89 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| Full Idea: Anaximander was the first to produce a philosophical book (later conventionally titled 'On Nature'), if not the first to produce a book at all. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by István Bodnár - Anaximander | |
| A reaction: Wow! Presumably there were Egyptian 'books', but this still sounds like a stupendous claim to fame. |
| 10468 | A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver] |
| Full Idea: A metaphysical theory hs two parts: ontology and ideology. The ontology consists of the entities which the theory says exist; the ideology consists of the ideas which are expressed within the theory using predicates. Ideology sorts into categories. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §02.1) | |
| A reaction: Say 'what there is', and 'what we can say about it'. The modern notion remains controversial (see Ladyman and Ross, for example), so it is as well to start crystalising what metaphysics is. I am enthusiastic, but nervous about what is being said. |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| Full Idea: Something which is established in the centre and has equality in relation to the extremes has no more reason to move up than it has down or to the sides (so the earth is stationary) | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A26) by Aristotle - On the Heavens 295b11 |
| 10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
| Full Idea: One might give Ockham's Razor a bit more content by advising belief in only those entities which are causally efficacious. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
| A reaction: He cites Armstrong as taking this line, but I immediately think of Shoemaker's account of properties. It seems to me to be the only account which will separate properties from predicates, and bring them under common sense control. |
| 10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
| Full Idea: The definition of truth-makers entails that a truth-maker for a given necessary truth is equally a truth-maker for every other necessary truth. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §24) | |
| A reaction: Maybe we could accept this. Necessary truths concern the way things have to be, so all realities will embody them. Are we to say that nothing makes a necessary truth true? |
| 10750 | Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver] |
| Full Idea: Slingshot Argument: if truth-makers work for equivalent sentences and co-referring substitute sentences, then if 'the numbers + S1 = the numbers' has a truth-maker, then 'the numbers + S2 = the numbers' will have the same truth-maker. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §24) | |
| A reaction: [compressed] Hence every sentence has the same truth-maker! Truth-maker fans must challenge one of the premises. |
| 9535 | 'Contradictory' propositions always differ in truth-value [Lemmon] |
| Full Idea: Two propositions are 'contradictory' if they are never both true and never both false either, which means that ¬(A↔B) is a tautology. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9509 | That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon] |
| Full Idea: If P and Q are any two propositions, the proposition that both P and Q is called the 'conjunction' of P and Q, and is written P∧Q. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.3) | |
| A reaction: [I use the more fashionable inverted-v '∧', rather than Lemmon's '&', which no longer seems to be used] P∧Q can also be defined as ¬(¬P∨¬Q) |
| 9508 | The sign |- may be read as 'therefore' [Lemmon] |
| Full Idea: I introduce the sign |- to mean 'we may validly conclude'. To call it the 'assertion sign' is misleading. It may conveniently be read as 'therefore'. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.2) | |
| A reaction: [Actually no gap between the vertical and horizontal strokes of the sign] As well as meaning 'assertion', it may also mean 'it is a theorem that' (with no proof shown). |
| 9511 | We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon] |
| Full Idea: We write 'if P then Q' as P→Q. This is called a 'conditional', with P as its 'antecedent', and Q as its 'consequent'. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.2) | |
| A reaction: P→Q can also be written as ¬P∨Q. |
| 9510 | That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon] |
| Full Idea: If P and Q are any two propositions, the proposition that either P or Q is called the 'disjunction' of P and Q, and is written P∨Q. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.3) | |
| A reaction: This is inclusive-or (meaning 'P, or Q, or both'), and not exlusive-or (Boolean XOR), which means 'P, or Q, but not both'. The ∨ sign is sometimes called 'vel' (Latin). |
| 9512 | We write the 'negation' of P (not-P) as ¬ [Lemmon] |
| Full Idea: We write 'not-P' as ¬P. This is called the 'negation' of P. The 'double negation' of P (not not-P) would be written as ¬¬P. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.2) | |
| A reaction: Lemmons use of -P is no longer in use for 'not'. A tilde sign (squiggle) is also used for 'not', but some interpreters give that a subtly different meaning (involving vagueness). The sign ¬ is sometimes called 'hook' or 'corner'. |
