"It is certain you have a nose when you can smell but not everyone with a nose can smell".

Or "It is certain you have a brain when you can think. But not everyone with a brain can think"

Note: As I said earlier on, these statements are just hypothetical. I just want you to understand what I'm trying to convey.

(EDIT) Please if you know any term related to it, feel free to say it.

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    I'm not sure to understand... It seems to me that you are expressing a condition that is necessary but not sufficient, because : "if you can smell, then you have a nose" is true but "if you have a nose, then you can smell" is not. Thus, having a nose is necessary but not sufficient to be able to smell. Mar 17, 2019 at 10:37
  • Thank you very much!! I just read the Wikipedia article and what you said is exactly what I wanted! — "necessary but not sufficient".
    – W. Bruce
    Mar 17, 2019 at 12:24

1 Answer 1


The propositions you're describing fit under the broad category of modal logic. According to the Stanford Encyclopaedia of Philosophy,

A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’.

When we talk of certainty, what we really mean is that that thing is necessary. So all we have to do is introduce a new logical operator: Define:

'it is necessary that A'≔L(A) for any formula A

'it is sufficient that A'≔M(A) for any formula A

Then your proposition(s) become: ∀x(M(Sx)→L(Nx))∧¬∀yM(Ny)→L(Sy))

This should be read literally as: 'Everything that sufficiently has the property Sx must necessarily have the property Nx, but not everything that sufficiently has the property Nx must necessarily have the property Sx'

Sx and Nx are just predicates, and since both propositions have the same form, you can just change what the predicates mean in each case.

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