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Full Idea
In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity.
Gist of Idea
Justication logics make explicit the reasons for mathematical truth in proofs
Source
Melvin Fitting (Intensional Logic [2007], 3.6.1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.23
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| 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] |
| 15377 | Definite descriptions pick out different objects in different possible worlds [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] |