| 9513 | We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon] |
| Full Idea: We write 'P if and only if Q' as P↔Q. It is called the 'biconditional', often abbreviate in writing as 'iff'. It also says that P is both sufficient and necessary for Q, and may be written out in full as (P→Q)∧(Q→P). | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.4) | |
| A reaction: If this symbol is found in a sequence, the first move in a proof is to expand it to the full version. |
| 9514 | If A and B are 'interderivable' from one another we may write A -||- B [Lemmon] |
| Full Idea: If we say that A and B are 'interderivable' from one another (that is, A |- B and B |- A), then we may write A -||- B. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9516 | A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon] |
| Full Idea: A 'well-formed formula' of the propositional calculus is a sequence of symbols which follows the rules for variables, ¬, →, ∧, ∨, and ↔. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.1) |
| 9517 | The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon] |
| Full Idea: The 'scope' of a connective in a certain formula is the formulae linked by the connective, together with the connective itself and the (theoretically) encircling brackets | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.1) |
| 9534 | Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon] |
| Full Idea: Two propositions are 'equivalent' if whenever A is true B is true, and whenever B is true A is true, in which case A↔B is a tautology. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9530 | A wff is 'contingent' if produces at least one T and at least one F [Lemmon] |
| Full Idea: If a well-formed formula of propositional calculus takes at least one T and at least one F for all the assignments of truth-values to its variables, it is said to be 'contingent'. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9532 | 'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon] |
| Full Idea: If A and B are expressible in propositional calculus notation, they are 'subcontrary' if they are never both false, which may be tested by the truth-table for A∨B, which is a tautology if they are subcontrary. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9533 | A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon] |
| Full Idea: One proposition A 'implies' a proposition B if whenever A is true B is true (but not necessarily conversely), which is only the case if A→B is tautologous. Hence B 'is implied' by A. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9528 | A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon] |
| Full Idea: If a well-formed formula of propositional calculus takes the value T for all possible assignments of truth-values to its variables, it is said to be a 'tautology'. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9518 | A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon] |
| Full Idea: A 'theorem' of logic is the conclusion of a provable sequent in which the number of assumptions is zero. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
| A reaction: This is what Quine and others call a 'logical truth'. |
| 9519 | A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon] |
| Full Idea: A 'substitution-instance' is a wff which results by replacing one or more variables throughout with the same wffs (the same wff replacing each variable). | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
| 9529 | A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon] |
| Full Idea: If a well-formed formula of propositional calculus takes the value F for all possible assignments of truth-values to its variables, it is said to be 'inconsistent'. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9531 | 'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon] |
| Full Idea: If A and B are expressible in propositional calculus notation, they are 'contrary' if they are never both true, which may be tested by the truth-table for ¬(A∧B), which is a tautology if they are contrary. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.3) |
| 9396 | DN: Given A, we may derive ¬¬A [Lemmon] |
| Full Idea: Double Negation (DN): Given A, we may derive ¬¬A as a conclusion, and vice versa. The conclusion depends on the assumptions of the premiss. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9393 | A: we may assume any proposition at any stage [Lemmon] |
| Full Idea: Assumptions (A): any proposition may be introduced at any stage of a proof. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9399 | ∧E: Given A∧B, we may derive either A or B separately [Lemmon] |
| Full Idea: And-Elimination (∧E): Given A∧B, we may derive either A or B separately. The conclusions will depend on the assumptions of the premiss. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9402 | RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon] |
| Full Idea: Reduction ad Absurdum (RAA): Given a proof of B∧¬B from A as assumption, we may derive ¬A as conclusion, depending on the remaining assumptions (if any). | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9395 | MTT: Given ¬B and A→B, we derive ¬A [Lemmon] |
