13 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. |
| 8329 | Either causal relations are given in experience, or they are unobserved and theoretical [Sosa/Tooley] |
| Full Idea: There is a fundamental choice between the realist approach to causation which says that the relation is immediately given in experience, and the view that causation is a theoretical relation, and so not directly observable. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: Even if immediate experience is involved, there is a step of abstraction in calling it a cause, and picking out events. A 'theoretical relation' is not of much interest there if no observations are involved. I don't think a choice is required here. |
| 3102 | Why don't we experience or remember going to sleep at night? [Magee] |
| Full Idea: As a child it was incomprehensible to me that I did not experience going to sleep, and never remembered it. When my sister said 'Nobody remembers that', I just thought 'How does she know?' | |
| From: Bryan Magee (Confessions of a Philosopher [1997], Ch.I) | |
| A reaction: This is actually evidence for something - that we do not have some sort of personal identity which is separate from consciousness, so that "I am conscious" would literally mean that an item has a property, which it can lose. |
| 8324 | The problem is to explain how causal laws and relations connect, and how they link to the world [Sosa/Tooley] |
| Full Idea: Causal states of affairs encompass causal laws, and causal relations between events or states of affairs; two key questions concern the relation between causal laws and causal relations, and the relation between these and non-causal affairs. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: This is the agenda for modern analytical philosophy. I'm not quite clear what would count as an answer. When have you 'explained' a relation? Does calling it 'gravity', or finding an equation, explain that relation? Do gravitinos explain it? |
| 8328 | Causation isn't energy transfer, because an electron is caused by previous temporal parts [Sosa/Tooley] |
| Full Idea: The temporal parts of an electron (for example) are causally related, but this relation does not involve any transfer of energy or momentum. Causation cannot be identified with physical energy relations, and physicalist reductions look unpromising. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: This idea, plus Idea 8327, are their grounds for rejecting Fair's proposal (Idea 8326). It feels like a different use of 'cause' when we say 'the existence of x was caused by its existence yesterday'. It is more like inertia. Destruction needs energy. |
| 8327 | If direction of causation is just direction of energy transfer, that seems to involve causation [Sosa/Tooley] |
| Full Idea: The objection to Fair's view that the direction of causation is the direction of the transference of energy and/or momentum is that the concept of transference itself involves the idea of causation. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: Does it? If a particle proceeds from a to b, how is that causation? ...But the problem is that the particle kicks open the door when it arrives (i.e. makes changes). We wouldn't call it causation if the transference didn't change any properties. |
| 8330 | Are causes sufficient for the event, or necessary, or both? [Sosa/Tooley] |
| Full Idea: An early view of causation (Mill and Hume) is whatever is (ceteris paribus) sufficient for the event. A second view (E.Nagel) is that the cause should just be necessary. Some (R.Taylor) even contemplate the cause having to be necessary and sufficient. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §2) | |
| A reaction: A cause can't be necessary if there is some other way to achieve the effect. A single cause is not sufficient if many other factors are also essential. If neither of those is right, then 'both' is wrong. Enter John Mackie... |
| 8325 | The dominant view is that causal laws are prior; a minority say causes can be explained singly [Sosa/Tooley] |
| Full Idea: The dominant view is that causal laws are more basic than causal relations, with relations being logically supervenient on causal laws, and on properties and event relations; some, though, defend the singularist view, in which events alone can be related. | |
| From: E Sosa / M Tooley (Introduction to 'Causation' [1993], §1) | |
| A reaction: I am deeply suspicious about laws (see Idea 5470). I suspect that the laws are merely descriptions of the regularities that arise from the single instances of causation. We won't explain the single instances, but then laws don't 'explain' them either. |