are our abstractions mysteriously agreeing with the world? — J
https://en.bab.la/dictionary/english/abstractorigin of abstract
Middle English: from Latin abstractus, literally ‘drawn away’, past participle of abstrahere, from ab- ‘from’ + trahere ‘draw off’
So where are abstractions taken from? I suggest "the world" is a sensible answer, and one that explains the "mystery" rather well — unenlightened
I can see that you wouldn't like this approach on the grounds that it shoots your fox and spoils the fun of the chase. — unenlightened
It is the "I" that sees a relation between many different objects in the world. It is not the world that is relating a particular set of objects together. — RussellA
It is indeed a sensible answer, but doesn't explain what appears to be the modally necessary character of the abstractions, and their role in explanation, if any. Have you read the target paper I cited? It might explain the problem better than I have. — J
I see what you mean, but we can construct an infinite number of worlds with different abstract entities highlighted (see "grue and bleen", Sider, p. 16) and most of them won't "work" at all, if by "work" you mean "give us a useful conceptual basis for navigating the world." — J
Yet there is nothing wrong, logically, with the way these abstractions are being matched to reality. — J
The larger puzzle is this: How is it the case that, no matter what definition we use, we discover these regularities between math/logic and the world? — J
The DLE problem assumes a linguistic stipulation that is uncontroversial or at least agreed-upon, or at the very least accepted for the purposes of discussion. With this stipulation in place, we then go on to ask about the relation between logic-or-math-as-necessity and the alleged necessity of events in the world, such as the 23 objects that can’t be evenly divided, or the cat that can’t be here and in Paris too. — J
So where are abstractions taken from? I suggest "the world" is a sensible answer, and one that explains the "mystery" rather well. — unenlightened
If you have 23 objects you have already mathematicised them by counting — unenlightened
Gravity, electromagnetism, chemical interactions, biological interactions, etc. work ways that impose on us their workings, not the other way around........................Kant, for example, seemed to conflate the two as part of the same "transcendental" constraints that our minds impose on "the thing-itself". — schopenhauer1
I just think this needs further explanation; logic and noncontradiction alone won't get us to why some matches seem more natural or reality-mirroring than others ("privileged structure"). — J
↪Philosophim I did read the summary. Is this the passage you're referring to (concerning "privileged structure" or the like)?: — J
Sider uses the "grue and bleen world" example (which you can read about here, p. 16) to refer to a situation that he believes needs explaining: If we encountered a people who used grue and bleen as their concepts, we'd be unable to fault them on any logical grounds. — J
Kant and a Transcendental Deduction that mathematical truths are necessary truths
In B276 of the CPR, Kant uses a Transcendental Deduction to prove the existence of objects in the world.
As the equation "d=0.5∗g∗t2
=
0.5
∗
∗
2
" does successfully and consistently predict what is observed in the world, we could use a similar Transcendental Deduction to prove that in the world is the underlying reality that d=0.5∗g∗t2
=
0.5
∗
∗
2
.
Using such a Transcendental Deduction, we could unify a world that imposes itself on the mind and a mind that imposes itself on the world. — RussellA
As for the analytic/synthetic distinction, I'm not sure we really have to go there. Perhaps it won't do as a description of the difference between logic and facts-about-the-world, but wouldn't you agree that Jha et al. are pointing to something that can be talked about, and represents a genuine question? — J
Q. You claim that a person’s information, if we trust mathematics, is still there after death, dispersed throughout the universe, forever. Are we immortal?
A. If you trust the mathematics, yes. But it is not an immortality in the sense that after death you will wake up sitting in hell or heaven, both of which – let’s be honest – are very earthly ideas. It is more that, since the information about you cannot be destroyed, it is in principle possible that a higher being someday, somehow re-assembles you and brings you back to life. And since you would have no memory of the time passing in between – which could be 10¹⁰⁰ billion years! – you would just find yourself in the very far future. — interview with Sabine Hossenfelder
Quine himself had very mixed feelings about whether the laws of logic were subject to revision. I think his final answer was yes, but it's a last resort, and they are very insulated, resistant to revision. — Srap Tasmaner
Why is math so faithful? It may be that we can't know that. — frank
Neoplatonic mathematics is governed by a fundamental distinction which is indeed inherent in Greek science in general, but is here most strongly formulated. According to this distinction, one branch of mathematics participates in the contemplation of that which is in no way subject to change, or to becoming and passing away. This branch contemplates that which is always such as it is and which alone is capable of being known: for that which is known in the act of knowing, being a communicable and teachable possession, must be something that is once and for all fixed. — Jacob Klein, Greek Mathematical Thought and the Origin of Algebra.
(Empiricists) view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all? — What is Math?
Let me try to work up an example that is less controversially stipulative. — J
OK. So no one of your factors would be something like "This set of concepts more accurately reflects the ontological structure of the world"? — J
In your other thread we touched on the Scholastic transcendentals or convertibles. Another transcendental besides being and truth is oneness (unum). — Leontiskos
There was consensus among the scholastics on both the convertibility of being and unity, and on the meaning of this ‘unity’—in all cases, it was taken to mean an entity’s intrinsic indivision or undividedness. [19] In this, the tradition was continuing and affirming a definition first proposed by Aristotle in the Metaphysics. [20] This undividedness, in the words of Aquinas in his Commentary on the Sentences, is said to lie “closest to being.”[21] For the most part, ens and unum were distinguished by these thinkers only logically or conceptually—unum adding nothing real to being, or more properly, adding only negation, only a privation of actual division.[22] It was common practice in medieval philosophy to distinguish the transcendental sense of unum, running through all of the categories, from the mathematical sense of unum, restricted to the category of quantity. These two ‘ones’ are each in their own way opposed to ‘multiplicity.’[23] Aquinas offers a succinct account of this in his Summa Theologiae (Ia. q. 11, art. 2).[24] The ‘one’ of quantity is the principle of number; it is that which, by being repeated, comprises the sum (the multiple).[25] Aquinas says that there is a direct opposition between ‘one’ and ‘many’ arithmetically, because they stand as measure to thing measured, as just-one to many-ones. Likewise, transcendental unity is opposed to multiplicity, but in this case not directly. Its opposition is not to the many-ones per se, but rather to the division essentially presupposed in and formal with respect to the multiplication of actual multiplicity. This tracks with a consistent distinction in Aquinas between division and plurality in which division is seen as ontologically and logically prior.[26] Transcendental unity then, has a certain priority to its predicamental counterpart.
We will return below to the consequences for contemporary ontology that follow upon this fact that, in its developed form, it was division, not plurality, that was taken by the classical tradition to be the precise contrary to transcendental unity. . . — Being without One, by Lucas Carroll, 121-2
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