78 ideas
| 4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
| Full Idea: The Social Turn is as defining a characteristic of contemporary philosophy as the Linguistic Turn has been of the earlier twentieth century period. | |
| From: Paul O'Grady (Relativism [2002], Ch.1) | |
| A reaction: A helpful observation. It ties in with externalism about concepts (Twin Earth), impossibility of Private Language, and externalism about knowledge. |
| 4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
| Full Idea: The four basic principles of rationality are 1) avoid contradiction, 2) enhance coherence, 3) avoid ignoring evidence, and 4) maximise evidence. | |
| From: Paul O'Grady (Relativism [2002], Ch.5) | |
| A reaction: I like this, and can't think of any additions. 'Coherence' is the vaguest of the conditions. Maximising evidence is still the driving force of science, even if it does sound quaintly positivist. |
| 4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
| Full Idea: A map that is identical in all respects with that which is mapped is just useless. So reductionism is not just a good thing - it is essential to thought. | |
| From: Paul O'Grady (Relativism [2002], Ch.6) | |
| A reaction: A useful warning, when thinking about truth. It is folly to want your thoughts to exactly correspond to reality. I want to understand the world, but not if it requires being the world. |
| 4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
| Full Idea: Weak alethic relativism holds that while a statement may be true in one framework, it is inexpressible in another. Strong alethic relativism is where a sentence is true relative to one framework, but false relative to another. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: The weak version will be Kuhn's 'incommensurability' of scientific theories, while the strong version will be full Protagorean relativism, saying all beliefs are true. |
| 4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
| Full Idea: The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality'. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: Dangerous nonsense. This leaves truth shifting as our theories change, it leads to different truths in different cultures, and no palpable falsehood in ignorant cultures. Don't give it house-room. |
| 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) |
| 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'. |
| 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). |
| 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) |
| 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). |
| 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) |
| 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. |
| 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) |
| 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'. |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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. |
| 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. |
| 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) |
| 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. |
| 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. |
| 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. |
| 4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
| Full Idea: Logical relativism emerges if one defends the existence of two or more rival systems that one may legitimately choose between, or move back and forth between. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: All my instincts rebel against this possibility. All of Aristotle's and Kant's philosophy would be rendered meaningless. Obviously you can create artificial logics (like games), but I believe there is a truth logic. (Pathetic, isn't it?) |
| 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. |
| 4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
| Full Idea: Suggestions for a third value for truth are "indeterminate", or a scale running from "true", through "mostly true", "mainly true", "half true", "mainly false", "mostly false", to "false", or maybe even "0.56 true". | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: Anything on a sliding scale sounds wrong, as it seems to be paracitic on an underlying fixed idea of 'true'. "Indeterminate", though, seems just right for the truth of predictions ('sea-fight tomorrow'). |
| 4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
| Full Idea: While Russell and Whitehead used five primitive logical symbols in their system, Wittgenstein suggested in his 'Tractatus' that this be reduced to one. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: This certainly captures why Russell was so impressed by him. In retrospect what looked like progress presumably now looks like the beginning of the collapse of the enterprise. |
| 4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
| Full Idea: The anti-realist says we have theories about the world that are incompatible with each other, and irreducible to each other. They often cite wave-particle duality, which postulate incompatible properties to reality. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: Most physicists, of course, hate this duality, precisely because they can't conceive how the two properties could be real. I say realism comes first, and the theories must try to accommodate that assumption. |
| 4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
| Full Idea: What counts as a fact partly depends on human input, such as the availability of concepts to describe such facts. | |
| From: Paul O'Grady (Relativism [2002], Ch.1) | |
| A reaction: The point must be taken. I am happy to generalise about 'The Facts', meaning 'whatever is the case', but the individuation of specific facts is bound to hit the current problem. |
| 4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
| Full Idea: Those defending the claim that objects exist with identity conditions not imposed by us, do not have to say that there is just one account of those objects possible. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: This seems right, but the test question is whether the mind of God contains a single unified theory/account. Are multiple accounts the result of human inadequacy? Yes, I surmise. |
| 14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
| Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8) | |
| A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it. |
| 14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
| Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms. | |
| From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1) | |
