105 ideas
| 18019 | People have dreams which involve category mistakes [Magidor] |
| Full Idea: It is an empirical fact that people often sincerely report having had dreams which involve category mistakes. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.4) | |
| A reaction: She doesn't give any examples, but I was thinking that this might be the case before I read this idea. Dreams seem to allow you to live with gaps in reality that we don't tolerate when awake. |
| 17998 | Category mistakes are either syntactic, semantic, or pragmatic [Magidor] |
| Full Idea: A plausible case can be made for explaining the phenomenon of category mistakes in terms of each of syntax, semantics, and pragmatics. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: I want to explain them in terms of (structured) ontology, but she totally rejects that on p.156. Her preferred account is that they are presupposition failures, which is pragmatics. She splits the semantic view into truth-valued and non-truth-valued. |
| 18011 | Category mistakes seem to be universal across languages [Magidor] |
| Full Idea: The infelicity of category mistakes seems to be universal across languages. | |
| From: Ofra Magidor (Category Mistakes [2013], 2.3) | |
| A reaction: Magidor rightly offers this fact to refute the claim that category mistakes are purely syntax (since syntax obviously varies hugely across languages). I also take the fact to show that category mistakes concern the world, and not merely language. |
| 18012 | Category mistakes as syntactic needs a huge number of fine-grained rules [Magidor] |
| Full Idea: A syntactic theory of category mistakes would require not only general syntactic features such as must-be-human, but also highly particular ones such as must-be-a-grape. | |
| From: Ofra Magidor (Category Mistakes [2013], 2.3) | |
| A reaction: Her grape example comes from Hebrew, but an English example might be the verb 'to hull', which is largely exclusive to strawberries. The 'must-be' form is one of Chomsky's 'selectional features'. |
| 18013 | Embedded (in 'he said that…') category mistakes show syntax isn't the problem [Magidor] |
| Full Idea: The embedding data (such as 'John said that the number two is green', compared to '*John said that me likes apples') strongly suggests that category mistakes are not syntactically ill-formed. | |
| From: Ofra Magidor (Category Mistakes [2013], 2.4) | |
| A reaction: Sounds conclusive. The report of John's category error, unlike the report of his remark about apples, seems perfectly syntactically acceptable. |
| 18021 | Category mistakes are meaningful, because metaphors are meaningful category mistakes [Magidor] |
| Full Idea: Metaphors must have literal meanings. …Since many metaphors involving category mistakes manage to achieve their metaphorical purpose, they must also have literal meanings, so category mistakes must be (literally) meaningful. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Hm. 'This guy is so weird that to meet him is to encounter a circular square'. |
| 18015 | The normal compositional view makes category mistakes meaningful [Magidor] |
| Full Idea: The principle that if a competent speaker understands some terms then they understand a sentence made up of them entails that category mistakes are meaningful (as in understanding 'the number two' and 'is green'). | |
| From: Ofra Magidor (Category Mistakes [2013], 3.2.1) | |
| A reaction: [compressed version] It is normal to impose restrictions on plausible compositionality, and thus back away from this claim, but I rather sympathise with it. She adds to a second version of the principle the proviso 'IF the sentence is meaningful'. |
| 18017 | If a category mistake is synonymous across two languages, that implies it is meaningful [Magidor] |
| Full Idea: Two sentences are synonymous if they have the same meaning, suggesting that they must both be meaningful. On the face of it the English 'two is green' and French 'deux est vert' are synonymous, suggesting meaningful category mistakes. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.3) | |
| A reaction: I'm fairly convinced already that most category mistakes are meaningful, and this seems to confirm the view. Some mistakes could be so extreme that no auditor could compute their meaning, especially if you concatenated lots of them. |
| 18031 | If a category mistake has unimaginable truth-conditions, then it seems to be meaningless [Magidor] |
| Full Idea: One motivation for taking category mistakes to be meaningless is that one cannot even imagine what it would take for 'Two is green' to be true. …Underlying this complaint is sometimes the thought that the meaning of a sentence is its truth-conditions. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6) | |
