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) |
| 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) |
| 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'. |
| 6237 | Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury] |
| Full Idea: Conscience is to find horribly offensive the reflection of any unjust action or behaviour; to have awe and terror of the Deity, does not, of itself, imply conscience; …thus religious conscience supposes moral or natural conscience. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], II.II.I) | |
| A reaction: The reply from religion would be that the Deity has implanted natural conscience in each creature, though this seems to deny our freedom of moral judgment. Personally I am inclined to think that values are just observations of the world - such as health. |
| 6234 | If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury] |
| Full Idea: If a creature wanting reason has many good qualities and affections, it is certain that if you give this creature a reflecting faculty, it will at the same instant approve of gratitude, kindness and pity. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], I.III.III) | |
| A reaction: A wonderful denunciation of the authority of reason, which must have influenced David Hume. I think, though, that the inverse of this case must be considered (if suddenly given feelings, they would fall in line with reasoning). We reason about feelings. |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
| Full Idea: Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted. | |
| From: Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5 | |
| A reaction: A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763. |
| 6233 | A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury] |
| Full Idea: We do not say that he is a good man when, having his hands tied up, he is hindered from doing the mischief he designs; …hence it is by affection merely that a creature is esteemed good or ill, natural or unnatural. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], I.II.I) | |
| A reaction: Note that he more or less equates being morally 'ill' with being 'unnatural'. We tend to reserve 'unnatural' for extreme or perverse crimes. Personally I would place more emphasis on evil judgements, and less on evil feelings. |
| 6236 | People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury] |
| Full Idea: How much the social pleasures are superior to any other may be known by visible tokens and effects; the marks and signs which attend this sort of joy are more intense and clear than those which attend the satisfaction of thirst and hunger. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], II.II.I) | |
| A reaction: He presumably refers to smiles and laughter, but they could be misleading as they are partly a means of social communication. You should ask people whether they would prefer a nice conversation or a good pork chop. Nice point, though. |
| 6235 | Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury] |
| Full Idea: Though no creature can be called good merely for possessing the self-preserving affections, it is impossible that public good can be preserved without them; so that a creature wanting in them is wanting in natural rectitude, and may be esteemed vicious. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], II.I.III) | |
| A reaction: Aristotle held a similar view (Idea 92). I think maybe Shaftesbury was the last call of the Aristotelians, before being engulfed by utilitarians and Kantians. This idea is at the core of capitalism. |
| 6232 | Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury] |
| Full Idea: We know there is a right and a wrong state of every creature; and that his right one is by nature forwarded, and by himself affectionately sought. There being therefore in every creature a certain interest or good; there must also be a natural end. | |
| From: 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699], I.II.I) | |
| A reaction: This is an early modern statement of Aristotelian teleology, just at the point where it was falling out of fashion. The underlying concept is that of right function. I agree with Shaftesbury, but you can't stop someone damaging their health. |
| 5642 | For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton] |
| Full Idea: Shaftesbury argued that no morality could be founded in religious obedience, or piety. On the contrary, a man is motivated to such obedience only because conscience tells him that the divine being is worthy of it. | |
| From: report of 3rd Earl of Shaftesbury (Inquiry Concerning Virtue or Merit [1699]) by Roger Scruton - Short History of Modern Philosophy Ch.8 | |
| A reaction: This seems to me a good argument. The only alternative is that we are brought to God by a conscience which was planted in us by God, but then how would you know you were being obedient to the right hypnotist? |