# Are these two propositions equivalent?

Are the propositions "Everything happens for a reason", and "Nothing happens without a reason" logically equivalent?

• i think the answer you have is fine, though you may want to be careful you don't equivocate 'reason' or indeed 'nothing' when interpreting it
– user46524
Jul 4 '20 at 19:07
• Add a truth table to your post for each statement. Are the two tables identical? Jul 4 '20 at 21:25
• In classical logic, yes. ¬∃¬R(x) is obtained from∀x R(x) by applying the De Morgan's law for quantifiers, which works in both directions. Jul 5 '20 at 0:16

We may introduce two predicates, thinghood, τ(x), and happening for a reason, ρ(x). Then we can translate the statements into the standard first-order language as follows:

‘Everything happens for a reason’

∀x(τ(x) → ρ(x)) ↔ ∀x(¬τ(x) ∨ ρ(x))

‘Nothing happens without a reason’

¬∃x(τ(x) ∧ ¬ρ(x)) ↔ ∀x(¬τ(x) ∨ ρ(x))

We see that they are logically equivalent. However, the translation hinges on the idea of thinghood, and the related issue of quantifying over absolute generality is a matter of metaphysical dispute.

• Thinghood... I don't think so. Jul 4 '20 at 18:24
• why not @ClydeFrog ? how else are you going to answer the question?
– user46524
Jul 4 '20 at 19:05
• Whatever a good answer might be, it won't need "thinghood" to reformulate events and reasons for events. Jul 4 '20 at 19:38
• Doesn’t τ(x) ∧ ¬ρ(x) cover things that did not happen at all, whether with a reason or not? Jul 7 '20 at 9:38
• @user3840170 The task of the thinghood predicate is, so to speak, to reduce 'everything' and 'nothing' to a common denominator; from a philosophical point of view, what to ascribe it to is directly related to one's metaphysical presumptions. One might ascribe thinghood to an idea, a possibility, etc. Whatever it is, one has to specify the same domain for both 'everything' and 'nothing'. Jul 7 '20 at 12:27

1: Everything happens for a reason 2:nothing happens without a reason.

In 1, maybe Reason is there but nothing happens but in 2 there has to be a reason for things to happen.

I definitely see a difference between the two. So I translated the propositions into French and,again, perceived a difference between the two: 1 (il y a une raison pour tout) has a connotation of explanation. No randomness but 2 (rien ne se passe sans une bonne raison) indicates that there has to be a reason for things to happen.