23 ideas
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) |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
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. |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
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) |
13437 | A CAR and its major PART can become identical, yet seem to have different properties [Gallois] |
Full Idea: At t1 there is a whole CAR, and a PART of it, which is everything except the right front wheel. At t2 the wheel is removed, leaving just PART, so that CAR is now PART. But PART was a proper part of CAR, and CAR had the front wheel. Different properties! | |
From: André Gallois (Occasions of Identity [1998], 1.II) | |
A reaction: [compressed summary] The problem is generated by appealing to Leibniz's Law. My immediate reaction is that this is the sort of trouble you get into if you include such temporal truths about things as 'properties'. |
16233 | Gallois hoped to clarify identity through time, but seems to make talk of it impossible [Hawley on Gallois] |
Full Idea: A problem for Gallois is that he leaves us no way to talk about questions of genuine identity through time, and thus undercuts one motivation for his own position. | |
From: comment on André Gallois (Occasions of Identity [1998]) by Katherine Hawley - How Things Persist 5.8 | |
A reaction: Gallois seems to need a second theory of identity to support his Occasional Identity theory. Two things need an identity each, before we can say that the two identities coincide. (Time to read Gallois!) |
14755 | Gallois is committed to identity with respect to times, and denial of simple identity [Gallois, by Sider] |
Full Idea: Gallois's core claim is that the identity relation holds with respect to times, ...and he must claim that there is no such thing as the relation of identity simpliciter. | |
From: report of André Gallois (Occasions of Identity [1998]) by Theodore Sider - Four Dimensionalism 5.5 | |
A reaction: Gallois is essentially responding to the statue and clay problem, but it seems a bit drastic to entirely change our concept of two things being identical, such as Hesperus and Phosphorus. 'Identity' seems to have several meanings; let's sort them out. |
16231 | Occasional Identity: two objects can be identical at one time, and different at others [Gallois, by Hawley] |
Full Idea: Gallois' Occasional Identity Thesis is that objects can be identical at one time without being identical at all times. | |
From: report of André Gallois (Occasions of Identity [1998]) by Katherine Hawley - How Things Persist 5.4 | |
A reaction: The analogy is presumably with two crossing roads being identical at one place but not at others. It is a major misunderstanding to infer from Special Relativity that time is just like space. |
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'. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |