display all the ideas for this combination of philosophers
10 ideas
| 3093 | Any two states are logically linked, by being entailed by their conjunction [Harman] |
| Full Idea: Any two states of affairs are logically connected, simply because both are entailed by their conjunction. | |
| From: Gilbert Harman (Thought [1973], 8.1) |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| Full Idea: There is as yet no substantial theory of inference or reasoning. To be sure, logic is well developed; but logic is not a theory of inference or reasoning. Logic is a theory of implication and inconsistency. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2) | |
| A reaction: One problem is that animals can draw inferences without the use of language, and I presume we do so all the time, so it is hard to see how to formalise such an activity. |
| 3098 | Deductive logic is the only logic there is [Harman] |
| Full Idea: Deductive logic is the only logic there is. | |
| From: Gilbert Harman (Thought [1973], 10.4) |
| 3094 | You don't have to accept the conclusion of a valid argument [Harman] |
| Full Idea: We may say "From P and If-P-then-Q, infer Q" (modus ponens), but there is no rule of acceptance to say that we should accept Q. Maybe we should stop believing P or If-P-then-Q rather than believe Q. | |
| From: Gilbert Harman (Thought [1973], 10.1) |
| 3084 | Our underlying predicates represent words in the language, not universal concepts [Harman] |
| Full Idea: The underlying truth-conditional structures of thoughts are language-dependent in the sense that underlying predicates represent words in the language rather than universal concepts common to all languages. | |
| From: Gilbert Harman (Thought [1973], 6.3) |
| 3080 | Logical form is the part of a sentence structure which involves logical elements [Harman] |
| Full Idea: The logical form of a sentence is that part of its structure that involves logical elements. | |
| From: Gilbert Harman (Thought [1973], 5.2) |
| 3081 | A theory of truth in a language must involve a theory of logical form [Harman] |
| Full Idea: Some sort of theory of logical form is involved in any theory of truth for a natural language. | |
| From: Gilbert Harman (Thought [1973], 5.2) |
| 12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
| Full Idea: Principles of implication imply there is not a purely probabilistic rule of acceptance for belief. Otherwise one might accept P and Q, without accepting their conjunction, if the conjuncts have a high probability, but the conjunction doesn't. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2) | |
| A reaction: [Idea from Scott Soames] I am told that my friend A has just won a very big lottery prize, and am then told that my friend B has also won a very big lottery prize. The conjunction seems less believable; I begin to suspect a conspiracy. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |