77 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] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10988 | Any first-order theory of sets is inadequate [Read] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
11016 | Would a language without vagueness be usable at all? [Read] |
11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
3906 | If possible worlds are needed to define properties, maybe we should abandon properties [Scruton] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
3888 | Hume assumes that necessity can only be de dicto, not de re [Scruton] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
3903 | The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
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] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
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] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
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] |
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] |