7 ideas
| 7085 | The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling] |
| Full Idea: The 'Tractatus' concerns the theory of what can be expressed by propositions (and, which comes to the same thing, can be thought), and what cannot be expressed by propositions, but can only be shown; which, I believe, is the main problem of philosophy. | |
| From: report of Ludwig Wittgenstein (Letters to Russell [1919]) by A.C. Grayling - Wittgenstein Ch.2 | |
| A reaction: This contains what a I consider the heresy of making thought depend on language, but his main question remains, of the limits of thought. It is dramatised nicely in the 'mysterian' view of the mind-body problem (e.g. Idea 2540). |
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 23463 | Atomic facts correspond to true elementary propositions [Wittgenstein] |
| Full Idea: Atomic fact [Sachverhalt] is what corresponds to an elementary proposition [Elementarsatz] if it is true. | |
| From: Ludwig Wittgenstein (Letters to Russell [1919], CL 125) | |
| A reaction: This is perhaps the key to the Tractatus, because it is the binding point between world and language. A true realist would allow for atomic facts that may go beyond even possible propositions. |
| 23490 | A thought is mental constituents that relate to reality as words do [Wittgenstein] |
| Full Idea: Does a Gedanke [thought] consist of words? No! But of psychical constituents that have the same sort of relation to reality as words. | |
| From: Ludwig Wittgenstein (Letters to Russell [1919], p.125), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 4B | |
| A reaction: This is roughly my view of propositions, as non-lingustic mental events. The 'psychical constituents' seem to be concepts, in a psychological rather than a Fregean sense. This idea allowed transfer of his representation theory from thought to language. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |