84 ideas
| 7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
| Full Idea: Philosophical problems are problems about how what is actual is possible, given that what is actual appears, because of some faulty argument, to be impossible. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: [She is discussing universals when she makes this comment] A very appealing remark, given that most people come into philosophy because of a mixture of wonder and puzzlement. It is a rather Wittgensteinian view, though, that we must cure our own ills. |
| 7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
| Full Idea: In 'She did it for the sake of her country' no one thinks that the expression 'the sake' refers to an individual thing, a sake. But given that, how can we work out what the ontological commitments of a theory actually are? | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.1) | |
| A reaction: For these sorts of reasons it rapidly became obvious that ordinary language analysis wasn't going to reveal much, but it is also a problem for a project like Quine's, which infers an ontology from the terms of a scientific theory. |
| 7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
| Full Idea: The fallacy of composition makes the erroneous assumption that every property of the things that constitute a thing is a property of the thing as well. But every large object is constituted by small parts, and every red object by colourless parts. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.5) | |
| A reaction: There are nice questions here like 'If you add lots of smallness together, why don't you get extreme smallness?' Colours always make bad examples in such cases (see Idea 5456). Distinctions are needed here (e.g. Idea 7007). |
| 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) |
| 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) |
| 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). |
| 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) |
| 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) |
| 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'. |
| 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) |
| 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) |
| 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) |
| 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. |
| 7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
| Full Idea: There are four kinds of reduction: the identifying of entities of two theories by means of bridge or correlation laws; the elimination of entities in favour of the other theory; reducing by bridge laws and property identities; and merely reducing talk. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3 n5) | |
| A reaction: [She gives references] The idea of 'bridge laws' I regard with caution. If bridge laws are ceteris paribus, they are not much help, and if they are strict, or necessary, then there must be an underlying reason for that, which is probably elimination. |
| 7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
| Full Idea: In statements attributing relational properties ('Felix is my favourite cat'), it seems clear that the property truly attributed to the substance is not essential to it. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: A fairly obvious point, but an important one when mapping out (cautiously) what we actually mean by 'property'. However, maybe the relational property is essential: the ceiling is ('is' of predication!) above the room. |
| 7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
| Full Idea: The relation of being taller than is an external relation, since it relates two independent material substances, but the relation of instantiation or exemplification is internal, in that it relates a substance with a property. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: An interesting revival of internal relations. To be plausible it would need clear notions of 'property' and 'substance'. We are getting a long way from physics, and I sense Ockham stropping his Razor. How do you individuate a 'relation'? |
| 7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
| Full Idea: An object's being two inches long seems to guarantee an infinite number of other properties, such as being less than three inches long. If we must understand the second property to understand the first, then there seems to be a vicious infinite regress. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: She dismisses this by saying that we don't need to know an infinity of numbers in order to count. I would say that we just need to distinguish between intrinsic and relational properties. You needn't know all a thing's relations to know the thing. |
| 7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
| Full Idea: Tropes are abstract entities, at least in the sense that more than one can be in the same place at the same time (e.g. redness and roundness). But they are not universals, because they have unique and particular locations. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: I'm uneasy about the reification involved in this kind of talk. Does a coin possess a thing called 'roundness', which then has to be individuated, identified and located? I am drawn to the two extreme views, and suspicious of compromise. |
| 7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
| Full Idea: Trope Nominalism says properties are classes or sets of exactly similar or resembling tropes, where tropes are what we might called 'property-tokens' or 'particularized properties'. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: We still seem to have the problem of 'resembling' here, and we certainly have the perennial problem of why any given particular should be placed in any particular set. See Idea 7959. |
| 7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
| Full Idea: Trope 'Nominalism' is not a version of nominalism, because tropes are abstract particulars, rather than concrete particulars. Of course, a trope account of the relations between particulars and their properties has ramifications for concrete particulars. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16) | |
