18 ideas
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| Full Idea: Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283) | |
| A reaction: This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence. |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| Full Idea: Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: Thagard picked this remark out, in support of his work on coherence. |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| Full Idea: The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) |
| 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. |
| 17629 | Which premises are ultimate varies with context [Russell] |
| Full Idea: Premises which are ultimate in one investigation may cease to be so in another. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| Full Idea: In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| Full Idea: The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282) | |
| A reaction: I identify this as the 'fruitfulness' that results when the essence of something is discovered. |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| Full Idea: It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) | |
| A reaction: Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments? |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) |
| 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. |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| Full Idea: Even where there is the highest degree of obviousness, we cannot assume that we are infallible - a sufficient conflict with other obvious propositions may lead us to abandon our belief, as in the case of a hallucination afterwards recognised as such. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: This approach to fallibilism seems to arise from the paradox that undermined Frege's rather obvious looking axioms. After Peirce and Russell, fallibilism has become a secure norm of modern thought. |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| Full Idea: Although intrinsic obviousness is the basis of every science, it is never, in a fairly advanced science, the whole of our reason for believing any one proposition of the science. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) |
| 17631 | Induction is inferring premises from consequences [Russell] |
| Full Idea: The inferring of premises from consequences is the essence of induction. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) | |
| A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| Full Idea: The law of gravitation leads to many consequences which could not be discovered merely from the apparent motions of the heavenly bodies. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.275) |