Search results

....

I want to share this video of Fr. Leo Clifford. It may inspire some discussion concerning humility and related topics. My grandfather belongs to a Franciscan Church, and I remember thinking as a child that there is no finer sight than a pious man in the poor brown robe of St. Francis.

...

Many, many thanks for the kind words. I too enjoy our conversations. I certainly hope you might become part of the nascent community I recently launched. Now, back to the issue at hand. I am still working on an essay wherein I hope to demonstrate a necessary connection between certain...

I have offered what I regard as incontrovertible evidence of Mathematical Platonism, but I acknowledge that I may not have made the case as clearly as I could have. To that end, I am working on an article that shows quite clearly how (a) Gödel's Incompleteness Theorems imply Platonism and (b)...

To be clear, nothing in my work suggests that Gödel's Incompleteness Theorems imply the unprovability or undecidability of all mathematical statements. That is not an implication of Gödel's work, and it is not a view that I have ever held. For every consistent system S that entails a certain...

I think we should talk in greater detail about the Incompleteness Theorems, but not now. First, let me address the issue that keeps popping up, namely: the entanglement of mind and reality. I'm not necessarily opposed to Bishop Berkeley's thesis esse est percipi. Of course, considerations of...

That would only follow if mathematical truths depend on the human mind, which is exactly what Gödel disproved. My argument, in outline, is: The eternal (or immutable) truths of mathematics could only root in the Necessary Being. If you wonder what the argument for the Necessary Being is, see...

I'm not trying to squeeze out the mind. In fact, one of the central theses of Gödelian Incompleteness, Platonism, & the Mind of God is that the mathematical structure of the world depends on God's mind.

The crux of the matter is as follows: If axiomatic provability and mathematical truth are not the same, then in what does mathematical truth inhere? It is natural to think that a mathematical statement is true because it is provable, but Gödel proved that the set of provable mathematical...

You got me searching for a criterion of real existence, so I have proposed one in Reality & Infinity. To me, it seems plausible, but I don't think it will convince you. My argument is not baseless; it is, I think, supported by both mathematics and science. I agree that all things involve mind --...

While I agree that the mind is always involved with human experience (trivial), it seems wrong to say that Gödel's result is psychological. It is, in fact, a logical result. Or did I misunderstand you? Please advise.

It seems to me that Gödel's incompleteness results constitute strong evidence against your view of mathematics. You can, of course, choose different axioms, but you would only change how you are describing an underlying reality. Moreover, Gödel proved that axiomatic provability and mathematical...

I hadn't realized John Conway died! He was (and is) a truly marvelous mathematician. I'd like to read On Quaternions and Octonions. I remember reading one of his books on the surreal numbers, which I believe he discovered.

Many thanks for the insightful comments. Gödel did prove the existence of true yet (axiomatically) unprovable statements. We are not on shaky ground here: the Incompleteness Theorems are generally accepted. I offer a sketch of the proof in my article Gödelian Incompleteness, Platonism, & the...

The Principle of Sufficient Reason and the Principle of Causality are inequivalent. I will not offer a demonstration here, but I may write one soon. On the question of determinism, please see my essay A Solution to Modal Collapse. I also have a forthcoming paper which uses calculus to disprove...

Many thanks for the reply. I've used this as an opportunity to write down my thoughts on the matter: Why Philosophy Is Necessary.

I've used this as an opportunity to write down my thoughts on the matter: Why Philosophy Is Necessary.