48 ideas
| 3879 | Philosophy aims to provide a theory of everything [Scruton] |
| 3891 | If p entails q, then p is sufficient for q, and q is necessary for p [Scruton] |
| 3894 | We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton] |
| 3883 | A true proposition is consistent with every other true proposition [Scruton] |
| 3884 | The pragmatist does not really have a theory of truth [Scruton] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
| 3906 | If possible worlds are needed to define properties, maybe we should abandon properties [Scruton] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 3888 | Hume assumes that necessity can only be de dicto, not de re [Scruton] |
| 3903 | The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton] |
| 3897 | Epistemology is about the justification of belief, not the definition of knowledge [Scruton] |
| 3881 | In the Cogito argument consciousness develops into self-consciousness [Scruton] |
| 3887 | Maybe our knowledge of truth and causation is synthetic a priori [Scruton] |
| 3901 | Touch only seems to reveal primary qualities [Scruton] |
| 3885 | We only conceive of primary qualities as attached to secondary qualities [Scruton] |
| 3910 | If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton] |
| 3899 | The representational theory says perceptual states are intentional states [Scruton] |
| 3898 | My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton] |
| 3880 | Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton] |
| 3878 | Why should you believe someone who says there are no truths? [Scruton] |
| 3892 | Every event having a cause, and every event being determined by its cause, are not the same [Scruton] |
| 3911 | The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton] |
| 3882 | Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton] |
| 3896 | Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 3886 | Membership is the greatest source of obligation [Scruton] |
| 3895 | The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton] |
| 3890 | 'Cause' used to just mean any valid explanation [Scruton] |
| 3904 | Measuring space requires no movement while I do it [Scruton] |
| 3905 | 'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton] |