| Full Idea: Modus Tollendo Tollens (MTT): Given ¬B and A→B, we derive ¬A as a conclusion. ¬A depends on any assumptions that have been made | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9400 | ∨I: Given either A or B separately, we may derive A∨B [Lemmon] |
| Full Idea: Or-Introduction (∨I): Given either A or B separately, we may derive A∨B as conclusion. This depends on the assumption of the premisses. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9401 | ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon] |
| Full Idea: Or-Elimination (∨E): Given A∨B, we may derive C if it is proved from A as assumption and from B as assumption. This will also depend on prior assumptions. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9398 | ∧I: Given A and B, we may derive A∧B [Lemmon] |
| Full Idea: And-Introduction (&I): Given A and B, we may derive A∧B as conclusion. This depends on their previous assumptions. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9397 | CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon] |
| Full Idea: Conditional Proof (CP): Given a proof of B from A as assumption, we may derive A→B as conclusion, on the remaining assumptions (if any). | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9394 | MPP: Given A and A→B, we may derive B [Lemmon] |
| Full Idea: Modus Ponendo Ponens (MPP): Given A and A→B, we may derive B as a conclusion. B will rest on any assumptions that have been made. | |
| From: E.J. Lemmon (Beginning Logic [1965], 1.5) |
| 9521 | 'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon] |
| Full Idea: 'Modus tollendo ponens' (MTP) says that if a disjunction holds and also the negation of one of its disjuncts, then the other disjunct holds. Thus ¬P, P ∨ Q |- Q may be introduced as a theorem. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
| A reaction: Unlike Modus Ponens and Modus Tollens, this is a derived rule. |
| 9522 | 'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon] |
| Full Idea: 'Modus ponendo tollens' (MPT) says that if the negation of a conjunction holds and also one of its conjuncts, then the negation of the other conjunct holds. Thus P, ¬(P ∧ Q) |- ¬Q may be introduced as a theorem. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
| A reaction: Unlike Modus Ponens and Modus Tollens, this is a derived rule. |
| 9525 | We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon] |
| Full Idea: The proof that P→Q -||- ¬(P ∧ ¬Q) is useful for enabling us to change conditionals into negated conjunctions | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
| 9524 | We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon] |
| Full Idea: The proof that P→Q -||- ¬P ∨ Q is useful for enabling us to change conditionals into disjunctions. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
| 9523 | De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon] |
| Full Idea: The forms of De Morgan's Laws [P∨Q -||- ¬(¬P ∧ ¬Q); ¬(P∨Q) -||- ¬P ∧ ¬Q; ¬(P∧Q) -||- ¬P ∨ ¬Q); P∧Q -||- ¬(¬P∨¬Q)] transform negated conjunctions and disjunctions into non-negated disjunctions and conjunctions respectively. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
| 9527 | The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon] |
| Full Idea: The Distributive Laws say that P ∧ (Q∨R) -||- (P∧Q) ∨ (P∧R), and that P ∨ (Q∨R) -||- (P∨Q) ∧ (P∨R) | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
| 9526 | We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon] |
| Full Idea: The proof that P∧Q -||- ¬(P → ¬Q) is useful for enabling us to change conjunctions into negated conditionals. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) |
| 9537 | Truth-tables are good for showing invalidity [Lemmon] |
| Full Idea: The truth-table approach enables us to show the invalidity of argument-patterns, as well as their validity. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.4) |
| 9538 | A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon] |
| Full Idea: A truth-table test is entirely mechanical, ..and in propositional logic we can even generate proofs mechanically for tautological sequences, ..but this mechanical approach breaks down with predicate calculus, and proof-discovery is an imaginative process. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.5) |
| 9536 | If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon] |
| Full Idea: If any application of the nine derivation rules of propositional logic is made on tautologous sequents, we have demonstrated that the result is always a tautologous sequent. Thus the system is consistent. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.4) | |
| A reaction: The term 'sound' tends to be used now, rather than 'consistent'. See Lemmon for the proofs of each of the nine rules. |
| 9539 | Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon] |
| Full Idea: A logical system is complete is all expressions of a specified kind are derivable in it. If we specify tautologous sequent-expressions, then propositional logic is complete, because we can show that all tautologous sequents are derivable. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.5) | |
