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Arguing against belief in 'abstract objects' 2 Years, 1 Month ago
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When abstract object denotes entities described as existing apart from space and time, I don't think it denotes anything. For those unfamiliar with maybe the most prominent relevant argument, here it is (except for "mathematical" put anything supposedly "abstract"):
Human beings exist entirely within spacetime.
If there exist any abstract mathematical objects, then they do not exist in spacetime. Therefore, it seems very plausible that:
If there exist any abstract mathematical objects, then human beings could not attain knowledge of them. Therefore,
If mathematical platonism is correct, then human beings could not attain mathematical knowledge.
Human beings have mathematical knowledge. Therefore,
Mathematical platonism is not correct. (Balaguer, "Platonism in Metaphysics," sec. 5)
Worse, all our concepts exist inside our minds which in turn exist inside space and time, so it almost seems as if the phrase "not spatiotemporal" is something like self-contradictory (in the sense that anything that causes a concept to negate itself is self-contradictory). (This is why I don't accept even Kant's claim that free will transcends the physical world: that would make "free will," to me, a set of words with no possible corresponding meaning.)
But then this kind of argument seems so simple to come up with that I imagine it has before, and something unsound or invalid put to its name. Anyone here familiar with that kind of thing in turn?
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Last Edit: 2010/04/04 17:49 By Szavieur.
Reason: fix title
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¡¿
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Re:Arguing against belief in "abstract objects" 2 Years, 1 Month ago
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We have concepts of objects that can exist beyond space and time, for example, God. Certainly all concepts of objects that exist outside of space and time are thought about in time, these objects don't seem to be self-contradictory.
(For Kantian eyes or the daring: consider the transcendental subject. We do not know this subject positively, but must think it.)
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Re:Arguing against belief in "abstract objects" 2 Years, 1 Month ago
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Isn't the problem to specify what is meant by "abstract object." Clearly, saying both that they exist and that they are nonspatiotemporal is problematic. For if they existed, we would normally ask whether it can be demonstrated that they exist; and if they were spatiotemporal, we would normally ask that they exist or could exist.
For instance, a subject's ability to recognize the color red can be an abstract object. For we talk about descriptions of states of that subject, i.e., their recognitions of red objects. Thus we talk about conceptual capacities, which are properties of subjects, as objects, although they are clearly recurring events.
What about other abstract objects? Presumably, being an abstract object means being able to be the intension of a thought which lacks a definite reference, but may refer indefinitely, indirectly, and so on (in Hume and Berkeley's jargon, they are "relative ideas"). So if "exists" means "is an actual or possible spatiotemporal object," the only way that intensions can exist is if thoughts and their objects are reducible to physical phenomena, or explainable in terms of them.
What is the motivation, then, for the assertion that "exists" entails "is spatiotemporal," and of denying that concepts lacking actual extensions do not exist? Surely I can' think of Caesar in some "non-Humean" way?
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Last Edit: 2010/04/03 01:12 By quickly.
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Re:Arguing against belief in 2 Years, 1 Month ago
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Szavieur wrote:When abstract object denotes entities described as existing apart from space and time, I don't think it denotes anything. Human beings exist entirely within spacetime.
If there exist any abstract mathematical objects, then they do not exist in spacetime. Therefore, it seems very plausible that:
If there exist any abstract mathematical objects, then human beings could not attain knowledge of them. Therefore,
If mathematical platonism is correct, then human beings could not attain mathematical knowledge.
Human beings have mathematical knowledge. Therefore,
Mathematical platonism is not correct. (Balaguer, "Platonism in Metaphysics," sec. 5) Worse, all our concepts exist inside our minds which in turn exist inside space and time, so it almost seems as if the phrase "not spatiotemporal" is something like self-contradictory (in the sense that anything that causes a concept to negate itself is self-contradictory).
A red flag against this argument is that all of mathematical physics is platonic. It is purely deductive from best-guess premises whose deductions turn out to be more-or-less correct. So, one could argue that our strongest claims to knowledge are mathematical platonism.
Therefore, I would have to attempt to reverse the argument and ask what went wrong? Is it the philosopher's conception of object, existence, or abstraction? Seemingly all three are vacuous or misdirected. What is an object, can it "exist"? What is not abstract?
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Re:Arguing against belief in 2 Years, 1 Month ago
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Yadayada
A red flag against this argument is that all of mathematical physics is platonic. It is purely deductive from best-guess premises whose deductions turn out to be more-or-less correct. So, one could argue that our strongest claims to knowledge are mathematical platonism.
Mathematical Physics is just mathematical models serving Physics.
(not vice versa)
The 'less' correct is washed away pretty quickly (why bother
with it otherwise?), but it is math trying to model a physical
thing, or an ideal theory. Platonism seems a bit off, because
the Platonic "shapes" are ideals, leaders for reality.
In Physics, math is only a lagger of reality. That is: a tool
with known defects. The importance is....our "strongest claims
to knowledge" aren't only about the math. The math is almost
always trying to approximate some other idea we have (things
like 'boundary conditions' or a 'field').
Math aside, though, you could probably say that areas where
our knowledge is still shaky have various models as Platonism.
Or am I misunderstanding mathematical physics?
I had a course in it, but to be honest, we didn't
peck at its definition, just the math mayhem.
It isn't a primary means of knowing, though...
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Last Edit: 2010/04/03 14:31 By leonardomenderes.
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Re:Arguing against belief in 2 Years, 1 Month ago
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The definition and description of mathematical physics from Wikipedia seems good enough to me: Mathematical Physics as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories."
You seem to be referring to application of math to solve problems in physics. I mean the bolded parts of the definition, the application of math for the formulation of physical theories.
In other words, mathematical physics is formulated (as in formulas and formalities) in purely mathematical terms. F=ma, E=mc2, etc. Mathematics is not just the backbone of physics, but to theoretical physicists the entirety of physics.
When we talk physics in English, we are actually talking about reasonable or sensible interpretations of the math.
The difference is substantial. Formally, that is mathematically or on a graph, the Newtonian bullet always hits the target with 100% precision. It is fully deterministic. However, in real life, or to an engineer, there are always extraneous factors (such as wind direction and friction) that introduce probabilistic considerations. |
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