32 ideas
5750 | Consistency is modal, saying propositions are consistent if they could be true together [Melia] |
18951 | For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam] |
18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
18949 | The universal syllogism is now expressed as the transitivity of subclasses [Putnam] |
5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia] |
18952 | '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam] |
5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia] |
18958 | In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam] |
18954 | Before the late 19th century logic was trivialised by not dealing with relations [Putnam] |
18956 | Asserting first-order validity implicitly involves second-order reference to classes [Putnam] |
18962 | Unfashionably, I think logic has an empirical foundation [Putnam] |
18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
5740 | Second-order logic needs second-order variables and quantification into predicate position [Melia] |
18955 | Having a valid form doesn't ensure truth, as it may be meaningless [Putnam] |
5741 | If every model that makes premises true also makes conclusion true, the argument is valid [Melia] |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
5735 | Maybe names and predicates can capture any fact [Melia] |
5736 | No sort of plain language or levels of logic can express modal facts properly [Melia] |
18957 | Nominalism only makes sense if it is materialist [Putnam] |
18950 | Physics is full of non-physical entities, such as space-vectors [Putnam] |
5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia] |
5738 | We may be sure that P is necessary, but is it necessarily necessary? [Melia] |
5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia] |
5739 | Sometimes we want to specify in what ways a thing is possible [Melia] |
5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia] |
5742 | In possible worlds semantics the modal operators are treated as quantifiers [Melia] |
5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia] |
5749 | Possible worlds could be real as mathematics, propositions, properties, or like books [Melia] |
5751 | The truth of propositions at possible worlds are implied by the world, just as in books [Melia] |
18960 | Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam] |
5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |