9

In the world of physics, things can get very very large, but not infinite. For example, if a physical model of some phenomenon predicts an infinite result in some circumstance, it signals a hard limit on that model's applicability, and it means there are physics that the model does not contain which are important in that particular case. It is then the job ...


7

First, let's concede there are two conceptions of the infinite. One is the potential and the other is the actual. As for excluding the infinite, I think it's fair to say that the answer is a resounding no. One of the greatest advancements of science was Galileo's quantization of science; of course, one often then mentions the great leap of Newton and ...


5

The set-theoretic definition of infinity is not "countable or uncountable," i.e. is not read off the concept of countability. Afaik the definition is, "A set is infinite if and only if it can be put into a one-to-one correspondence with one of its proper subsets." Or even, "A set is finite if it is not infinite," that's ...


3

There is Frege: Philosophy of Mathematics. It is written by Michael Dummett, a modern British philosopher and civil rights activist. It explains the philosophy, but focuses on mathematician and philosopher Friedrich Ludwig Gottlob Frege who was interested in the philosophy of mathematics. There is also Philosophy of Mathematics Today by Kit Fine, but it only ...


3

Mathematically, infinities fall into two distinct classes; countable and uncountable. For example the set or rational numbers is countable, the set of real numbers is not. Note that Newtonian countability is still a countable infinity, being merely the sequential terms in a convergent infinite series. Another answer has explained that infinities in a ...


3

No, there's no need whatsoever to exclude the infinite from science. The gold standard for a scientific hypothesis is that the hypothesis is consistent with all known observations, successfully predicts observations made after the hypothesis was formulated, and is the simplest hypothesis that fulfills the first two criteria. If a hypothesis meets these ...


2

Aristotle discusses how to note differences between terms in Topics book 1 §16 (108a1-5): The differences which things present to each other should be examined within the same genera, e. g. ‘Wherein does justice differ from courage, and wisdom from temperance?’—for all these belong to the same genus*; and also from one genus to another, provided they be not ...


2

I shall suggest that you first make sure that you fully understand basic FOL (first-order logic) and the technical details and proofs of some of the crucial theorems about it up to and including the semantic completeness of FOL and the Godel-Rosser incompleteness theorems. The reason for this is that it is impossible to have a proper discussion about the ...


2

The belief that the infinite does not really exist goes back at least to Aristotle. Parmenides even questioned the reality of plurality and change. (Einstein's vision has much in common with Parmenides). Towards the end of the nineteenth century an acrimonious exchange took place between Kronecker and Cantor regarding the reality of the actual (as opposed to ...


1

Infinity is a useful concept. Using infinities like in mathematics, we can get answers which are measurable, meaningful. The question may be whether there is really anything that exists and indeed an infinite. The infinities just as a mathematical concept can be explained and may be argued to exist eg integer series 1,2,3,... so on. But it's just logical or ...


1

I do judge Plato as a racist advocate of propaganda, and as Popper put it 'enemy of the open society'. Dawkins recently tripped up over a very similar attitude to the word eugenics that you are showing. He attempted to use the term eugenics to mean any strategic non individually decided influence on reproduction. But that's not how the term is used. It ...


1

In the UK 'Philosophy Now' and 'The Philosophers' Magazine' - the first more basic than the second - give a reasonably reliable picture of the current state of philosophy in both the UK and the US. Subscription to these magazines has the extra benefit - certainly in the case of 'Philosophy Now' and I believe in that of 'The Philosophers' Magazine'also - of ...


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