26 ideas
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
16024 | I could have died at five, but the summation of my adult stages could not [Noonan] |
16023 | Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan] |
16015 | Problems about identity can't even be formulated without the concept of identity [Noonan] |
16017 | Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan] |
16016 | Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan] |
16020 | Identity can only be characterised in a second-order language [Noonan] |
16018 | Indiscernibility is basic to our understanding of identity and distinctness [Noonan] |
16019 | Leibniz's Law must be kept separate from the substitutivity principle [Noonan] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |