# Tagged Questions

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans. That is, given a set of axioms, the only propositions that can exist are those that ...

1k views

55 views

### Completeness theorem for intuitionistic logic

Reading from Wikipedia about intuitionistic logic, I am guessing that there is a formal proof system for intuitionistic logic. (Note: My knowledge of intuitionistic logic is almost nil). My ...
60 views

I'm working a bit with Heyting algebras (which are pseudocomplemented distributive lattives, right?) and I have a question about DeMorgan's laws. I know that, in general, it's not the case that $-(X ... 1answer 68 views ### If$\phi$is$\Delta^{0}_{1}$in the language of arithmetic, does Heyting Arithmetic prove$\forall x [\phi (x) \vee \neg \phi (x)]$? PA is conservative over HA for$\Pi^{0}_{2}$sentences. If$\phi$is$\Delta^{0}_{1}$, then$\forall x [\phi (x) \vee \neg \phi (x)]$is equivalent to a$\Pi^{0}_{2}$sentence. Since PA trivially ... 1answer 49 views ###$(\forall x,\, p\vee q(x))\leftrightarrow p\vee\forall x,\, q(x)$Consider the logical formula$(\forall x,\, p\vee q(x))\leftrightarrow p\vee\forall x,\, q(x)$where x does not appear free in p. This formula is not derivable in intuitionistic logic, but it is in ... 0answers 27 views ### Algorithm to force decidability of statements using an intuitionistic series of new axioms Consider pairs$(\Phi,n)$where$\Phi$is a finite set of statements in Peano arithmetic and$n$is an integer. Say that$p'=(\Phi',n')$is an elementary intuitionistic extension of$p=(\Phi,n)$iff ... 1answer 173 views ### How is the double negation translation similar to CPS in functional programming languages? In Wikipedia's Double-negation translation article, I found that any formula in classical logic has its double negation as its intuitionist equivalent: It is also possible to define φN by ... 2answers 73 views ### Compound interest coumpounded n time per year formula.$A=P\left(1+\frac{r}{n}\right)^{nt}\$ intuition behind it.

I know that the compound interest formula for the interest compounded annually is given by $$A=P(1+r)^t$$ I know the intuition behind it. But why the compound interest formula for the interest ...
53 views

### Why do you only need to show validity in one world when using trees in institutionist/constructivist logic?

Depicted below, my prof used a tree to prove that an argument is valid according to intuitionist logic. However, I can't find a contradiction in world 0. Why is invalidity ascertained when all ...
147 views

### A question on intuitionistc propositional logic

Prove that: Two finite rooted frames are isomorphic iff they validate the same formulas. (This is an exercise in the book "Modal Logic" by A.Chagrov and M.Zakharyaschev)