15 ideas
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5 | |
| A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems. |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete. | |
| From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1 | |
| A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed. |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2 | |
| A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert. |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt. |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality. |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6 | |
| A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it. |
| 3978 | Associations are held to connect Ideas together in the way the world is connected together [Fodor] |
| Full Idea: The laws of associations were held to explicate the semantic coherence of intentional processes, which adjust the causal relations among Ideas to reflect corresponding relations among the things that they're ideas of. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.296) | |
| A reaction: With the support of evolution, and the backing of a correspondence theory of truth, plus more sophistication in the associations, this might work. |
| 3976 | Intentional science needs objects with semantic and causal properties, and which obey laws [Fodor] |
| Full Idea: If there is to be an intentional science, there must be semantically evaluable things which have causal powers, and there must be laws relating beliefs and desires to one another, and to actions. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.293) | |
| A reaction: The semantics and causation sound fair enough, but the prospect of finding laws looks bleak (though, contrary to Davidson, I don't see why they can't exist). |
| 3980 | Intentional states and processes may be causal relations among mental symbols [Fodor] |
| Full Idea: It may be that intentional states are relations to mental symbols, and mental processes are implemented by causal relations among these symbols. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.296) | |
| A reaction: It is hard to see how something could have causal powers just by being a symbol. The theory needs something else to drive the causation. |
| 3981 | Most psychological properties seem to be multiply realisable [Fodor] |
| Full Idea: These days most philosophers of mind suppose that most psychological properties are multiply realisable. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.298) | |
| A reaction: This is just speculation. The physical part may seem very different, but turn out to be identical in the ways that matter (like a knife made of two different metals). |
| 3975 | Folk psychology explains behaviour by reference to intentional states like belief and desire [Fodor] |
| Full Idea: Folk psychology is primarily intentional explanation; it's the idea that people's behaviour can be explained by reference to the contents of their beliefs and desires. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.292) | |
| A reaction: Sounds good. To reject folk psychology (as reductivists tend to) is to reject the existence of significant intentional states which have causal properties |
| 3982 | How could the extrinsic properties of thoughts supervene on their intrinsic properties? [Fodor] |
| Full Idea: It is hard to see how the extrinsic properties of thoughts could supervene on their intrinsic properties. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.299) | |
| A reaction: This doesn't seem a big problem. Sometimes represented experiences establish the match; sometimes the match is not very good, or even wrong. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 3977 | Laws are true generalisations which support counterfactuals and are confirmed by instances [Fodor] |
| Full Idea: Laws are true generalisations that support counterfactuals and are confirmed by their instances. | |
| From: Jerry A. Fodor (Jerry A. Fodor on himself [1994], p.293) | |
| A reaction: This seems correct, but it doesn't disentangle laws as mental states from laws as features of nature |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |