Without judging the claim, a lack of data does not falsify a hypothesis. It may make it unnecessary and unparsimonious.Wouldn’t the claim of the existence of such a bodily substance be an empirical claim? If it’s a substance, then either it can be detected by scientific means, or it can be declared a false hypothesis. — Wayfarer
Wouldn’t the claim of the existence of such a bodily substance be an empirical claim? — Wayfarer
Are you denying that discrete objects can be counted? Or continuous quantities measured? I am not sure what you are objecting to. — Dfpolis
So, you think a potential statue is no different from an actual statue? A block of marble and the Pieta carved from it are the same? I cannot believe that that is your position.I see no difference between the claim that a number-potential is guaranteed to exist and the claim that a number is guaranteed to exist. — Heiko
As I already explained, they are in the sets that can be counted or in the various things we can measure.Where are those potentials? — Heiko
So, you think there is no difference between a group of sheep and the number that results from counting them.I think you are just giving the numbers a fancy name. — Heiko
To give you the courtesy of an answer, possibility may always exist, potentials do not. There seems to have been a point early in the evolution of the universe, when it was not yet discrete objects (and so had nothing countable) and nothing measurable (because of problems associated with Planck scale objects). At that point, there was no basis in reality for our number concepts, and so no potential numbers -- only the possibility of numbers in the future when beings capable of counting, measuring, and conceiving numbers would come to be.There is a 1 potential which must always have existed actually as I can count to 1.
There is a 2 potential which must always have existed actually as I can count to 2.
.... — Heiko
Aristotle's astronomy tried to account for how beings found within the 'sublunary sphere' had anything to do with those observed outside of it. Now that we understand that they are not different kinds of beings, the view of all beings belonging to a single cosmos is strengthened by our increase in knowledge. — Paine
It is the "fourth study" after solid geometry. It is the study "which treats motion of what has depth" (528e)
Glaucon says "astronomy compels the soul to see what's above and leads it there away from the things here". Socrates corrects him. When studied in this way it causes the soul to look downward. (529a)
He calls the stars "decorations in the heavens embroidered on a vaulted ceiling". The image of the starry night, is the opposite of the image of Good in the sun. Astronomy when studied as Socrates proposes is not the study of visible things in the heavens, it is about "what must be grasped by argument and thought, not sight" (529d)
There is a 1 potential which must always have existed actually as I can count to 1.
There is a 2 potential which must always have existed actually as I can count to 2. — Heiko
If there is something that is capable of moving things or acting on them, but that is not actively doing so, there will not [necessarily] be movement, since it is possible for what has a capacity not to activate it. There is no benefit, therefore, in positing eternal substances, as those who accept the Forms do, unless there is to be present in them some starting-point that is capable of causing change. Moreover, even this is not enough, and neither is another substance beyond the Forms. For if it will not be active, there will not be movement. Further, even if it will be active, it is not enough, if the substance of it is a capacity. For then there will not be eternal movement, since what is potentially may possibly not be. There must, therefore, be such a starting-point, the very substance of which is activity. Further, accordingly, these substances must be without matter. For they must be eternal, if indeed anything else is eternal. Therefore they must be activity. — Metaphysics, 1071b12–22, translated by C.D.C Reeve
If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? — jgill
Any rational sentient beings would presumably make some of the same discoveries. That’s the meaning of ‘true in all possible worlds.’ — Wayfarer
If you are interested in the Greek, the passage I quoted is here. — Paine
These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they.
The problem of reification in philosophy refers to the tendency to treat abstract concepts or mental constructs as if they were concrete objects with independent existence. It involves treating something that is abstract or conceptual as if it were a physical thing that exists independently of our thoughts or language.
If the potential of existence of rational beings is extinguished, would the potential of mathematics vanish as well? — jgill
those who accept the Forms — Metaphysics, 1071b12–22, translated by C.D.C Reeve
some starting-point that is capable of causing change. — Metaphysics, 1071b12–22, translated by C.D.C Reeve
Perhaps your belief is a fine one and mine innocent. (229c)
must be grasped by argument and thought, not sight. (529c-d)
There must, therefore, be such a starting-point, the very substance of which is activity. — Metaphysics, 1071b12–22, translated by C.D.C Reeve
So then, Socrates, if, in saying many things on many topics concerning gods and the birth of the all, we prove to be incapable of rendering speeches that are always and in all respects in agreement with themselves and drawn with precision, don’t be surprised. (29c)
What 'bodily substance' he talking about? Endocrines? — Wayfarer
For the nature of the stars is eternal, because it is a certain sort of substance, and the mover is eternal and prior to the moved, and what is prior to a substance must be a substance. It is evident, accordingly, that there must be this number of substances that are in their nature eternal and intrinsically immovable, and without magnitude (due to the cause mentioned earlier). It is evident, then, that the movers are substances, and that one of these is first and another second, in accord with the same order as the spatial movements of the stars. But when we come to the number of these spatial movements, we must investigate it on the basis of the mathematical science that is most akin to philosophy, namely, astronomy. For it is about substance that is perceptible but eternal that this produces its theoretical knowledge, whereas the others are not concerned with any substance at all—for example, the one concerned with numbers and geometry. — Metaphysics 1073a30, translated by C.D.C Reeve
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