathematicians only use pure math for investigation of the ground rules concerning applied math, pure math is merely higher-order applied math.
— ucarr

Mysteries never cease :roll: — jgill

Thank-you for your time, attention and commentary. Its not easy to get them from authentic experts. I like having the attention of important people. What you say in your below quote is what I attempted to say in my above quote. One salient difference is the absence of arrogance and pretension, hallmarks of my statement. I was trying to characterize pure math in total isolation, whereas you nuanced the separation of pure and applied math with anecdotes from your professional experience. Your nuanced separation speaks to my theme: math applies well to the natural world because it’s of the natural world. It’s of the mind a well; It’s not simply of just one or the other. However, in my opinion, it is more at discovery than at invention.

The distinction between pure and applied math is somewhat vague, one reason being that pure math may become applied math at times. A researcher in applied math could be working on a math scheme to solve a particular problem, like calculating the stresses on a modern fighter plane during sharp turns. Or, he could be pursuing a topic purely for its own sake, curious about what comes next - and then finds someone has used his results in an applied manner.

This happened to me. My interests are always in "pure" math (complex analysis) and I published a paper in 1991, I think, with no thoughts of it ever being "useful", only to find my principle result was employed in a multiple author sociology paper about decision making in a group. Of course, the author who cited and used my result paid no attention to the details. — jgill

Tosh. Kant detested materialism, as do I. — Wayfarer

So, you detest materialism? Post herein a picture of your right index finger after you’ve chopped it off.

whether differentiable — ucarr

What do you mean by differentiable here?

So, there too must be a starting-point counting number. — ucarr

You failed to show how that follows but since it is too early into the argument to be making contentions, I will just grant you.

Everything from "There’s no reductio ad absurdum re:" to "Since any and all material objects, individually, present as a countable one, oneness, a countable number, acts as an essential attribute of each and every material object." sounds like Christopher Langan, meaning complete gibberish.

The text after is confusing as well, though not undeciphrable.

Conclusion: number-as-property, being essential and physically real, and being tied inextricably to material objects, is discovered. They are not purely conceptual objects, accessible to the mind only. — ucarr

Now I understand what you are saying. It seems that, for you, numbers are something found physically in every object. That 2+2=4 is the law manifested when you push a pile of 2 objects onto another a pile of 2 and you end up with a pile of 4 objects every time. The problem with that lots of mathematics deals with infinities. The natural numbers are an infinite set, and the set of real numbers are infinitely bigger than the set of natural numbers, and it gets worse as you go into the complex field. Calculus relies on the concept of infinity. You can have an infinite amount of infinities in mathematics that just keep growing. This does not seem to relate to the physical world. There is something about mathematics that is not about just the physical world.

but that concept was brought about from observing the physical world — mentos987

I can't see how things such as calculus, vector spaces, and higher dimension geometry are somehow derived from our physical world.

Number is an essential, material property. — ucarr

Numbers, like the bridge itself, are physically_materially real. — ucarr

If numbers are physically_materially real, then how long and heavy are they? What shape and colour are numbers?

I can't see how things such as calculus, vector spaces, and higher dimension geometry are somehow derived from our physical world. — Lionino

All complicated math is derived from simpler math. The basics of math are taken straight from reality. More complicated math is simply us running away with the tools we have formed.

Practicing mathematicians pay virtually no attention to this philosophical discussion. — jgill

And thus you are a dearly valuable exception to the rank and file establishment.

All of it? A priori reasoning doesn't come from sensory stimuli, by definition. — Hallucinogen

What does it come from? If you say reasoning about reasoning about the world, that lands it in higher-order reasoning about the world. Now, I challenge you to name what a priori reasoning responds to in total separation from the world.

"How can mental “objects” have causal effects upon the physics of the natural world? The answer is numbers." -- To me it seems incorrect, since our numbers are just us mimicking what is already there. — mentos987

Your premise presupposes what it seeks to contradict. Don’t take my word for; take your own words for it. Re-examine your closing sentence.

Your premise presupposes what it seeks to contradict. Don’t take my word for; take your own words for it. Re-examine your closing sentence. — ucarr

Any action we take, based on our concept of math or physical law, will still have its origin in physical reality. We observe -> we form concepts -> we let the concepts affect our physical actions. — mentos987

With this I seek to claim that our concept of math did not build the bridge. It was a fallen tree over a creek a long time ago that did. The mental concept of math is an intermediary.

since our numbers are just us mimicking what is already there. — ucarr

I claim here that our concept is mimicking a more complete set of math that is governing the universe.

Take all this with a bucket of salt, I am on loose footing here and I know it ^^

Edit: Thinking about it some more... I don't believe in pure mental concepts at all, not the way you guys are talking about it, so I don't know what I am arguing. I don't think that a human mind can conceive of anything that is completely outside our prior experience, and I think our experience is locked to physical reality.

What does it come from? If you say reasoning about reasoning about the world, that lands it in higher-order reasoning about the world. Now, I challenge you to name what a priori reasoning responds to in total separation from the world. — ucarr

I wouldn't say it "responds", it's not a mechanism. It's intentional content and it's abstract and propositional. You have a mind, so you have it.

To you it seems that apples and oranges are numbers, to me their numeration may simply be external properties that are only acquired in relationship. — JuanZu

Ever seen a toddler who, knowing next to nothing about numbers in their head, fails to distinguish one offered lollipop from two offered lollipops?

