Joel David Hamkins
@joeldavidhamkins.bsky.social
Mathematics and Philosophy of the Infinite
Professor of Logic, University of Notre Dame
University of Oxford
#InfinitelyMore #BookOfInfinity #PanoramaOfLogic #PhilMaths
https://buymeacoffee.com/joeldavidhamkins
Professor of Logic, University of Notre Dame
University of Oxford
#InfinitelyMore #BookOfInfinity #PanoramaOfLogic #PhilMaths
https://buymeacoffee.com/joeldavidhamkins
More images of what I experienced tonight.
November 10, 2025 at 2:37 AM
More images of what I experienced tonight.
I think this is basically similar to what she is arguing, although she is concerned with the consciousness angle. I take her point to be that what we mean by consciousness (and intelligence) will be changing (and improving) in light of the kinds of machines we can build.
November 8, 2025 at 4:22 PM
I think this is basically similar to what she is arguing, although she is concerned with the consciousness angle. I take her point to be that what we mean by consciousness (and intelligence) will be changing (and improving) in light of the kinds of machines we can build.
Her essay is not about AGI and indeed is rather pointing us towards a more nuanced, plural understanding of what counts as "intelligence," as well as "consciousness". Obviously the machines are intelligent in *some* sense. Her point is that our notions of these concepts will bend to what faces us.
November 8, 2025 at 3:51 PM
Her essay is not about AGI and indeed is rather pointing us towards a more nuanced, plural understanding of what counts as "intelligence," as well as "consciousness". Obviously the machines are intelligent in *some* sense. Her point is that our notions of these concepts will bend to what faces us.
Followers, please provide your own answers to my questions, answering below each question or quote. Can you identify the authors for each quote? If so, what would you have to say about the view in question?
November 8, 2025 at 12:47 AM
Followers, please provide your own answers to my questions, answering below each question or quote. Can you identify the authors for each quote? If so, what would you have to say about the view in question?
E. In which respects does Feynman's account of science align with Popper, Kuhn, and Feyerabend, respectively?
November 8, 2025 at 12:47 AM
E. In which respects does Feynman's account of science align with Popper, Kuhn, and Feyerabend, respectively?
D. Give a complete, self-contained proof that there are different sizes of infinity.
November 8, 2025 at 12:47 AM
D. Give a complete, self-contained proof that there are different sizes of infinity.
Questions B and C. Select two of the quotes above and provide fuller context of the issue or argument, either criticizing the view in question or defending the view from a relevant criticism.
November 8, 2025 at 12:47 AM
Questions B and C. Select two of the quotes above and provide fuller context of the issue or argument, either criticizing the view in question or defending the view from a relevant criticism.
Question A. Identify the author of each quotation.
November 8, 2025 at 12:47 AM
Question A. Identify the author of each quotation.
It has the most elaborate and the most fascinating technique, and gives unrivaled openings for the display of sheer professional skill. Finally, as history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all."
November 8, 2025 at 12:47 AM
It has the most elaborate and the most fascinating technique, and gives unrivaled openings for the display of sheer professional skill. Finally, as history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all."
(xiii) "If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician. His subject is the most curious of all—there is none in which truth plays such odd pranks...
November 8, 2025 at 12:47 AM
(xiii) "If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician. His subject is the most curious of all—there is none in which truth plays such odd pranks...
(xii) "The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."
November 8, 2025 at 12:47 AM
(xii) "The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."
...Nevertheless, I claim that Cantor’s argument, undertaken properly, is actually constructive and does provide specific transcendental numbers."
November 8, 2025 at 12:47 AM
...Nevertheless, I claim that Cantor’s argument, undertaken properly, is actually constructive and does provide specific transcendental numbers."
(xi) "One occasionally, or even often, finds mathematicians asserting that indeed, Cantor's argument [for the existence of transcendental numbers] is not constructive; I once saw an extremely prominent mathematician make this assertion to hundreds of people in a big public lecture.
November 8, 2025 at 12:47 AM
(xi) "One occasionally, or even often, finds mathematicians asserting that indeed, Cantor's argument [for the existence of transcendental numbers] is not constructive; I once saw an extremely prominent mathematician make this assertion to hundreds of people in a big public lecture.
Philosophers may try to teach you by telling you qualitatively about nature. I am trying to describe her. But it is not getting across because it is impossible. Perhaps it is because their horizons are limited in this way that some people are able to imagine that the centre of the universe is man."
November 8, 2025 at 12:47 AM
Philosophers may try to teach you by telling you qualitatively about nature. I am trying to describe her. But it is not getting across because it is impossible. Perhaps it is because their horizons are limited in this way that some people are able to imagine that the centre of the universe is man."
(x) "All the intellectual arguments that you can make will not communicate to deaf ears what the experience of music really is. In the same way all the intellectual arguments in the world will not convey an understanding of nature to those of 'the other culture'...
November 8, 2025 at 12:47 AM
(x) "All the intellectual arguments that you can make will not communicate to deaf ears what the experience of music really is. In the same way all the intellectual arguments in the world will not convey an understanding of nature to those of 'the other culture'...
Painting is not about what hangs in the museum, it's about what you do—the experience you have with brushes and paint."
November 8, 2025 at 12:47 AM
Painting is not about what hangs in the museum, it's about what you do—the experience you have with brushes and paint."
(ix) "Finally, I want to stress again that it's not the fact that consecutive odd numbers add up to squares that really matters here; it's the discovery, the explanation, the analysis. Mathematical truths are merely the incidental by-products of these activities...
November 8, 2025 at 12:47 AM
(ix) "Finally, I want to stress again that it's not the fact that consecutive odd numbers add up to squares that really matters here; it's the discovery, the explanation, the analysis. Mathematical truths are merely the incidental by-products of these activities...
(viii)By themselves they cannot and will not falsify that philosophical theory, for its defenders will do what we have already seen scientists doing when confronted by anomaly. They will devise numerous articulations and ad hoc modifications of the theory in order to eliminate any apparent conflict.
November 8, 2025 at 12:47 AM
(viii)By themselves they cannot and will not falsify that philosophical theory, for its defenders will do what we have already seen scientists doing when confronted by anomaly. They will devise numerous articulations and ad hoc modifications of the theory in order to eliminate any apparent conflict.
(I repeat: without any theory, for there is not a single theory that is not in some trouble or other.)"
November 8, 2025 at 12:47 AM
(I repeat: without any theory, for there is not a single theory that is not in some trouble or other.)"
(vii) "According to our present results, hardly any theory is consistent with the facts. The demand to admit only those theories which are consistent with the available and accepted facts again leaves us without any theory....
November 8, 2025 at 12:47 AM
(vii) "According to our present results, hardly any theory is consistent with the facts. The demand to admit only those theories which are consistent with the available and accepted facts again leaves us without any theory....
(vi) "The saddest part of all this 'reform' are the attempts to 'make math interesting' and 'relevant to kids' lives.' You don't need to make math interesting—it's already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives."
November 8, 2025 at 12:47 AM
(vi) "The saddest part of all this 'reform' are the attempts to 'make math interesting' and 'relevant to kids' lives.' You don't need to make math interesting—it's already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives."
(v) "...it will become clear that there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes."
November 8, 2025 at 12:47 AM
(v) "...it will become clear that there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes."