22 ideas
| 6259 | Why can't a wise man doubt everything? [Montaigne] |
| Full Idea: Why cannot a wise man dare to doubt anything and everything? | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0562) | |
| A reaction: This question seems to be the start of the Enlightenment Project, of attempting to prove everything. MacIntyre warns of the dangers of this in ethical theory. The story of modern philosophy is the discovery of its impossibility. E.g. Davidson on truth. |
| 6263 | No wisdom could make us comfortably walk a wide beam if it was high in the air [Montaigne] |
| Full Idea: Take a beam wide enough to walk along: suspend it between two towers: there is no philosophical wisdom, however firm, which could make us walk along it just as we would if we were on the ground. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0672) | |
| A reaction: This proposes great scepticism about the practical application of philosophical wisdom, but if we talk in terms of the wise assessment of risk in any undertaking, our caution on the raised beam makes perfectly good sense. |
| 6258 | Virtue is the distinctive mark of truth, and its greatest product [Montaigne] |
| Full Idea: The distinctive mark of the Truth we hold ought to be virtue, which is the most exacting mark of Truth, the closest one to heaven and the most worthy thing that Truth produces. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0493) | |
| A reaction: A long way from Tarski and minimalist theories of truth! But not so far from pragmatism. Personally I think Montaigne is making an important claim, which virtue theorists should be attempting to incorporate into their theory. Aristotle would sympathise. |
| 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
| Full Idea: Propositional logic can deal with negation, disjunction and conjunction of propositions, but predicate logic goes beyond it to deal with quantifiers, predicates and relations. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.1) | |
| A reaction: This is on the first page of an introduction to the next stage, which is to include modal notions like 'must' and 'possibly'. |
| 7798 | There are three axiom schemas for propositional logic [Girle] |
| Full Idea: The axioms of propositional logic are: A→(B→A); A→(B→C)→(A→B)→(A→C) ; and (¬A→¬B)→(B→A). | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |
| Full Idea: The operators of propositional logic are defined as follows: 'or' (v) is not-A implies B; 'and' (ampersand) is not A-implies-not-B; and 'identity' (three line equals) is A-implies-B and B-implies-A. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle] |
| Full Idea: An axiom system for a logic contains three elements: a set of axioms; a set of inference rules; and definitions for proofs and theorems. There are also definitions for the derivation of conclusions from sets of premises. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7794 | There are seven modalities in S4, each with its negation [Girle] |
| Full Idea: In S4 there are fourteen modalities: no-operator; necessarily; possibly; necessarily-possibly; possibly-necessarily; necessarily-possibly-necessarily; and possibly-necessarily-possibly (each with its negation). | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.5) | |
| A reaction: This is said to be 'more complex' than S5, but also 'weaker'. |
| 7793 | ◊p → □◊p is the hallmark of S5 [Girle] |
| Full Idea: The critical formula that distinguishes S5 from all others is: ◊p → □◊p. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.3) | |
| A reaction: If it is possible that it is raining, then it is necessary that it is possible that it is raining. But if it is possible in this world, how can that possibility be necessary in all possible worlds? |
| 7795 | S5 has just six modalities, and all strings can be reduced to those [Girle] |
| Full Idea: In S5 there are six modalities: no-operator; necessarily; and possibly (and their negations). In any sequence of operators we may delete all but the last to gain an equivalent formula. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.5) | |
| A reaction: Such drastic simplification seems attractive. Is there really no difference, though, between 'necessarily-possibly', 'possibly-possibly' and just 'possibly'? Could p be contingently possible in this world, and necessarily possible in another? |
| 7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
| Full Idea: In possible worlds logics a statement is true-in-a-world rather than just true. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.1) | |
| A reaction: This sounds relativist, but I don't think it is. It is the facts which change, not the concept of truth. So 'donkeys can talk' may be true in a world, but not in the actual one. |
| 7788 | Modal logic has four basic modal negation equivalences [Girle] |
| Full Idea: The four important logical equivalences in modal logic (the Modal Negation equivalences) are: ¬◊p↔□¬p, ◊¬p↔¬□p, □p↔¬◊¬p, and ◊p↔¬□¬p. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.2) | |
| A reaction: [Possibly is written as a diamond, necessarily a square] These are parallel to a set of equivalences between quantifiers in predicate logic. They are called the four 'modal negation (MN) equivalences'. |
| 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |
| Full Idea: Modal logics were, for a long time, studied in terms of axiom systems. The advent of possible worlds semantics made it possible to study them in a semantic way as well. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| Full Idea: Necessary implication is often called 'strict implication'. The sort of strict implication found in valid arguments, where the conjunction of the premises necessarily implies the conclusion, is often called 'entailment'. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.2) | |
| A reaction: These are basic concept for all logic. |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| Full Idea: The truth trees method for establishing the validity of arguments and formulas is easy to use, and has the advantage that if an argument or formula is not valid, then a counter-example can be retrieved from the tree. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.4) |
| 6262 | We lack some sense or other, and hence objects may have hidden features [Montaigne] |
| Full Idea: We may all lack some sense or other; because of that defect, most of the features of objects may be concealed from us. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0666) | |
| A reaction: This strikes me as simple, straightforward common sense, and right. I cannot make sense of the claim that reality really is just the way it appears. We do not have a built-in neutrino detector, for example. |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| Full Idea: It has been customary to see analytic truths as dividing into the logically necessary and the conceptually necessary. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 7.3) | |
| A reaction: I suspect that this neglected distinction is important in discussions of Quine's elimination of the analytic/synthetic distinction. Was Quine too influenced by what is logically necessary, which might shift with a change of axioms? |
| 7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
| Full Idea: Qualified modalities seem to form a hierarchy, if we say that 'the possibility that there might be no hunger' is possible logically, theoretically, physically, economically, and humanly. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 7.3) | |
| A reaction: Girle also mentions conceptual possibility. I take 'physically' to be the same as 'naturally'. I would take 'metaphysically' possible to equate to 'theoretically' rather than 'logically'. Almost anything might be logically possible, with bizarre logic. |
| 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
| Full Idea: When one world generates another then it has 'access' to the world it generated. The accessibility relation between worlds is very important in possible worlds semantics. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.2) | |
| A reaction: This invites the obvious question what is meant by 'generates'. |
| 6260 | Sceptics say there is truth, but no means of making or testing lasting judgements [Montaigne] |
| Full Idea: Pyrrhonians say that truth and falsehood exist; within us we have means of looking for them, but not of making any lasting judgements: we have no touchstone. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0564) | |
| A reaction: This states the key difference between sceptics and relativists. The latter are more extreme as they say there is no such thing as truth. The former concede truth, and their scepticism is about the abilities of human beings. I am an anti-relativist. |
| 6261 | The soul is in the brain, as shown by head injuries [Montaigne] |
| Full Idea: The seat of the powers of the soul is in the brain, as is clearly shown by the fact that wounds and accidents affecting the head immediately harm the faculties of the soul. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0614) | |
| A reaction: At last someone has finally got the facts clear. It seems surprising that the Greeks never clearly grasped this piece of irrefutable evidence - even those Greeks who speculated that the brain was the key. Here we have a fixed fact of philosophy of mind. |
| 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'). |