| A reaction: I defend the view that most sentences are meaningful if they compose from meaningful parts, but you have to acknowledge this view. It seems to come in degrees. Sentences can have fragmentary meaning, or be almost meaningful, or offer a glimpse of meaning? |
| 18030 | A good explanation of why category mistakes sound wrong is that they are meaningless [Magidor] |
| Full Idea: The meaninglessness view does seem to offer a simple and compelling explanation for the fact that category mistakes are highly infelicitous. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6) | |
| A reaction: However, I take there to be quite a large gulf between why meaningless sentences like 'squares turn happiness into incommensurability', which I would call 'category blunders', and subtle category mistakes, which are meaningful. |
| 18032 | Category mistakes are neither verifiable nor analytic, so verificationism says they are meaningless [Magidor] |
| Full Idea: No sense experience shows that 'two is green' is true or false. But neither is 'two is green' analytically true or false. So it fails to have legitimate verification conditions and hence, by the lights of traditional verificationism, it is meaningless. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6.2) | |
| A reaction: If a category mistake is an error in classification, then it would seem to be analytically false. If it wrongly attributes a property to something, that makes it verifiably false. The problem is to verify anything at all about 'two'. |
| 18034 | Category mistakes play no role in mental life, so conceptual role semantics makes them meaningless [Magidor] |
| Full Idea: One might argue that conceptual role semantics entails that category mistakes are meaningless. Sentences such as 'two is green' play no role in the cognitive life of any agent. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.6.2) | |
| A reaction: [She quotes Block's definition of conceptual role semantics] I would have thought that if a category mistake is believed by an agent, it could play a huge role in their cognitive life. |
| 18037 | Maybe when you say 'two is green', the predicate somehow fails to apply? [Magidor] |
| Full Idea: One might argue that although 'two' refers to the number two, and 'is green' expresses the property of being green, in 'two is green' the property somehow fails to apply to the number two. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.2) | |
| A reaction: It is an interesting thought that you say something which applies a predicate to an object, but the predicate then 'fails to apply' for reasons of its own, over which you have no control. The only possible cause of the failure is the nature of reality. |
| 18039 | If category mistakes aren't syntax failure or meaningless, maybe they just lack a truth-value? [Magidor] |
| Full Idea: Having rejected the syntactic approach and the meaninglessness view, one might feel that the last resort for explaining the defectiveness of category mistakes is to claim that they are truth-valueless (even if meaningful). | |
| From: Ofra Magidor (Category Mistakes [2013], 4.3.1) | |
| A reaction: She rejects this one as well, and votes for a pragmatic explanation, in terms of presupposition failure. The view I incline towards is just that they are false, despite being well-formed, meaningful and truth-valued. |
| 18016 | Two good sentences should combine to make a good sentence, but that might be absurd [Magidor] |
| Full Idea: The principle that if 'p' and 'q' are meaningful sentences then 'p and q' is a meaningful sentence seems highly plausible. But now consider the following example: 'That is a number and that is green'. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.2.2) | |
| A reaction: This challenges the defence of the meaningfulness of category mistakes on the basis of strong compositionality. |
| 18058 | Maybe the presuppositions of category mistakes are the abilities of things? [Magidor] |
| Full Idea: The most promising way to characterise the presuppositions involved in category mistakes might be to rephrase them in modal terms ('x is able to be pregnant', 'x is able to be green'). | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.3) | |
| A reaction: This catches my attention because it suggests that category mistakes contradict dispositions, rather than contradicting classifications or types. 'Let's use a magnet to repel this iron'? The dispositions of 'two' and 'green' in 'two is green'? Hm |
| 18041 | Category mistakes suffer from pragmatic presupposition failure (which is not mere triviality) [Magidor] |
| Full Idea: I argue that category mistakes are infelicitous because they suffer from (pragmatic) presupposition failure, ...but I reject the 'naive pragmatic approach' according to which category mistakes are infelicitous because they are trivially true or false. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.1) | |
