13 ideas
| 19259 | If 2-D conceivability can a priori show possibilities, this is a defence of conceptual analysis [Vaidya] |
| Full Idea: Chalmers' two-dimensional conceivability account of possibility offers a defence of a priori conceptual analysis, and foundations on which a priori philosophy can be furthered. | |
| From: Anand Vaidya (Understanding and Essence [2010], Intro) | |
| A reaction: I think I prefer Williamson's more scientific account of possibility through counterfactual conceivability, rather than Chalmers' optimistic a priori account. Deep topic, though, and the jury is still out. |
| 8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
| Full Idea: Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought. | |
| From: report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3 | |
| A reaction: The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one. |
| 7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
| Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once. | |
| From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege | |
| A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven? |
| 8686 | Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend] |
| Full Idea: Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning. | |
| From: report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet. |
| 3299 | In logic identity involves reflexivity (x=x), symmetry (if x=y, then y=x) and transitivity (if x=y and y=z, then x=z) [Baillie] |
| Full Idea: In logic identity is an equivalence relation, which involves reflexivity (x=x), symmetry (if x=y, then y=x), and transitivity (if x=y and y=z, then x=z). | |
| From: James Baillie (Problems in Personal Identity [1993], Intr p.4) |
| 22277 | Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter] |
| Full Idea: Boole's work was an early example of the axiomatic method, whereby intellectual economy is achieved by studying a set of axioms in which the primitive terms have multiple interpretations. | |
| From: report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole' | |
| A reaction: Unclear about this. I suppose the axioms are just syntactic, and a range of semantic interpretations can be applied. Are De Morgan's Laws interpretations, or implications of the syntactic axioms? The latter, I think. |
| 19262 | Essential properties are necessary, but necessary properties may not be essential [Vaidya] |
| Full Idea: When P is an essence of O it follows that P is a necessary property of O. However, P can be a necessary property of O without being an essence of O. | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Knowledge') | |
| A reaction: This summarises the Kit Fine view with which I sympathise. However, I dislike presenting essence as a mere list of properties, which is only done for the convenience of logicians. But was Jessie Owens a great athlete after he lost his speed? |
| 19267 | Define conceivable; how reliable is it; does inconceivability help; and what type of possibility results? [Vaidya] |
| Full Idea: Conceivability as evidence for possibility needs four interpretations. How is 'conceivable' defined or explained? How strongly is the idea endorsed? How does inconceivability fit in? And what kind of possibility (logical, physical etc) is implied? | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Application') | |
| A reaction: [some compression] Williamson's counterfactual account helps with the first one. The strength largely depends on whether your conceptions are well informed. Inconceivability may be your own failure. All types of possibility can be implied. |
| 19268 | Inconceivability (implying impossibility) may be failure to conceive, or incoherence [Vaidya] |
| Full Idea: If we aim to derive impossibility from inconceivability, we may either face a failure to conceive something, or arrive at a state of incoherence in conceiving. | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Application') | |
| A reaction: [summary] Thus I can't manage to conceive a multi-dimensional hypercube, but I don't even try to conceive a circular square. In both cases, we must consider whether the inconceivability results from our own inadequacy, rather than from the facts. |
| 19265 | Can you possess objective understanding without realising it? [Vaidya] |
| Full Idea: Is it possible for an individual to possess objectual understanding without knowing they possess the objectual understanding? | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Objections') | |
| A reaction: Hm. A nice new question to loose sleep over. We can't demand a regress of meta-understandings, so at some point you just understand. Birds understand nests. Equivalent: can you understand P, but can't explain P? Skilled, but inarticulate. |
| 19260 | Gettier deductive justifications split the justification from the truthmaker [Vaidya] |
| Full Idea: In the Gettier case of deductive justification, what we have is a separation between the source of the justification and the truthmaker for the belief. | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Distinction') | |
| A reaction: A very illuminating insight into the Gettier problem. As a fan of truthmakers, I'm wondering if this might quickly solve it. |
| 19266 | In a disjunctive case, the justification comes from one side, and the truth from the other [Vaidya] |
| Full Idea: The disjunctive belief that 'either Jones owns a Ford or Brown is in Barcelona', which Smith believes, derives its justification from the left disjunct, and its truth from the right disjunct. | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Application') | |
| A reaction: The example is from Gettier's original article. Have we finally got a decent account of the original Gettier problem, after fifty years of debate? Philosophical moves with delightful slowness. |
| 19264 | Aboutness is always intended, and cannot be accidental [Vaidya] |
| Full Idea: A representation cannot accidentally be about an object. Aboutness is in general an intentional relation. | |
| From: Anand Vaidya (Understanding and Essence [2010], 'Objections') | |
| A reaction: 'Intentional' with a 't', not with an 's'. This strikes me as important. Critics dislike the idea of 'representation' because if you passively place a representation and its subject together, what makes the image do the representing job? Answer: I do! |