| A reaction: [See Lemmon 2.5 for details of the proofs] |
| 13909 | Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon] |
| Full Idea: Just as '(∀x)(...)' is to mean 'take any x: then....', so we write '(∃x)(...)' to mean 'there is an x such that....' | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.1) | |
| A reaction: [Actually Lemmon gives the universal quantifier symbol as '(x)', but the inverted A ('∀') seems to have replaced it these days] |
| 13902 | 'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon] |
| Full Idea: A predicate letter followed by one name expresses a property ('Gm'), and a predicate-letter followed by two names expresses a relation ('Pmn'). We could write 'Pmno' for a complex relation like betweenness. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.1) |
| 13911 | The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon] |
| Full Idea: I define a 'symbol' (of the predicate calculus) as either a bracket or a logical connective or a term or an individual variable or a predicate-letter or reverse-E (∃). | |
| From: E.J. Lemmon (Beginning Logic [1965], 4.1) |
| 13910 | Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon] |
| Full Idea: Quantifier-notation might be thus: first, render into sentences about 'properties', and use 'predicate-letters' for them; second, introduce 'variables'; third, introduce propositional logic 'connectives' and 'quantifiers'. Plus letters for 'proper names'. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.1) |
| 13904 | Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon] |
| Full Idea: Our rule of universal quantifier elimination (UE) lets us infer that any particular object has F from the premiss that all things have F. It is a natural extension of &E (and-elimination), as universal propositions generally affirm a complex conjunction. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.2) |
| 13906 | With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon] |
| Full Idea: If there are just three objects and each has F, then by an extension of &I we are sure everything has F. This is of no avail, however, if our universe is infinitely large or if not all objects have names. We need a new device, Universal Introduction, UI. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.2) |
| 13908 | UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon] |
| Full Idea: Univ Elim UE - if everything is F, then something is F; Univ Intro UI - if an arbitrary thing is F, everything is F; Exist Intro EI - if an arbitrary thing is F, something is F; Exist Elim EE - if a proof needed an object, there is one. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.3) | |
| A reaction: [My summary of Lemmon's four main rules for predicate calculus] This is the natural deduction approach, of trying to present the logic entirely in terms of introduction and elimination rules. See Bostock on that. |
| 13901 | Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon] |
| Full Idea: In predicate calculus we take over the propositional connectives and propositional variables - but we need additional rules for handling quantifiers: four rules, an introduction and elimination rule for the universal and existential quantifiers. | |
| From: E.J. Lemmon (Beginning Logic [1965]) | |
| A reaction: This is Lemmon's natural deduction approach (invented by Gentzen), which is largely built on introduction and elimination rules. |
| 13903 | Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon] |
| Full Idea: The elimination rule for the universal quantifier concerns the use of a universal proposition as a premiss to establish some conclusion, whilst the introduction rule concerns what is required by way of a premiss for a universal proposition as conclusion. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.2) | |
| A reaction: So if you start with the universal, you need to eliminate it, and if you start without it you need to introduce it. |
| 13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
| Full Idea: If all objects in a given universe had names which we knew and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex conjunction. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.2) |
| 13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
| Full Idea: It is a common mistake to render 'some Frenchmen are generous' by (∃x)(Fx→Gx) rather than the correct (∃x)(Fx&Gx). 'All Frenchmen are generous' is properly rendered by a conditional, and true if there are no Frenchmen. | |
| From: E.J. Lemmon (Beginning Logic [1965], 3.1) | |
| A reaction: The existential quantifier implies the existence of an x, but the universal quantifier does not. |
| 9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
| Full Idea: The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q. That is, since Napoleon was French, then if the moon is blue then Napoleon was French; and since Napoleon was not Chinese, then if Napoleon was Chinese, the moon is blue. | |
| From: E.J. Lemmon (Beginning Logic [1965], 2.2) | |