| A reaction: She supports her case quite well, but I vote for them being false. The falsity may involve presuppositions. 'Two is green' is a category mistake, and false, because 'two' lacks the preconditions for anything to be coloured (notably, emitting light). |
| 18056 | Category mistakes because of presuppositions still have a truth value (usually 'false') [Magidor] |
| Full Idea: I am assuming that even in those contexts in which the presupposition of 'the number two is green' fails and the utterance is infelicitious, it nevertheless receives a bivalent truth-value (presumably 'false'). | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.1) | |
| A reaction: It seems to me obvious that, in normal contexts, 'the number two is green' is false, rather than meaningless. Is 'the number eight is an odd number' meaningless? |
| 18055 | In 'two is green', 'green' has a presupposition of being coloured [Magidor] |
| Full Idea: My proposal is that the truth-conditional content of 'green' (in 'two is green') is the property of being green, and its presuppositional content is the property of being coloured. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.1) | |
| A reaction: This requires a two-dimensional semantics of truth-conditional and presuppositional content. I fear it may have a problem she spotted elsewhere, of overgenerating presuppositions. Eyes are presupposed by 'green'. Ambient light is required. |
| 18057 | 'Numbers are coloured and the number two is green' seems to be acceptable [Magidor] |
| Full Idea: 'The number two is green' is normally infelicitous, but, interestingly, 'numbers are coloured and the number two is green' is not infelicitous. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.4.1) | |
| A reaction: A nice example, which gives good support for her pragmatic account of category mistakes in terms of presupposition failure. But how about 'figures can have contradictory shapes, and this square is circular'? Numbers are not coloured!!! |
| 18059 | The presuppositions in category mistakes reveal nothing about ontology [Magidor] |
| Full Idea: My pragmatic account of category mistakes does not support a key role for them in metaphysics. It is highly doubtful that the presuppositions associated with category mistakes reveal anything about the fundamental nature of ontological categories. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.6) | |
| A reaction: Thus she dashes my hope, without even bothering to offer a reason. I think she should push her enquiry further, and ask why we presuppose things. Why do we take presuppositions for granted? Why are they obvious? |
| 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) |
| 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) |
| 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'. |
| 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) |
| 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) |
| 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. |
| 18040 | Intensional logic maps logical space, showing which predicates are compatible or incompatible [Magidor] |
| Full Idea: Intensional logic aims to capture necessary relations between certain predicates, such as that 'green all over' and 'red all over' cannot be co-instantiated. Each predicate is allocated a set of points in logical space, and every object has one point. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.4) | |
| A reaction: This produces an intriguing model of reality, as a vast and rich space of multiply overlapping modal predicates. Things can be blue, square, dangerous and large. They can't be small and large, or square and round. Objects are optional extras! |
| 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. |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |
| Full Idea: Various authors have argued that identity statements arising in the context of the 'Julius Caesar' problem in philosophy of mathematics constitute category mistakes. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1 n1) | |
| A reaction: [She cites Benacerraf 1965 and Shapiro 1997:79] |
| 18060 | We can explain the statue/clay problem by a category mistake with a false premise [Magidor] |
| Full Idea: Since 'the lump of clay is Romanesque' is a category mistake, a pragmatic account of that phenomenon is key to pursuing the strategy of saying that the problem rests on a false premise. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.6) | |
| A reaction: [compressed] |
| 18020 | Propositional attitudes relate agents to either propositions, or meanings, or sentence/utterances [Magidor] |
| Full Idea: Three views of the semantics of propositional attitudes: they are relations between agents and propositions ('propositional' view); relations between individuals and meanings (Fregean); or relations of individuals and sentences/utterances ('sentential'). | |
| From: Ofra Magidor (Category Mistakes [2013], 3.4) | |
