18 ideas
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 15034 | Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry] |
| Full Idea: I shall beg off talking of a) whether genera and species are real or situated in bare thoughts alone, b) whether as real they are bodies or incorporeals, and c) whether they are separated or in sensibles and have their reality in connection with them. | |
| From: Porphyry (Isagoge ('Introduction') [c.295], (2)) | |
| A reaction: This passage, picking up on Aristotle, seems to be the original source that grew into the medievel debate about universals. It seems to rather neatly lay out the agenda for the universals debate which is still with us. |
| 4983 | There are no rules linking thought and behaviour, because endless other thoughts intervene [Davidson] |
| Full Idea: We know too much about thought and behaviour to trust exact and universal statements linking them. Beliefs and desires issue in behaviour only as modified and mediated by further beliefs and desires, attitudes and attendings, without limit. | |
| From: Donald Davidson (Mental Events [1970], p.217) | |
| A reaction: Now seen as a key objection to behaviourism, and rightly so. However, I am not sure about "without limit", which implies an implausible absolute metaphysical freedom. Davidson goes too far in denying any nomological link between thought and brain. |
| 3529 | Reduction is impossible because mind is holistic and brain isn't [Davidson, by Maslin] |
| Full Idea: Davidson rejects ontological reduction of mental to physical because propositional attitudes are holistic; there must be extensive coherence among someone's attitudes to treat them as a rational person, and this has no counterpart in physical theory. | |
| From: report of Donald Davidson (Mental Events [1970]) by Keith T. Maslin - Introduction to the Philosophy of Mind 7.5 | |
| A reaction: I don't find this view persuasive. We treat the weather in simple terms, even though it is almost infinitely complex. Davidson has a Kantian overconfidence in our rationality. A coherence among the parts is needed to be a tree. |
| 2307 | Anomalous monism says nothing at all about the relationship between mental and physical [Davidson, by Kim] |
| Full Idea: Davidson's anomalous monism says no more about the relationship between the mental and the physical than the claim that all objects with a colour have a shape says about the relationship between colours and shapes. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Mind in a Physical World §1 p.005 | |
| A reaction: Indeed, I find the enthusiasm for property dualism etc. quite baffling, given that we are merely told that mind is 'an anomaly'. I take it to be old fashioned dualism in trendy clothes. |
| 5497 | Mind is outside science, because it is humanistic and partly normative [Davidson, by Lycan] |
| Full Idea: For Davidson, mental types are individuated by considerations that are nonscientific, distinctly humanistic, and part normative, so will not coincide with any types that are designated in scientific terms. | |
| From: report of Donald Davidson (Mental Events [1970]) by William Lycan - Introduction - Ontology p.8 | |
| A reaction: I just don't believe this, mainly because I don't accept that there is a category called 'nonscientific'. All we are saying is that a brain is a hugely complicated object, and we don't properly understand its operations, though we relate to it very well. |
| 4081 | Anomalous monism says causes are events, so the mental and physical are identical, without identical properties [Davidson, by Crane] |
| Full Idea: Davidson's anomalous monism says that events are causes, so we can identify mental and physical events without having to identify their properties. | |
| From: report of Donald Davidson (Mental Events [1970]) by Tim Crane - Elements of Mind 2.18 | |
| A reaction: As Fodor insists, a thing like a mountain has properties at different levels of description. We can have 'property dualism' and full-blown reductive identity. |
| 2321 | If rule-following and reason are 'anomalies', does that make reductionism impossible? [Davidson, by Kim] |
| Full Idea: Davidson takes mental anomalism (that the mind exhibits normativity and rationality), and in particular his claim that there are no laws connecting mental and physical properties, to undermine mind-body reductionism. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Mind in a Physical World §4 p.092 | |
| A reaction: A nice summary of the core idea of property dualism. Personally I expect the whole lot to be reducible, and to follow laws, but the sheer complexity of the brain permanently bars us from actually doing the reduction. |
| 3404 | Davidson claims that mental must be physical, to make mental causation possible [Davidson, by Kim] |
| Full Idea: Davidson's thesis is that if mental events of a particular kind cause physical events of a particular kind, and the two kinds are connected by a law, then they must both be physical kinds. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Philosophy of Mind p.137 | |
| A reaction: Davidson would pretty obviously be right. The whole problem here is the idea of a 'law'. You can only have strict law for simple entities, like particles and natural kinds. The brain is a mess, like weather or explosions. |
| 3405 | If mental causation is lawless, it is only possible if mental events have physical properties [Davidson, by Kim] |
| Full Idea: Since no laws exist connecting mental and physical properties, purely physical laws must do the causal work, which means mental events enter into causal relations only because they possess physical properties that figure in laws. | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Philosophy of Mind p.138 | |
| A reaction: Surely no such laws exist 'yet'? I can see no plausible argument that psycho-physical laws are impossible. However, the conclusion of this remark seems right. Interaction requires some sort of equality. |
| 16041 | Supervenience of the mental means physical changes mental, and mental changes physical [Davidson] |
| Full Idea: The supervenience [of mental characteristics on the physical] might be taken to mean that there cannot be two events alike in all physical respects but differing in some mental respect, or an object cannot differ mentally without altering physically. | |
| From: Donald Davidson (Mental Events [1970], I) | |
| A reaction: This is the first occasion on which Davidson introduced his notion of supervenience. Supervenience is often taken to be one-way. The first implies physical causing mental; his second implies that mental causes physical. |
| 6620 | Davidson sees identity as between events, not states, since they are related in causation [Davidson, by Lowe] |
| Full Idea: Davidson's version of the identity theory is couched in terms of events rather than states, because he regards causation as a relation between events. | |
| From: report of Donald Davidson (Mental Events [1970]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.2 n12 | |
| A reaction: I think it may be more to the point that the mind is a dynamic thing, and so it consists of events rather than states, and hence we want to know what those events are made up from. I think my chair is causing me to rest above the floor… |
| 3429 | Multiple realisability was worse news for physicalism than anomalous monism was [Davidson, by Kim] |
| Full Idea: Davidson's argument about psychophysical anomalism has not been embraced by everyone; multiple realisability of mental properties has had a much greater impact in undermining reductionism (and hence type physicalism). | |
| From: report of Donald Davidson (Mental Events [1970]) by Jaegwon Kim - Philosophy of Mind p.218 | |
| A reaction: My view is that functional states are multiply realisable, but phenomenal states aren't. Fear functions in frogs much as it does in us, but being a frightened frog is nothing like being a frightened human. Their brains are different! |
| 3524 | Causation is either between events, or between descriptions of events [Davidson, by Maslin] |
| Full Idea: According to Davidson analyses of causality proceed at two different levels: at the lower level it holds between events regardless of how they are described; higher level explanations hold between descriptions of events, which pick out properties. | |
| From: report of Donald Davidson (Mental Events [1970]) by Keith T. Maslin - Introduction to the Philosophy of Mind 7.4 |
| 3526 | Whether an event is a causal explanation depends on how it is described [Davidson, by Maslin] |
| Full Idea: Davidson says causal explanations hold between descriptions of events and not between the events themselves, so the possibility of events as explanations depends on how they are described (e.g. a wind collapsing a bridge). | |
| From: report of Donald Davidson (Mental Events [1970]) by Keith T. Maslin - Introduction to the Philosophy of Mind 7.4 |