| A reaction: This is why the symbol → does not really mean the 'if...then' of ordinary English. Russell named it 'material implication' to show that it was a distinctively logical operator. |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| Full Idea: Anaximander discovers the contradictory character of our world: it perishes from its own qualities. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Friedrich Nietzsche - Unpublished Notebooks 1872-74 19 [239] | |
| A reaction: A lovely gloss on Anaximander, though I am not sure that I understand what Nietzsche means. |
| 10747 | Accepting properties by ontological commitment tells you very little about them [Oliver] |
| Full Idea: The route to the existence of properties via ontological commitment provides little information about what properties are like. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §22) | |
| A reaction: NIce point, and rather important, I would say. I could hardly be committed to something for the sole reason that I had expressed a statement which contained an ontological commitment. Start from the reason for making the statement. |
| 10748 | Reference is not the only way for a predicate to have ontological commitment [Oliver] |
| Full Idea: For a predicate to have a referential function is one way, but not the only way, to harbour ontological commitment. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §22) | |
| A reaction: Presumably the main idea is that the predicate makes some important contribution to a sentence which is held to be true. Maybe reference is achieved by the whole sentence, rather than by one bit of it. |
| 10719 | There are four conditions defining the relations between particulars and properties [Oliver] |
| Full Idea: Four adequacy conditions for particulars and properties: asymmetry of instantiation; different particulars can have the same property; particulars can have many properties; two properties can be instantiated by the same particulars. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
| A reaction: The distinction between particulars and universals has been challenged (e.g. by Ramsey and MacBride). There are difficulties in the notion of 'instantiation', and in the notion of two properties being 'the same'. |
| 10721 | If properties are sui generis, are they abstract or concrete? [Oliver] |
| Full Idea: If properties are sui generis entities, one must decide whether they are abstract or concrete. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
| A reaction: A nice basic question! I take the real properties to be concrete, but we abstract from them, especially from their similarities, and then become deeply confused about the ontology, because our language doesn't mark the distinctions clearly. |
| 10716 | There are just as many properties as the laws require [Oliver] |
| Full Idea: One conception of properties says there are only as many properties as are needed to be constituents of laws. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
| A reaction: I take this view to the be precise opposite of the real situation. The properties are what lead to the laws. Properties are internal to nature, and laws are imposed from outside, which is ridiculous unless you think there is an active deity. |
| 10720 | We have four options, depending whether particulars and properties are sui generis or constructions [Oliver] |
| Full Idea: Both properties and particulars can be taken as either sui generis or as constructions, so we have four options: both sui generis, or both constructions, or one of each. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
| A reaction: I think I favour both being sui generis. God didn't make the objects, then add their properties, or make the properties then create some instantiations. There can't be objects without properties, or objectless properties (except in thought). |
| 10714 | The expressions with properties as their meanings are predicates and abstract singular terms [Oliver] |
| Full Idea: The types of expressions which have properties as their meanings may vary, the chief candidates being predicates, such as '...is wise', and abstract singular terms, such as 'wisdom'. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §02) | |
| A reaction: This seems to be important, because there is too much emphasis on predicates. If this idea is correct, we need some account of what 'abstract' means, which is notoriously tricky. |
| 10715 | There are five main semantic theories for properties [Oliver] |
| Full Idea: Properties in semantic theory: functions from worlds to extensions ('Californian'), reference, as opposed to sense, of predicates (Frege), reference to universals (Russell), reference to situations (Barwise/Perry), and composition from context (Lewis). | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §02 n12) | |
| A reaction: [compressed; 'Californian' refers to Carnap and Montague; the Lewis view is p,67 of Oliver]. Frege misses out singular terms, or tries to paraphrase them away. Barwise and Perry sound promising to me. Situations involve powers. |
| 10738 | Tropes are not properties, since they can't be instantiated twice [Oliver] |
