# How to infer ¬Q when there seems to be no way to

Rule #1: No man shall hit another man.

Rule #2: If someone breaks Rule #1, then Rule #1 does not apply to such a one.

My specific question is: How can someone infer that Rule #1 does apply to him?

It’s not enough to say, “I am not breaking Rule #1—hence, it applies to me.” Such reasoning would be denying the antecedent, which is a formal fallacy. How can someone infer “¬Q” in this case?

• What do you imagine not Q to be? You never supply your formalization other than that single bit. – virmaior Jul 21 '16 at 4:31
• @virmaior Well the P→Q statement is “If someone breaks Rule #1, then Rule #1 does not apply to such a one,” so ¬Q would be “Rule #1 does apply to [X].” – London Jennings Jul 21 '16 at 6:09
• Try symbolizing it completely and adding that to your question by editing. (Note also that in sentential logic there's no way to include a variable in the symbolization in that way). – virmaior Jul 21 '16 at 7:43
• From P→Q alone, you cannot derive ¬Q (try with a valuation v such that v(Q)=true). – Mauro ALLEGRANZA Jul 21 '16 at 8:47