Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

1. 01 · yt0.761

   You you set these are the rules that we are we adopt to prove things. Then you what Gödel shows is an amazing thing. I always thought it was amazing. There is a statement which you by virtue of your trust in these rules, you can see that it's true. Yet, you can't prove it by the rules. Now, I found this absolutely amazing because it means you're you don't use the rules to to understand things because how do you know this thing is true? Well, you know it's true but because you trust the rules. Well, it's you're you're if you're using the rules, then how do you know that using the rules only giv…

   yt/OoDi856wLPM-sir-roger-penrose-stuart-hameroff-collapsing-a-theory-of-qua/transcript.txt

2. 02 · blog0.759

   Constructing Curry Sentences 2.1 Curry’s First Method, and Set-Theoretic Curry Sentences 2.2 Curry’s Second Method, and Truth-Theoretic Curry Sentences 3. Deriving the Paradox 3.1 The Curry-Paradox Lemma 3.2 Alternative Premises 4. Responses to Curry’s Paradox 4.1 Curry-Incompleteness Responses 4.2 Curry-Completeness Responses 4.2.1 Contraction-Free Responses 4.2.2 Detachment-Free Responses 4.2.3 Application to the Informal Argument 5. The Significance of Curry’s Paradox 5.1 Dashing Hopes for Solutions to Negation Paradoxes 5.1.1 Paraconsistent Solutions Frustrated 5.1.2 Paracomplete Solutions…

   blog/plato-stanford-edu/curry-s-paradox.md

3. 03 · yt0.753

   Well, sure, if somebody proves the theorem, I mean, Andrew Wiles proved that there were no x to the n, that you can have a sum of two squares which is another square, but there's no other power which the sum of two of that powers gives you another thing which has the same power I mean, that's mathematical statement and that would be true. Whether the universe had different physical laws and it's completely independent is a mathematical statement is objectively true. How we come across to understand why it is true, maybe very difficult question, very few people really understand, how many peopl…

   yt/0nOtLj8UYCw-quantum-consciousness-debate-does-the-wave-function-actually/transcript.txt

4. 04 · blog0.749

   Löb, who doesn’t mention Curry’s work, credits the paradox to a referee’s observation about the proof of what is now known as Löb’s theorem concerning provability (see entry on Gödel’s incompleteness theorems ). The referee, now known to have been Leon Henkin (Halbach & Visser 2014: 257), suggested that the method Löb used in his proof “leads to a new derivation of paradoxes in natural language”, namely the informal argument of section 1.1 above. [ 12 ] 3. Deriving the Paradox Suppose that we have used one of the above methods to show, for some theory of truth, sets, or properties, that the th…

   blog/plato-stanford-edu/curry-s-paradox.md

5. 05 · yt0.744

   Um, well, it's a curious word you used there, which was explain. Ah, because Yes. Yeah. I I should take that back, right? Yes. You know, because the the right I mean, I don't think this was exactly Boore's attitude. The common attitude is calculate. Predict tell me what the numbers will be, and if the numbers are right, that's all I want. Absolutely. Boore was actually trying to make a much more profound argument which was that a certain sort of explanation which had been provided by classical physics was no longer available. Just could not could not be found. There wasn't that nature didn't p…

   yt/VbXEc9vpeIM-what-we-ve-gotten-wrong-about-quantum-physics-world-science-/transcript.txt

6. 06 · blog0.742

   Under the supposition that \(k\) is true, we have thus derived a conditional together with its antecedent. Using modus ponens within the scope of the supposition, we now derive the conditional’s consequent under that same supposition: (3) Under the supposition that \(k\) is true, it is the case that time is infinite . The rule of conditional proof now entitles us to affirm a conditional with our supposition as antecedent: (4) If \(k\) is true then time is infinite. But, since (4) just is \(k\) itself, we thus have (5) \(k\) is true. Finally, putting (4) and (5) together by modus ponens , we ge…

   blog/plato-stanford-edu/curry-s-paradox.md

7. 07 · blog0.742

   To think it likely that \({\sim}A\) is to think it likely that a sufficient condition for the truth of “\(A \supset B\)” obtains. Take someone who thinks that the Republicans won’t win the election \(({\sim}R)\), and who rejects the thought that if they do win, they will double income tax \((D)\). According to Hook, this person has grossly inconsistent opinions. For if she thinks it’s likely that \({\sim}R\), she must think it likely that at least one of the propositions, \(\{{\sim}R, D\}\) is true. But that is just to think it likely that \(R \supset D\). (Put the other way round, to reject \…

   blog/plato-stanford-edu/indicative-conditionals.md

8. 08 · yt0.742

   And uh one of the amazing things that I argue in this article that I've just finished, I I I claim at least that it was regarded as a theorem in Platonist days that the corporeal world, which thus represents the lowest of the three strata, is itself tripartite. In other words, the tripartite uh division of the cosmos in its integrality is repeated on the on the corporeal level itself. And guess what? The tripartite uh division uh which we associate with the Ptolemaic uh division into the sidereal world, the world of the stars, the Earth at the center. Platonism is incurably geocentric. And the…

   yt/1Lm3y_4a--0-wolfgang-smith-and-john-vervaeke-the-perpetual-promise-inexh/transcript.txt

9. 09 · gutenberg0.741

   Explanation--Existence of this kind is conceived as an eternal truth, like the essence of a thing, and, therefore, cannot be explained by means of continuance or time, though continuance may be conceived without a beginning or end.

   gutenberg/PG-3800-ethics/PG-3800.txt

10. 10 · blog0.741

    \] Since evidently we may assert \(\Phi(U)\) and \(\Phi(V)\), it follows from (2) that we may assert \(U(KU)\) and \(V(KV)\), whence also, using (1), \[ [A \vee KU = 0] \wedge [A \vee KV = 1]. \] Using the distributive law (which holds in intuitionistic logic), it follows that we may assert \[ A \vee [KU = 0 \wedge KV = 1]. \] From the presupposition that \(0 \ne 1\) it follows that \[ \tag{3} A \vee KU \ne KV \] is assertable. But it follows from (1) that we may assert \(A \rightarrow U ≈ V\), and so also, using the Extensionality of Functions, \(A \rightarrow KU = KV\). This yields the asser…

    blog/plato-stanford-edu/the-axiom-of-choice.md