| Full Idea: I rule that tropes are not properties, because it is not true that one and the same trope of redness is instantiated by two books. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: This seems right, but has very far-reaching implications, because it means there are no properties, and no two things have the same properties, so there can be no generalisations about properties, let alone laws. ..But they have equivalence sets. |
| 10739 | The property of redness is the maximal set of the tropes of exactly similar redness [Oliver] |
| Full Idea: Using the predicate '...is exactly similar to...' we can sort tropes into equivalence sets, these sets serving as properties and relations. For example, the property of redness is the maximal set of the tropes of redness. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: You have somehow to get from scarlet and vermilion, which have exact similarity within their sets, to redness, which doesn't. |
| 10740 | The orthodox view does not allow for uninstantiated tropes [Oliver] |
| Full Idea: It is usual to hold an aristotelian conception of tropes, according to which tropes are present in their particular instances, and which does not allow for uninstantiated tropes. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: What are you discussing when you ask what colour the wall should be painted? Presumably we can imagine non-existent tropes. If I vividly imagine my wall looking yellow, have I brought anything into existence? |
| 10741 | Maybe concrete particulars are mereological wholes of abstract particulars [Oliver] |
| Full Idea: Some trope theorists give accounts of particulars. Sets of tropes will not do because they are always abstract, but we might say that particulars are (concrete) mereological wholes of the tropes which they instantiate. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: Looks like a non-starter to me. How can abstract entities add up to a mereological whole which is concrete? |
| 10742 | Tropes can overlap, and shouldn't be splittable into parts [Oliver] |
| Full Idea: More than one trope can occupy the same place at the same time, and a trope occupies a place without having parts which occupy parts of the place. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
| A reaction: This is the general question of the size of a spatial trope, or 'how many red tropes in a tin of red paint?' |
| 10472 | 'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver] |
| Full Idea: The 'structural universals' methane and butane are each made up of the same universals, carbon and hydrogen. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §07) | |
| A reaction: He cites Lewis 1986, who is criticising Armstrong. If you insist on having universals, they might (in this case) best be described as 'patterns', which would be useful for structuralism in mathematics. They reduce to relations. |
| 10724 | Located universals are wholly present in many places, and two can be in the same place [Oliver] |
| Full Idea: So-called aristotelian universals have some queer features: one universal can be wholly present at different places at the same time, and two universals can occupy the same place at the same time. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: If you want to make a metaphysical doctrine look ridiculous, stating it in very simple language will often do the job. Belief in fairies is more plausible than the first of these two claims. |
| 7963 | Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver] |
| Full Idea: Properties and relations of abstract objects may need to be acknowledged, but they would have no spatio-temporal location, so they cannot instantiate Aristotelian universals, there being nowhere for such universals to be. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11), quoted by Cynthia Macdonald - Varieties of Things | |
| A reaction: Maybe. Why can't the second-order properties be in the same location as the first-order ones? If the reply is that they would seem to be in many places at once, that is only restating the original problem of universals at a higher level. |
| 10730 | If universals ground similarities, what about uniquely instantiated universals? [Oliver] |
| Full Idea: If universals are to ground similarities, it is hard to see why one should admit universals which only happen to be instantiated once. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: He is criticising Armstrong, who holds that universals must be instantiated. This is a good point about any metaphysics which makes resemblance basic. |
| 10727 | Uninstantiated universals seem to exist if they themselves have properties [Oliver] |
| Full Idea: We may have to accept uninstantiated universals because the properties and relations of abstract objects may need to be acknowledged. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: This is the problem of 'abstract reference'. 'Courage matters more than kindness'; 'Pink is more like red than like yellow'. Not an impressive argument. All you need is second-level abstraction. |
| 7962 | Uninstantiated properties are useful in philosophy [Oliver] |
| Full Idea: Uninstantiated properties and relations may do some useful philosophical work. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11), quoted by Cynthia Macdonald - Varieties of Things | |