With this I seek to claim that our concept of math did not build the bridge. It was a fallen tree over a creek a long time ago that did — mentos987

Excellent example of the natural world practicing physical number for counting! What person in the village thinks two trees or four trees have fallen over the creek?

No. A natural number one let’s everyone pass over the risen creek without getting wet. Real number in the real world built number sign within the head. What are number signs in the head without real number in the real world? They’re Kant’s empty concept without percept.

Excellent example of the natural world practicing physical number for counting! What person in the village thinks two trees or four trees have fallen over the creek? — ucarr

Well, I mention this because you used bridge building as an example of mental concepts taking physical form. I am trying to add to that that the mental concept in turn came from an original physical form.

Real number in the real world built number sign within the head. What are number signs in the head without real number in the real world? — ucarr

I am unsure what we are talking about. I do not claim that math isn't real, just that it isn't man made. The symbol "3" may be manmade, but the symbol isn't building any bridges, it is just part of the shared concept. We have constructed ourselves a concept that we implement in engineering sure, but I think that all inspiration for it comes from physical reality.

I should maybe be excluded from this discussion..

I don't believe in pure mental concepts at all, not the way you guys are talking about it — mentos987

Well, if he doesn't know how to count he probably doesn't know that there are two things. He knows that there is a difference and that they are separated in space, that one thing is not the other, that they are similar, etc. Then perhaps a proto-two will appear in his mind that will then finally be objectified and solidified as knowledge thanks to teaching and learning. But obviously "the two" will not have arisen from the thing itself, rather it is something that happens to the thing when it enters into a relationship with someone who defines the measure and sees the difference between the two, and the Lollipops.

Greed. Even a toddler have enough inbuilt math to enable them to be greedy and want what they think is "more".

I wouldn't say "in-built math". Toddler can differentiate and identify. The quantity appear in another level perception. After all, when we think in numbers we don't think at the same time all the things we have counted.

So, you detest materialism? Post herein a picture of your right index finger after you’ve chopped it off. — ucarr

If you feel that crude metaphor conveys anything about the point at issue, perhaps it is because you don't understand it.

Practicing mathematicians pay virtually no attention to this philosophical discussion.
— jgill

And thus you are a dearly valuable exception to the rank and file establishment. — ucarr

What does this mean, exactly? That paying no attention to a philosophical discussion is a virtue? And 'the rank and file' of what organisation, exactly?

I wouldn't say "in-built math — JuanZu

Ye "in-built" may not be true. I do think toddlers do a calculation to determine what is more and what is less. It is a form of math.

Yesterday I went to the market and told a worker "give me two of those melons." He gave me the two melons.

But! The imaginary worker-philosopher might have told me "there are not two, there are 57." I wonder, is number two in number 57? But objectively there are not 2 melons, there are 57. Or maybe there are two and 57 at the same time, objectively. There can also be 4 and 57 at the same time. Are there also two pairs? where is the rule for counting? Surely it is not in the thing itself! Isn't it the case that when I said "two" I have given something that wasn't there, a difference, a partition, a slice, a rule, a number simply different from 57 regardless of whether they are melons, apples or anything else? So number is different from numbered things.

What does this mean, exactly? That paying no attention to a philosophical discussion is a virtue? — Wayfarer

Oh my, you are on a roll. :gasp: First you suggest machine gunning people crossing the Rio Grande, and now you suggest the obvious. Sad days, indeed. :cool:

My question was addressed to ucarr, about a remark he made to you. It wasn't addressed to you.

So, you detest materialism? Post herein a picture of your right index finger after you’ve chopped it off.
— ucarr

If you feel that crude metaphor conveys anything about the point at issue, perhaps it is because you don't understand it. — Wayfarer

Perhaps this is the Tarantino inspired version of Johnson's, "I refute it thus!"

:rofl:

(although, not being one to point the finger.... :lol: )

That's how I see myself and many others: Explorers. It's no wonder you find mathematicians among rock climbers and mountaineers. — jgill

I love that statement, it's so ........ exciting, when thoughts of "well what can I do with my life, what 'meaning' or 'significance,' can I nurture and what legacy can I produce?", dominate a persons rationale.

Everything that quantum computing allegedly does is mathematical. If by physical you mean something more generic than existing at a point, then you'd have to mention what it is. — Hallucinogen

With @ucarr's indulgence and as a retired teacher of Computing Science, I would assume that ucarr is referring to quantum computings use of the very real physical phenomena of superposition.

Giant Molecules Exist in Two Places at Once in Unprecedented Quantum Experiment

In quantum computing a qbit can have more states than the two of the traditional binary bit.

"Just like classical bits, a quantum bit must have two distinct states: one representing “0” and one representing “1”. Unlike a classical bit, a quantum bit can also exist in superposition states, be subjected to incompatible measurements, and even be entangled with other quantum bits."

These states are quite 'real.' For me, its a bit like fully accepting the three physical states of solid, liquid and gas, and then being a little disturbed when you find out about 'plasma.'

Is this what you were referring to @ucarr? with:

Quantum computing has something contrary to say about the last part of your claim. — ucarr

And here we go, the word "quantum".

I should maybe be excluded from this discussion..
I don't believe in pure mental concepts at all, not the way you guys are talking about it
— mentos987 — mentos987

You’re welcome to continue weighing into this conversation on the physicalist side, if that position isn’t also averse to your inclinations. Hoping you’ll give us more goodies like the tree-bridge.