13 ideas
| 6253 | Reason is our power of finding out true propositions [Hutcheson] |
| Full Idea: Reason is our power of finding out true propositions. | |
| From: Francis Hutcheson (Treatise 4: The Moral Sense [1728], §I) | |
| A reaction: This strikes me as a very good definition. I don't see how you can define reason without mentioning truth, and you can't believe in reason if you don't believe in truth. The concept of reason entails the concept of a good reason. |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4 | |
| A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions. |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject. |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4 |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10 |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl) | |
| A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass. |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| Full Idea: I call 'entitlement' (as opposed to justification) the epistemic rights or warrants that need not be understood by or even be accessible to the subject. | |
| From: Tyler Burge (Content Preservation [1993]), quoted by Paul Boghossian - Analyticity Reconsidered §III | |
| A reaction: I espouse a coherentism that has both internal and external components, and is mediated socially. In Burge's sense, animals will sometimes have 'entitlement'. I prefer, though, not to call this 'knowledge'. 'Entitled true belief' is good. |
| 6256 | Can't the moral sense make mistakes, as the other senses do? [Hutcheson] |
| Full Idea: Can there not be a right and wrong state of our moral sense, as there is in our other senses? | |
| From: Francis Hutcheson (Treatise 4: The Moral Sense [1728], §IV) | |
| A reaction: Hutcheson replies by saying something like they are both fully reliable in normal conditions. It remains, though, a very good question for the intuitionist to face, as the moral sense is supposed to be direct and reliable, but how do you check? |
| 6252 | Happiness is a pleasant sensation, or continued state of such sensations [Hutcheson] |
| Full Idea: In the following discourse, happiness denotes pleasant sensation of any kind, or continued state of such sensations. | |
| From: Francis Hutcheson (Treatise 4: The Moral Sense [1728], Intro) | |
| A reaction: This is a very long way from Greek eudaimonia. Hutcheson seems to imply that I would be happy if I got high on drugs after my family had just burnt to death. Socrates points out that scratching an itch is a very pleasant sensation (Idea 132). |
| 6257 | You can't form moral rules without an end, which needs feelings and a moral sense [Hutcheson] |
| Full Idea: What rule of actions can be formed, without relation to some end proposed? Or what end can be proposed, without presupposing instincts, desires, affections, or a moral sense, it will not be easy to explain. | |
| From: Francis Hutcheson (Treatise 4: The Moral Sense [1728], §IV) | |
| A reaction: We have no reason to think that 'instincts, desires and affections' will give us the remotest guidance on how to behave morally well (though we would expect them to aid our survival). How could a moral sense give a reason, without spotting a rule? |
| 6254 | We are asked to follow God's ends because he is our benefactor, but why must we do that? [Hutcheson] |
| Full Idea: The reasons assigned for actions are such as 'It is the end proposed by the Deity'. But why do we approve concurring with the divine ends? The reason is given 'He is our benefactor', but then, for what reason do we approve concurrence with a benefactor? | |
| From: Francis Hutcheson (Treatise 4: The Moral Sense [1728], §I) | |
| A reaction: Characteristic of what MacIntyre calls the 'Enlightenment Project', which is the application of Cartesian scepticism to proving the foundations of morals. Proof beyond proof is continually demanded. If you could meet God, you would obey without question. |
| 6255 | Why may God not have a superior moral sense very similar to ours? [Hutcheson] |
| Full Idea: Why may not the Deity have something of a superior kind, analogous to our moral sense, essential to him? | |
| From: Francis Hutcheson (Treatise 4: The Moral Sense [1728], §I) | |
| A reaction: This is Plato's notion of the gods, as beings who are profoundly wise, and understand all the great moral truths, but are not the actual originators of those truths. The idea that God creates morality actually serves to undermine morality. |