| A reaction: I am a propositionalist on this one. Meanings are too vague, and sentences are too linguistic. |
| 18035 | Two sentences with different meanings can, on occasion, have the same content [Magidor] |
| Full Idea: It is commonly assumed that meaning and content can come apart: the sentence 'I am writing' and 'Ofra is writing' may have different meanings, even if, as currently uttered, they express the same content. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.1) | |
| A reaction: From that, I would judge 'content' to mean the same as 'proposition'. |
| 18018 | To grasp 'two' and 'green', must you know that two is not green? [Magidor] |
| Full Idea: Is it a necessary condition on possessing the concepts of 'two' and 'green' that one does not believe that two is green? I think this claim is false. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.4) | |
| A reaction: To see that it is false one only has to consider much more sophisticated concepts, which are grasped without knowing their full implications. I might think two is green because I fully grasp 'two', but have not yet mastered 'green'. |
| 18008 | Generative semantics says structure is determined by semantics as well as syntactic rules [Magidor] |
| Full Idea: Generative semanticists claimed that the structure of a sentence is determined by both 'syntactic' and 'semantic' considerations which interact with each other in complex ways. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.3) | |
| A reaction: [She mentions George Lakoff for this view] You need to study a range of examples, but this sounds a better view to me than the tidy picture of producing a syntactic structure and then adding a semantics. We make up sentences while speaking them. |
| 18010 | 'John is easy to please' and 'John is eager to please' have different deep structure [Magidor] |
| Full Idea: The sentences 'John is easy to please' and 'John is eager to please' can have very different deep structure (with the latter concerning John as a pleaser, while the former concerns John as the one being pleased). | |
| From: Ofra Magidor (Category Mistakes [2013], 2.1) | |
| A reaction: This demolishes the old idea of grammar as 'parts of speech' strung together according to superficial rules. The question is whether we now just have deeper syntax, or whether semantics is part of the process. |
| 18053 | The semantics of a sentence is its potential for changing a context [Magidor] |
| Full Idea: The basic semantics of sentences are not truth-conditions, but rather context change potential, which is a rule which determines what the effect of uttering the sentence would be on the context. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: [I. Heim's 'renowned' 1983 revision of Stalnaker] This means the semantics of a sentence can vary hugely, depending on context. It is known as 'dynamic semantics'. 'I think you should go ahead and do it'. |
| 18000 | Weaker compositionality says meaningful well-formed sentences get the meaning from the parts [Magidor] |
| Full Idea: A weaker principle of compositionality states that if a syntactically well-formed sentence is meaningful, then its meaning is a function of the meaning of its parts. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: I would certainly accept this as being correct. I take the meaning of a sentence to be something which you assemble in your head as you hear the parts of it unfold. ….However, irony might exhibit meaning that only comes from the whole sentence. Hm. |
| 17999 | Strong compositionality says meaningful expressions syntactically well-formed are meaningful [Magidor] |
| Full Idea: In the strong form of the principle of compositionality any meaningful expressions combined in a syntactically well-formed manner compose a meaningful expression. | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: [She cites Montague as holding this view] I find this plausible, at least. If you look at whole sentences they can seem meaningless, but if you track the process of composition a collective meaning emerges, despite the oddities. |
| 18014 | Understanding unlimited numbers of sentences suggests that meaning is compositional [Magidor] |
| Full Idea: The fact that speakers of natural languages have the capacity to understand indefinitely many new sentences suggests that meaning must be compositional. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.2.1) | |
| A reaction: To some extent, the compositionality of meaning is so obvious as to hardly require pointing out. It is the precise nature of the claim, and the extent to which whole sentences can add to the compositional meaning, that is of interest. |
| 18001 | Are there partial propositions, lacking truth value in some possible worlds? [Magidor] |
| Full Idea: Are there such things as 'partial propositions', which are truth-valueless relative to some possible worlds? | |
