And thus discovered/invented, together. What do you say, if you care to say? — tim wood
Quantum computing has something contrary to say about the last part of your claim. — ucarr
If mind emerges from brain — ucarr
Functional mind that has impact upon existentiality, meaning and usefulness is never uncoupled from the physicality of the natural world. — ucarr
What a priori reason is practiced by brain in a vat never in contact with the world? — ucarr
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
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
whether differentiable — ucarr
So, there too must be a starting-point counting number. — ucarr
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
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. — Lionino
All of it? A priori reasoning doesn't come from sensory stimuli, by definition. — Hallucinogen
"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. — 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
I claim here that our concept is mimicking a more complete set of math that is governing the universe.since our numbers are just us mimicking what is already there. — ucarr
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
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
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
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.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
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.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 don't believe in pure mental concepts at all, not the way you guys are talking about it — mentos987
So, you detest materialism? Post herein a picture of your right index finger after you’ve chopped it off. — ucarr
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
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
That's how I see myself and many others: Explorers. It's no wonder you find mathematicians among rock climbers and mountaineers. — jgill
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
Quantum computing has something contrary to say about the last part of your claim. — ucarr
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
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