14 ideas
| 18914 | Davidson controversially proposed to quantify over events [Davidson, by Engelbretsen] |
| Full Idea: An alternative, and still controversial, extension of first-order logic is due to Donald Davidson, who allows for quantification over events. | |
| From: report of Donald Davidson (The Individuation of Events [1969]) by George Engelbretsen - Trees, Terms and Truth 3 | |
| A reaction: I'm suddenly thinking this is quite an attractive proposal. We need to quantify over facts, or states of affairs, or events, or some such thing, to talk about the world properly. Objects, predicates and sets/parts is too sparse. I like facts. |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 9843 | You can't identify events by causes and effects, as the event needs to be known first [Dummett on Davidson] |
| Full Idea: Davidson's criterion for the identity of events is a mistake, because we cannot know the causes and effects of an event until we know what that event comprises. | |
| From: comment on Donald Davidson (The Individuation of Events [1969]) by Michael Dummett - Frege philosophy of mathematics Ch.10 | |
| A reaction: How many attempts by analytical philosophers to give necessary and sufficient conditions for things seem to founder in this way. Their predecessor is at the end of 'Theaetetus'; you have to know what the sun is before you can define it. |
| 14602 | Events can only be individuated causally [Davidson, by Schaffer,J] |
| Full Idea: Davidson claims that events can only be individuated causally. | |
| From: report of Donald Davidson (The Individuation of Events [1969], 3) by Jonathan Schaffer - Causation and Laws of Nature 3 | |
| A reaction: Schaffer rejects this in favour of individuating events by their spatiotemporal locations and intrinsic natures (which seem to be property instantiations, a la Kim). Schaffer was a pupil of David Lewis. |
| 14004 | We need events for action statements, causal statements, explanation, mind-and-body, and adverbs [Davidson, by Bourne] |
| Full Idea: Davidson claims that we require the existence of events in order to make sense of a) action statements, b) causal statements, c) explanation, d) the mind-body problem, and e) the logic of adverbial modification. | |
| From: report of Donald Davidson (The Individuation of Events [1969], Intro IIb) by Craig Bourne - A Future for Presentism | |
| A reaction: Events are a nice shorthand, but I don't like them in a serious ontology. Prior says there objects and what happens to them; Kim reduces events to other things. Processes are more clearly individuated than events. |
| 8278 | The claim that events are individuated by their causal relations to other events is circular [Lowe on Davidson] |
| Full Idea: Davidson has urged that events are individuated by the causal relations which they bear to one another, in accordance with the principle that events are identical just in case they have the same causes and effects. But the principle is viciously circular. | |
| From: comment on Donald Davidson (The Individuation of Events [1969]) by E.J. Lowe - The Possibility of Metaphysics 7.4 | |
| A reaction: You wouldn't want to identify a person just by their relationships, even though those will certainly be unique. Generally it is what I am (right now) naming as the Functional Fallacy: believing that specifying the function of x explains x. |
| 17945 | Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas] |
| Full Idea: The theory of Forms is not a theory of universals but a first attempt to explain how predication, the application of a single term to many objects - now considered one of the most elementary operations of language - is possible. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxvii) |
| 17946 | Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas] |
| Full Idea: Only Tallness and nothing else really is tall; everything else merely participates in the Forms and, being excluded from the realm of Being, belongs to the inferior world of Becoming. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxviii) | |
| A reaction: This is just as weird as the normal view (and puzzle of participation), but at least it makes more sense of 'metachein' (partaking). |
| 17944 | 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas] |
| Full Idea: The Greek 'episteme' is usually translated as 'knowledge' but, I argue, closer to our notion of understanding. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xvi) | |
| A reaction: He agrees with Julia Annas on this. I take it to be crucial. See the first sentence of Aristotle's 'Metaphysics'. It is explanation which leads to understanding. |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |