31 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) |
| 23708 | Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG] |
| Full Idea: The Humean view says properties are 'quiddities', which individuates properties by nothing more than their distinctness from one another, so that dispositions are not essential to them, and there is no limit to possible property recombination. | |
| From: report of Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.1) by PG - Db (ideas) | |
| A reaction: [my summary] All of this is implied by Hume, rather than stated. David Lewis supports this view. The theory of basic powers is the view's main opponent. This quidditist view is not found in physics, where a property's modal profile matters. |
| 23709 | Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye] |
| Full Idea: Dispositions constitute the essences of properties, and hence the identity of a property is not primitive ('quidditism'), but is given in terms of its dispositional relations to other properties. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.1) | |
| A reaction: I like the picture that powers are basic, giving rise to dispositions, which combine to produce qualitative and active properties. Powers are precise and relatively few, and properties are ill-defined and very numerous. Being 'influential', for example. |
| 23707 | Powers are properties which necessitate dispositions [Friend/Kimpton-Nye] |
| Full Idea: In broad terms: powers are properties that necessitate dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.2) | |
| A reaction: If powers are properties then they must be properties 'of' something, which then seems to be more fundamental than the powers. Maybe our concept of an electron helps, which seems to be a bundle of a few properties, but no one even asks 'of' what. |
| 23714 | Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye] |
| Full Idea: Dispositional essentialism yields the view that just fundamental properties and some evolved macro properties are powers. The grounding view, by contrast, seems to yield the result that all properties are powers. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.7) | |
| A reaction: For the second view, Mumford (for example) claims that the sphericity of a ball is a power, but that seems to miss the whole motivation for the powers ontology, which offers a fairly fundamental explanation of laws and modality. |
| 23711 | A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye] |
| Full Idea: In the 'dispositional essentialist' account (the main view) …what it is to be a power is to be a property whose essence is exhaustively constituted by dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.4) | |
| A reaction: [compressed] Sounds wrong to me. A very complex property (such as 'stormy' weather) could be nothing more than a large bundle of dispositions, but that wouldn't make it a 'power', which has to be simpler and more basic. |
| 23712 | Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye] |
| Full Idea: In the 'grounding' view of powers …powers are qualitative, because their essence can be specified independently of any dispositions or relations, but they fully ground dispositions. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.4) | |
| A reaction: [compressed] They give this as the rival view to dispositional essentialism. It may be a mistake to call a power a property (which needs to be 'of' something). Not sure how powers can be both fundamental and qualitative. Don't they also ground qualities? |
| 23698 | Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye] |
| Full Idea: The three platitudes about dispositions are that 1) they are directed towards some specific behaviour, 2) they can be triggered under specific conditions, and 3) their directedness is modal, meaning not 'when it is triggered' but 'it it were triggered'. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.1.1) | |
| A reaction: [PG summary] This is the preliminary to an attempt at a precise formal analysis, covering a number of hypothetical problem cases. 3) is the counterfactual rather than material conditional. Seems accurate. |
| 23699 | 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye] |
| Full Idea: A disposition is 'masked' when it fails to manifest due to interference, such as a fragile vase packed in bubble wrap, or an antidote taken after some poison. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.1) | |
| A reaction: [compressed] The easiest account of these would be to say that the stimulus or trigger of the disposition never completely occurs. Poisons are only disposed to kill when they are fully ingested. Bubble wrapped vases can't be properly struck. |
| 23700 | A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye] |
| Full Idea: A disposition is subject to 'altering' when the stimulus of the disposition influences whether (and to what degree) an object has that disposition. Either a live wire goes dead when it is touched, or a dead wire has a sensor making it live when touched. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.2) | |
| A reaction: The word 'fink' is used of such interference. Not much of a problem, I would say, because at the moment when the stimulus comes to do its job, there is no longer a disposition for it to trigger. No different from switching off a light. |
| 23701 | A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye] |
| Full Idea: A disposition is 'mimicked' by objects without that disposition which behave as though they do have it. Styrofoam plates are not fragile, but make a horrible sound when stressed, causing some annoyed person to break them. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.3) | |
| A reaction: A rather strained example! It shouldn't be a problem if the same cause (stress) leads to the same effect (breaking), but by a different path which is not the same as fragility. A formal analysis must obviously cover this case. |
| 23702 | A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye] |
| Full Idea: A 'trick' can behave like a disposition, as when someone says 'abracadabra' over a hot cup of coffee, stimulating it (?) to gradually cool down. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.2.4) | |
| A reaction: This is like Humean constant conjunction which is obviously not a cause, such as night following day. Only a problem is this cup of coffee is seen in isolation from all other cups of coffee. Post hoc propter hoc does not apply to all stimuli! |
| 23703 | Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye] |
| Full Idea: Some dispositions, such as loquaciousness or irascibility, are disposed to manifest whether they are provoked to do so. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.3.3) | |
| A reaction: We might surmise that such people have internal triggers that get them going, rather than overt ones. The Sun has a disposition to shine, without an external stimulus. The theory of powers says nature is active, rather than being disposed to activity. |
| 23704 | We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye] |
| Full Idea: We might abandon the relational analysis of dispositions (as stimulus-effect), and just say a disposition is a 'possibility', which simply can manifest, however that manifestation comes about. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 2.3.5) | |
| A reaction: [Compressed. He particularly cites Barbara Vetter] A mere 'possibility' seems to cover passive states as well as potentially active ones. A cushion can be dented, but I wouldn't say it was 'disposed' to dent. Radioactive decay is a disposition, though. |
| 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'. |
| 23710 | Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye] |
| Full Idea: Dispositionalism does not 'outsource' modality to other possible worlds, it roots modality in the powers of concrete individuals in this world. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.3.3) | |
| A reaction: Possible worlds are to abolish modality, by treating it as the non-modal facts of different worlds. I see the dispositional view as vastly superior, because the world is awash with vivid and undeniable potentialities, and one world is better ontology. |
| 23706 | Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye] |
| Full Idea: Hume's Dictum says there are no necessary connections between existences, …and also between the distinct properties that individuals instantiate. …It follows that an object's property of mass and its disposition to warp space-time could come apart. | |
| From: Friend/Kimpton-Nye (Dispositions and Powers [2023], 3.2) | |
| A reaction: [compressed] This nicely pinpoints the heart of the Humean view, to which scientific essentialists and fans of powers in nature object. The objectors include me. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |