The Concept of Infinity in Philosophy (w/ Dr. Graham Oppy)

Dr. Graham Oppy joins us to talk about different perspectives on the infinity.
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⏰Timestamps⏰:
0:55 What drew Dr. Oppy into Infinity
1:58 How has the concept of infinity developed in history?
5:35 The difference between potential and actual infinities
7:52 How are there different orders of infinity?
12:58 What are the difference between cardinals and ordinals?
15:23 Naive vs Axiomatic Set Theory
19:02 Infinity and Paradoxes
22:42 What are intuitionists?
24:30 Grim Reaper Paradox
28:10 The Application of Paradoxes in Reality
30:19 Impact of A or B Theory of Time
33:53 Responses to Abstract Paradoxes
38:05 Limits to discussions on infinity
41:05 Is there a danger of making an argument of irrelevance?
42:05 Infinity and the Properties of God
45:59 Other implications of infinity in philosophy of religion?
48:39 What are some other implications of infinity?
51:54 What are some books to learn more about the infinity?
54:29 Direction of Discussions on Infinity
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About the video:
Join us as we explore the enigmatic concept of infinity with Dr. Graham Oppy, delving into its philosophical implications and historical development. In this interview, we discuss the distinctions between potential and actual infinities, the different orders of infinity, and the nuances of cardinal and ordinal numbers. Dr. Oppy explains the differences between naive and axiomatic set theory, the role of paradoxes in understanding infinity, and how these concepts influence the philosophy of religion and our understanding of time. Whether you're a student of philosophy or a curious thinker, this conversation offers a profound insight into one of philosophy's most fascinating subjects.
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#philosophy #mathematics #interview

[@CjqNslXUcM]

small mistake: rational numbers are the quotient of integers, not just natural numbers.

[@thehairblairbunchjones6209]

Relatedly, intuitionists reject bivalence - the view that every proposition is either true or false. This means that they can’t straightforwardly accept the t-schema of p is true iff p, since in cases where a proposition is neither true nor false, we have ‘p is not true’ and ‘not not p.’

[@thehairblairbunchjones6209]

Slight correction RE intuitionism. Intuitionists don’t accept that there are cases where neither p nor not p. That would entail contradiction. Rather they don’t affirm p or not p in certain cases. But they will always affirm the double negation of p or not p and so will always reject ‘neither p nor not p.’ I know this was intended as an introduction and so the explanations were kept simple, but I felt a sudden urge to be the ‘well acktually’ guy.

[@MsJavaWolf]

43:30 I'm not sure what it means for God to know all the propositions like 1 = 1 and 2 = 2 and 3 = 3 etc. or what the difference is from when a human thinks about that. I would say that I also know those things, even if I can never actual write that infinite number of propositions down.
Of course you could also reduce those propositions to a single proposition with a quantifier over N but I think it's also reasonable to see them as an infinite number of propositions that all people with a basic understanding of mathematics know. Because of this I'm not sure if characterizing omniscience as knowing an infinite number of propositions is very useful.