| A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible? |
| 4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
| Full Idea: A weaker form of relativism holds that developments in logic, in maths and in geometry have shown how a relativised notion of the a priori is possible. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: This is non-Euclidean geometry, and multiple formalisations of logic. Personally I don't believe it. You can expand these subjects, and pursue whimsical speculations, but I have faith in their stable natural core. Neo-Platonism. |
| 4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
| Full Idea: The reason sense-data were immune from doubt was because they were so primitive; they were unstructured and below the level of conceptualisation. Once they were given structure and conceptualised, they were no longer safe from sceptical challenge. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: The question of whether sense-data are conceptualised doesn't have to be all-or-nothing. As concepts creep in, so does scepticism, but so what? Sensible philosophers live with scepticism, like a mad aunt in the attic. |
| 4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
| Full Idea: The two dichotomies which set the agenda in contemporary epistemology are the foundationalist-coherentist debate, and the internalist-externalist debate. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: Helpful. Roughly, foundationalists are often externalists (if they are empiricists), and coherentists are often internalists (esp. if they are rationalists). An eccentric combination would make a good PhD. |
| 4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
| Full Idea: Internalism about justification says that the reasons one has for a belief must be in some sense available to the knowing subject, ..while externalism holds that it is possible for a person to have a justified belief without having access to the reason. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: It strikes me that internalists are talking about the believer being justified, and externalists talk about the belief being justified. I'm with the internalists. If this means cats don't know much, so much the worse for cats. |
| 4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
| Full Idea: Coherentist justification is more than absence of contradictions, and will involve issues like explanatory support and evidential support, and perhaps issues about probability and confirmation too. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: Something like this is obviously essential. Is the notion of 'relevance' also needed (e.g. to avoid the raven paradox of induction)? Coherence of justification will combine with correspondence for truth. |
| 4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
| Full Idea: Ontological relativists are anti-realists in the strong sense; they hold as meaningless the view that our theories carve nature at the joints. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: This pinpoints my disagreement with such relativism, as it seems obvious to me that nature has 'joints', and that we would agree with any sensible alien about lots of things. |
| 4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
| Full Idea: Contextualist about knowledge say that "to know" means different things in different context. For example, a warehouse may be empty for a furniture owner, but not for a bacteriologist or a physicist. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: There is obviously some truth in this, but we might say that 'empty' is a secondary quality, or that 'empty for furniture' is not relative. We needn't accept relativism here. |
| 4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
| Full Idea: It is possible to conceive of one understanding the meaning of a realm of ideas, but holding that one cannot judge as to the truth or rationality of the claims made in it. | |
| From: Paul O'Grady (Relativism [2002], Ch.5) | |
| A reaction: I think Davidson gives good grounds for challenging this, by doubt whether one 'conceptual scheme' can know another without grasping its rationality and truth-conditions. |
| 4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
| Full Idea: Verificationism came under attack from empiricists who were friendly to the banishment of traditional metaphysics, but unfriendly to the analytic-synthetic distinction, on which the idea of a 'factual statement' depended. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: I don't accept this move because I don't consider the 'facts' to be language-dependent. They are pre-linguistic, they outrun that capacity of our language, and they are available to animals. |
| 4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
| Full Idea: There may be no way to avoid scepticism about meaning if you abandon the analytic-synthetic distinction in the way Quine does. | |
| From: Paul O'Grady (Relativism [2002], Ch.3) | |
| A reaction: My suspicion was always that Quine's proposal began the slippery road to hell. It appears to be pragmatists who are most drawn to Quine's idea. The proposal that all my analytic propositions could be treated as synthetic totally baffles me. |
| 4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
| Full Idea: In his earlier work, Quine defended the view that no belief (including logic) is in principle unrevisable, but in his later work (1970) he took the conservative view that we would always impute mistranslation rather than deviancy. | |
| From: Paul O'Grady (Relativism [2002], Ch.2) | |
| A reaction: I take it he was influenced by Davidson's 'principle of charity'. He says that if someone asserts 'p and not-p', we would assume a misunderstanding of 'and' or 'not'. |
| 4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
| Full Idea: It makes sense to think that one could recognise that something is a language without necessarily being able to translate it; cryptographers do this all the time. | |
| From: Paul O'Grady (Relativism [2002], Ch.5) | |
| A reaction: Maybe, but cryptographers usually have a lot of context to work with. If we met extraterrestrials if might not be so clear. One can only spot patterns, and crystals have those. |
| 4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |
| Full Idea: The chief problem for fideists is other fideists who hold contrary ideas. | |
| From: Paul O'Grady (Relativism [2002], Ch.4) | |
| A reaction: The other problem is trying to find grounds for sticking to the object of one's faith, rather than changing from time to time. |