Can p and q in modus tollens be stated negatively?


In a youtube video a commentator summarizes Andrew Klavan's argument as the following:

  1. If God does not exist, there are no objective moral values.
  2. There are objective moral values.
  3. God exists.

The commentator says it takes the form of modus tollens thus it is valid.

Is the commentator correct? It appears to me that you could substitute p for "God does not exist" and q for "there are no objective moral values". Then structure them as a modus tollens and get a valid argument:

  1. p -> q
  2. not q
  3. thus not p

which amounts to the argument above.

FYI what I mean by stated negatively is "God does not exist" vs if I stated it positively "God does exist".


Posted 2017-10-07T22:50:27.300

Reputation: 45

1While the logic is valid, the premises are debatable. – None – 2017-10-08T14:08:32.823

Yes. A placeholder in propositional logic can take the place of a negative statement (a denial that such and such is true); then, the negation of such a placeholder will then amount to a denial that a negative statement is true (an affirmation). The argument you presented is valid, but this alone says absolutely nothing about the veracity of the conclusion. – jeffreysbrother – 2017-10-10T03:55:59.647



Logical formulae are blind to the content of the assertions that fill them in, and evaluations of logical validity are accordingly content-blind. One can substitute for "P" and "Q" any given sentence, affirmative or negative, universal or existential, or otherwise. One gets to evaluate the content when considering the soundness of the argument.

Daniel Coimbra

Posted 2017-10-07T22:50:27.300

Reputation: 149


This reasoning is correct. The modus tollens technique is also called Denying the Consequent. The quirk is this example is that Statement 1 is negative, P thus not-Q; Statement 2 is the denial, and so it ends up affirmative, Q. That said, the premises support the conclusion.

Mark Andrews

Posted 2017-10-07T22:50:27.300

Reputation: 4 397

I think you mean the modus tollens technique rather than modus ponens. – virmaior – 2017-10-08T01:53:12.743

1"Modus pollen" is the way bees make honey logically. Thanks for the correction. – Mark Andrews – 2017-10-08T04:52:54.770


Premise 1 is the contrapositive of, and so equivalent to, "If there are objective moral values, then God exists," so if you like you can look at this as a modus ponens rather than a modus tollens. Comes to the same thing, and it's valid, though possibly not sound.

Srap Tasmaner

Posted 2017-10-07T22:50:27.300

Reputation: 11