| A reaction: Cf. Idea 7971. At this point the boundary between nominalist and realist theories seems to blur. Possibly that is bad news for tropes. Not many dilemmas can be solved by simply blurring the boundary. |
| 7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
| Full Idea: The problem is how a group of resembling tropes can be of the same type, that is, that they can resemble one another in the same way. This problem is not settled simply by positing tropes. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: There seems to be a fundamental fact that there is no resemblance unless the respect of resemblance is specified. Two identical objects could still said to be different because of their locations. Is resemblance natural or conventional? Consider atoms. |
| 7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
| Full Idea: Of all the nominalist solutions, Trope Nominalism is the only one that tries to solve the problem at issue by introducing entities; all the others try to get by with concrete particulars and sets of them. This might invite Ockham's Razor. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: We could reply that tropes are necessities. The issue seems to be a key one, which is whether our fundamental onotology should include properties (in some form or other). I am inclined to exclude them (Ideas 3322, 3906, 4029). |
| 7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
| Full Idea: We can distinguish between numerical identity and qualitative identity. Numerical sameness is explained by a theory of identity, but what explains qualitative sameness? | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: The distinction is between type and token identity. Tokens are particulars, and types are sets, so her question comes down to the one of what entitles something to be a member of a set? Nothing, if sets are totally conventional, but they aren't. |
| 7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
| Full Idea: The 'one over many' problem is to explain how universals can unify their instances if they are wholly other than them. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: If universals are self-predicating (beauty is beautiful) then they have a massive amount in common, despite one being general. You then have the regress problem of explaining the beauty of the beautiful. Baffling regress, or baffling participation. |
| 7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
| Full Idea: All real forms of Nominalism should hold that the only objects relevant to the explanation of generality are concrete particulars, words (i.e. word-tokens, not word-types), and perhaps sets. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6 n16) | |
| A reaction: The addition of sets seems controversial (see Idea 7970). The context is her rejection of the use of tropes in nominalist theories. I would doubt whether a theory still counted as nominalist if it admitted sets (e.g. Quine). |
| 7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
| Full Idea: Resemblance Nominalism cannot explain the fact that we know when and in what way new objects resemble old ones, and that we know when and in what ways new objects do not resemble old ones. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: It is not clear what sort of theory would be needed to 'explain' such a thing. Unless there is an explanation of resemblance waiting in the wings (beyond asserting that resemblance is a universal), then this is not a strong objection. |
| 7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
| Full Idea: The so-called 'laws of thinghood' govern particulars, saying that one thing cannot be wholly present at different places at the same time, and two things cannot occupy the same place at the same time. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.6) | |
| A reaction: Is this an empirical observation, or a tautology? Or might it even be a priori synthetic? What happens when two water drops or clouds merge? Or an amoeba fissions? In what sense is an image in two places at once? Se also Idea 2351. |
| 7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
| Full Idea: We can usefully refer to 'individuation conditions', to distinguish objects of that kind from objects not of that kind, and to 'identity conditions', to distinguish objects within that kind from one another. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: So we individuate types or sets, and identify tokens or particulars. Sounds good. Should be in every philosopher's toolkit, and on every introductory philosophy course. |
| 7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
| Full Idea: Substances have a kind of unity that mere collocations of properties do not have, namely an instrinsic unity. So substances cannot be collocations - bundles - of properties. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: A team is a unity. Compare a similar thought, Idea 1395, about personal identity. How can something which is a pure unity have more than one property? What distinguishes substances? Why can't a substance have a certain property? |
| 7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
| Full Idea: The bundle theory of substance requires unconditional commitment to the truth of the Principle of the Identity of Indiscernibles: that things that are alike with respect to all of their properties are identical. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Since the identity of indiscernibles is very dubious (see Ideas 1365, 4476, 5746, 7928), this is bad news for the bundle theory. I suspect that all of these problems arise because no one seems to have a clear concept of a property. |
| 7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
| Full Idea: Commitment to the view that only what can be an object of possible sensory experience can exist eliminates the possibility of distinguishing between substance and attribute, leaving only one alternative, namely the bundle view. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Phenomenalism strikes me as a paradigm case of confusing ontology with epistemology. Presumably physicists (even empiricist ones) are committed to the 'interior' of quarks and electrons, but no one expects to experience them. |