| A reaction: Their value isn't just philosophical; hopes and speculations depend on them. This doesn't make universals mind-independent. I think the secret is a clear understanding of the word 'abstract' (which I don't have). |
| 10722 | Instantiation is set-membership [Oliver] |
| Full Idea: One view of instantiation is that it is the set-membership predicate. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §10) | |
| A reaction: This cuts the Gordian knot rather nicely, but I don't like it, if the view of sets is extensional. We need to account for natural properties, and we need to exclude mere 'categorial' properties. |
| 10744 | Nominalism can reject abstractions, or universals, or sets [Oliver] |
| Full Idea: We can say that 'Harvard-nominalism' is the thesis that there are no abstract objects, 'Oz-nominalism' that there are no universals, and Goodman's nominalism rejects entities, such as sets, which fail to obey a certain principle of composition. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §15 n46) | |
| A reaction: Personally I'm a Goodman-Harvard-Oz nominalist. What are you rebelling against? What have you got? We've been mesmerized by the workings of our own minds, which are trying to grapple with a purely physical world. |
| 10726 | Things can't be fusions of universals, because two things could then be one thing [Oliver] |
| Full Idea: If a particular thing is a bundle of located universals, we might say it is a mereological fusion of them, but if two universals can be instantiated by more than one particular, then two particulars can have the same universals, and be the same thing. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: This and Idea 10725 pretty thoroughly demolish the idea that objects could be just bundles of universals. The problem pushes some philosophers back to the idea of 'substance', or some sort of 'substratum' which has the universals. |
| 10725 | Abstract sets of universals can't be bundled to make concrete things [Oliver] |
| Full Idea: If a particular thing is a bundle of located universals, we might say that it is the set of its universals, but this won't work because the thing can be concrete but sets are abstract. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
| A reaction: This objection applies just as much to tropes (abstract particulars) as it does to universals. |
| 10745 | Science is modally committed, to disposition, causation and law [Oliver] |
| Full Idea: Natural science is up to its ears in modal notions because of its use of the concepts of disposition, causation and law. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §15) | |
| A reaction: This is aimed at Quine. It might be possible for an auster physicist to dispense with these concepts, by merely describing patterns of observed behaviour. |
| 10746 | Conceptual priority is barely intelligible [Oliver] |
| Full Idea: I find the notion of conceptual priority barely intelligible. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §19 n48) | |
| A reaction: I don't think I agree, though there is a lot of vagueness and intuition involved, and not a lot of hard argument. Can you derive A from B, but not B from A? Is A inconceivable without B, but B conceivable without A? |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| Full Idea: Anaximander said that the first principle and element of existing things was the boundless; it was he who originally introduced this name for the first principle. | |
| From: report of Anaximander (fragments/reports [c.570 BCE], A09) by Simplicius - On Aristotle's 'Physics' 9.24.14- | |
| A reaction: Simplicius is quoting Theophrastus |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| Full Idea: The essential nature, whatever it is, of the non-limited is everlasting and ageless. | |
| From: Anaximander (fragments/reports [c.570 BCE], B2), quoted by (who?) - where? |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| Full Idea: Those thinkers are in error who postulate ...a single matter, for this cannot exist without some 'perceptible contrariety': this Boundless, which they identify with the 'original real', must be either light or heavy, either hot or cold. | |
| From: comment on Anaximander (fragments/reports [c.570 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 329a10 | |
| A reaction: A dubious objection, I would say. If there has to be a contrasting cold thing to any hot thing, what happens when the cold thing is removed? |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| Full Idea: The non-limited is the original material of existing things; their source is also that to which they return after destruction, according to necessity; they give justice and make reparation to each other for injustice, according to the arrangement of Time. | |
| From: Anaximander (fragments/reports [c.570 BCE], B1), quoted by Simplicius - On Aristotle's 'Physics' 24.13- | |
| A reaction: Simplicius is quoting Theophrastus |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |
| Full Idea: The parts of all things are susceptible to change, but the whole is unchangeable. | |
| From: report of Anaximander (fragments/reports [c.570 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.An.2 |