| From: Ofra Magidor (Category Mistakes [2013], 1.1) | |
| A reaction: Presumably this could be expressed without possible worlds. Are there propositions meaningful in New Guinea, and meaningless in England? Do some propositions require the contingent existence of certain objects to be meaningful? |
| 18036 | A sentence can be meaningful, and yet lack a truth value [Magidor] |
| Full Idea: 'That is red' in a context where the demonstrative fails to refer is truth-valueless, despite being meaningful, as is 'the queen of France in 2010 is bald'. ...The claim that some sentences are meaningful but truth-valueless is, then, widely accepted. | |
| From: Ofra Magidor (Category Mistakes [2013], 4.1) | |
| A reaction: The lack of truth value is usually because of reference failure. It is best to say the words are meaningful, but no proposition is expressed. |
| 18051 | In the pragmatic approach, presuppositions are assumed in a context, for successful assertion [Magidor] |
| Full Idea: According to the pragmatic approach, presuppositions are constraints on the context: if a sentence s generates a presupposition p, an assertion of s cannot proceed smoothly unless the context already entails p (p is taken for granted). | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: She credits Stalnaker for this approach. There is a choice between the presuppositions being largely driven by internal features of the sentence, or by external features of context. You may not know the context of some statements. |
| 18043 | The infelicitiousness of trivial truth is explained by uninformativeness, or a static context-set [Magidor] |
| Full Idea: In Grice's theory if a sentence is trivially true, asserting it would violate the maxim of quantity. For Stalnaker, if p is trivially true, it involves no update to the context-set, and is thus pointless. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.2) | |
| A reaction: 'Let us remind ourselves, before we proceed, of the following trivial truth: p'. |
| 18042 | The infelicitiousness of trivial falsity is explained by expectations, or the loss of a context-set [Magidor] |
| Full Idea: In Grice's theory if a sentence is trivially false, asserting it would violate the maxim of quality. For Stalnaker if p is trivially false, removing all worlds incompatible with p would result in an empty context-set, preventing any further communication. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.2) | |
| A reaction: [compressed] I'm not sure whether we need to 'explain' the inappropriateness of uttering trivial falsities. I take the main rule of conversation to be 'don't be boring', but we all violate that. |
| 18047 | A presupposition is what makes an utterance sound wrong if it is not assumed? [Magidor] |
| Full Idea: The most obvious test for presupposition would be this: if s generates the presupposition p, then an utterance of s would be infelicitous, unless p is taken for granted by participants in the conversation. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.1.1) | |
| A reaction: The principle of charity seems to be involved here - that we try to make people's utterances sound right, so we add in the presuppositions which would achieve that. The problem, she says, is that the infelicity may have other causes. |
| 18048 | A test for presupposition would be if it provoked 'hey wait a minute - I have no idea that....' [Magidor] |
| Full Idea: A proposed test for presupposition is the 'Hey, wait a minute' test. S presupposes that p, just in case it would be felictious to respond to an utterance of s with something like 'Hey, wait a minute - I had not idea that p!'. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.1.2) | |
| A reaction: [K. Von Finkel 2004 made the suggestion] That is, you think 'hm ...this statement seems to presuppose p'. She says the suggestion vastly over-generates possible presuppositions - unlikely ones, as well as the obvious ones. |
| 18049 | The best tests for presupposition are projecting it to negation, conditional, conjunction, questions [Magidor] |
| Full Idea: The most robust tests for presupposition are the projection tests. If s presupposes p, then ¬s does too. If s1 presupposes p, then 'if s1 then s2' presupposes p. If s1 presupposes p, then 's1 and s2' presupposes p. If s presupposes p, then 's?' does too. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.1.3) | |
| A reaction: [compressed] She also discusses quantifiers. In other words, the presupposition remains stable through various transformations of the underlying proposition. |
| 18050 | If both s and not-s entail a sentence p, then p is a presupposition [Magidor] |
| Full Idea: In the traditional account, a sentence s presupposes p if and only if both s and ¬s entail p. Standardly, this entails that if s presupposes p, then whenever p is false, s must be neither true nor false. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: 'I'm looking down on the garden' presupposes 'I'm upstairs'. Why would 'I'm not looking down on the garden' entail 'I'm upstairs'? I seem to have missed something. |
