24 ideas
| 18859 | Metaphysics is a quest for truthmakers [Tallant] |
| Full Idea: In this book I will treat metaphysics as a quest for truthmakers. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 01) | |
| A reaction: I find this appealing, though obviously you have to say what sort of truthmakers generate 'metaphysical' truths, as opposed to physics or biology. I take it that would involve truthmakers that had a high level of generality, idealisation and abstraction. |
| 18861 | Maybe number statements can be paraphrased into quantifications plus identities [Tallant] |
| Full Idea: One strategy is whenever we are presented with a sentence that might appear to entail the existence of numbers, all that we have to do is paraphrase it using a quantified logic, plus identity. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 03.5) | |
| A reaction: This nominalist strategy seems fine for manageable numbers, but gets in trouble with numbers too big to count (e.g. grains of sand in the world) , or genuine infinities. |
| 18866 | Maybe only 'positive' truths need truth-makers [Tallant] |
| Full Idea: We might say that those truths that do not need truth-makers are those that are negative. Those that do need truth-makers are those that are positive. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 10.8) | |
| A reaction: If you deny the existence of something, there is always an implicit domain for the denial, such as 'on the table', or 'in this building', or 'in the cosmos'. So why can't that domain be the truthmaker for a negative existential? |
| 18860 | A truthmaker is the minimal portion of reality that will do the job [Tallant] |
| Full Idea: A 'minimal' truth-maker is the 'smallest' portion of reality required to make a given proposition true. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 01.2) | |
| A reaction: A nice suggestion. This seems to make Ockham's Razor an integral part of the theory of truth-makers. I would apply the same principle to explanations. An Ockhamist explanation is what explains the puzzling thing - and nothing else. |
| 18863 | What is the truthmaker for a possible new power? [Tallant] |
| Full Idea: What power will make true 'there could be a power that does not in fact exist'? | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 04.13) | |
| A reaction: Nice question. We can't know whether it is true that a new power could exist, so we can't expect an actual truthmaker for it. Though we might predict new powers (such as for a new transuranic element), on the basis of the known ones. |
| 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) |
| 18864 | The wisdom of Plato and of Socrates are not the same property [Tallant] |
| Full Idea: It is not the case that Plato's wisdom = Socrates's wisdom. Platonic-wisdom and Socratic-wisdom are not the same property. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 05.4) | |
| A reaction: This seems reasonable in the case of wisdom, but not so clear in the case of indistinguishable properties of redness or squareness or mass. Nevertheless it gives nice support for trope theory. |
| 18865 | Substance must have two properties: individuation, and property-bearing [Tallant] |
| Full Idea: It appears that substance has essential properties: it is of the essence of substance that it individuates, and it is of the essence of substance that it bears properties. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 06.2) | |
| A reaction: The point being that substances are not 'bear', because they have a role to perform, and a complete blank can't fulfil a role. We can't take substance, though, seriously in ontology. It is just a label for distinct individuals. |
| 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'. |
| 3449 | If parallelism is true, how does the mind know about the body? [Crease] |
| Full Idea: In parallelism, the idea that we have a body is like an astronaut hearing shouting on the moon, and reasoning that as this is impossible he must be simultaneously imagining shouting AND there is real shouting taking place! | |
| From: Jason Crease (works [2001]), quoted by PG - Db (ideas) | |
| A reaction: This seems to capture the absurdity of Leibniz's proposal. I experience what my brain is doing, but not because my brain is doing it. I would never know if God had made a slight error in setting His two 'clocks'; their accuracy is just a pious hope. |
| 18862 | Are propositions all the thoughts and sentences that are possible? [Tallant] |
| Full Idea: One might be tempted to the view that there are as many different propositions as there are thoughts that could be thought and sentences that could be uttered. | |
| From: Jonathan Tallant (Metaphysics: an introduction [2011], 04.5.3) | |
| A reaction: A fairly orthodox view I take to be crazy. I think it is a view designed for logic, rather than for how the world is. Why tie propositions to what can be thought, and then introduce unthought propositions? Why no unthinkable propositions? |