| 7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
| Full Idea: The bundle theory makes all true statements ascribing properties to substances uninformative, by making them logical truths. The property of being a feline animal is literally a constituent of a cat. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: The solution would seem to a distinction between accidental and essential properties. Compare 'that plane is red' with 'that plane has wings'. 'Of course it does - it's a plane'. We might still survive without a plane-substance. |
| 7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
| Full Idea: Substances are capable of persisting through change, where this involves change in properties; but the bundle theory has the consequence that substances cannot survive change. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Her example is an apple remaining an apple when it turns brown. It doesn't look, though, as if there is a precise moment when the apple-substance ceases. The end of an apple seems to be more a matter of a loss of crucial properties. |
| 7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
| Full Idea: Maybe a substance is not itself a bundle of properties, but a sum or sequence of bundles of properties, a bundle of bundles of properties (which 'perdures' rather than 'endures'). | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: There remains the problem of deciding when the bundle has drifted too far away from the original to perdure correctly. A caterpillar can turn into a butterfly (which is pretty bizarre!), but not into a cathedral. Why? She says this idea denies change. |
| 7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
| Full Idea: Because a statue and the lump of matter that constitute it have different persistence conditions, they are not identical. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.4) | |
| A reaction: Maybe being a statue is a relational property? All the relational properties of a thing will have different persistence conditions. Suppose I see a face in a bowl of sugar, and you don't? |
| 7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
| Full Idea: The three main theories of substance are the bundle theory (Leibniz, Berkeley, Hume, Ayer), the bare substratum theory (Locke and Bergmann), and the essentialist theory. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: Macdonald defends the essentialist theory. The essentialist view immediately appeals to me. Properties must be OF something, and the something must have the power to produce properties. So there. |
| 7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
| Full Idea: A rival to the bundle theory says that, for each substance, there is a constituent of it that is not a property but is both essential and unique to it, this constituent being referred to as a 'bare particular' or 'substratum'. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: This doesn't sound promising. It is unclear what existence devoid of all properties could be like. How could it 'have' its properties if it was devoid of features (it seems to need property-hooks)? It is an ontological black hole. How do you prove it? |
| 7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
| Full Idea: If there is a substratum or bare particular within a substance, this gives an explanation of the unity of substances, and it is something which can survive intact when a substance changes. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: [v. compressed wording] Many problems here. The one that strikes me is that when things change they sometimes lose their unity and identity, and that seems to be decided entirely from observation of properties, not from assessing the substratum. |
| 7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
| Full Idea: There seems to be no way of identifying a substratum as the bearer of qualities without qualifiying it as bare (having the property of being bare?), ..and they cannot be used to individuate things, because they are necessarily indiscernible. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.3) | |
| A reaction: The defence would probably be a priori, claiming an axiomatic necessity for substrata in our thinking about the world, along with a denial that bareness is a property (any more than not being a contemporary of Napoleon is a property). |
| 7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
| Full Idea: There are three distinct versions of Leibniz's Law, all traced to remarks made by Leibniz: the Identity of Indiscernibles (same properties, same thing), the Indiscernibility of Identicals (same thing, same properties), and the Substitution Principle. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2) | |
| A reaction: The best view seems to be to treat the second one as Leibniz's Law (and uncontroversially true), and the first one as being an interesting but dubious claim. |
| 7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
| Full Idea: One common argument to the conclusion that the Principle of the Identity of Indiscernibles is false is that it is not necessarily true. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.2 n32) | |
| A reaction: This sounds like a good argument. If you test the Principle with an example ('this butler is the murderer') then total identity does not seem to necessitate identity, though it strongly implies it (the butler may have a twin etc). |
| 7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
| Full Idea: What matters to continuity is not just the beginning and end states of the process by which a thing persists, perhaps through change, but the process itself. | |
| From: Cynthia Macdonald (Varieties of Things [2005], Ch.4) | |
| A reaction: This strikes me as being a really important insight. Compare Idea 4931. If this is the key to understanding mind and personal identity, it means that the concept of a 'process' must be a central issue in ontology. How do you individuate a process? |