| 18054 | Why do certain words trigger presuppositions? [Magidor] |
| Full Idea: We can ask why a range of lexical items (e.g. 'stop' or 'know') trigger the presuppositions they do. | |
| From: Ofra Magidor (Category Mistakes [2013], 5.3.2) | |
| A reaction: I'm not sure whether we'll get an answer, but I would approach the question by thinking about mental files. |
| 18024 | One theory says metaphors mean the same as the corresponding simile [Magidor] |
| Full Idea: On standard versions of the simile theory of metaphors, they mean the same as the corresponding simile. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Magidor points out that this allows the metaphor to work while being meaningless, since all the work is done by the perfectly meaningful simile. But the metaphor must at least mean enough to indicate what the simile is. |
| 18023 | Theories of metaphor divide over whether they must have literal meanings [Magidor] |
| Full Idea: There are theories of metaphors that require them to have literal meanings in order to achieve their metaphorical purpose, and those that do not. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: I take almost any string of proper language to have literal meaning (for compositional reasons), even if the end result is somewhat ridiculous. 'Churchill was a lion' obviously has literal meaning. And so does 'Churchill was a transcendental number'. |
| 18025 | The simile view of metaphors removes their magic, and won't explain why we use them [Magidor] |
| Full Idea: The simile theory of metaphors makes them too easy to figure out, when they cannot be paraphrased in literal terms, …and it does not explain why we use metaphors as well as similes. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: [She cites Davidson for these points] They might just be similes with the added frisson of leaving out 'like', so that they seem at first to be false, until you work out the simile and see their truth. |
| 18026 | Maybe a metaphor is just a substitute for what is intended literally, like 'icy' for 'unemotional' [Magidor] |
| Full Idea: According to the substitution view of metaphors, a word used metaphorically is merely a substitute for another word or phrase that expresses the same meaning literally. Thus 'John is an ice-cube' is a substitute for 'John is cruel and unemotional'. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: This seems to capture the denotation but miss the connotation. Whoever came up with this theory didn't read much poetry. |
| 18028 | Gricean theories of metaphor involve conversational implicatures based on literal meanings [Magidor] |
| Full Idea: Gricean theories of metaphor …assume that conversational implicatures are generated via literal contents, and hence that a sentence cannot generate an implicature without being literally meaningful. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Magidor gives not details of such theories, but presumably the metaphor is all in the speaker's intention, which is parasitic on the wayward literal meaning, as in cases of irony. |
| 18029 | Non-cognitivist views of metaphor says there are no metaphorical meanings, just effects of the literal [Magidor] |
| Full Idea: According to non-cognitivists there is no such thing as metaphorical meaning. …The effects on the hearer are induced directly via the literal meaning of the metaphor. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: [This is said to be Davidson's view] I wonder how many people defended some explicit 'metaphorical meaning', as opposed to connotations that accumulate as you take in the metaphor? Any second meaning is just a further literal meaning. |
| 18022 | Metaphors tend to involve category mistakes, by joining disjoint domains [Magidor] |
| Full Idea: The fact that most metaphors involve category mistakes is not a coincidence. …A big part of them is to do with connecting objects and properties that normally seem to belong to disjoint domains. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: Metaphysica poets took disjoint domains and 'yoked them together by violence', according to Dr Johnson. |
| 18027 | Metaphors as substitutes for the literal misses one predicate varying with context [Magidor] |
| Full Idea: A problem with the substitution view of metaphors is that the same predicate can have very different metaphorical contributions in different contexts. Consider 'Juliet is the sun' uttered by Romeo, and 'Stalin is the sun' from a devoted communist. | |
| From: Ofra Magidor (Category Mistakes [2013], 3.5) | |
| A reaction: The substitution view never looked good (especially if you like poetry), and now it looks a lot worse. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |