∼(C → Q), how do you state this formal sentence into English
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∼(C → Q), how do you state this formal sentence into English

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
Anyway, in translating between symbols and English, I find it helps to do all of the thinking/reasoning/rearrangement on the symbols side if that makes any sense.Hope this helped.......

For similar reasons, it is often unusual to assign "truth values" to English if-thens, particularly when the premise is false (e.g. "if it's snowing in Miami right now, then I am the Pope" would be regarded as meaningless, not true or false). Whereas *any* symbolic statement "P -> Q" has a well defined truth value, determined from those of P and Q according to fixed rules.

I find these kinds of problems easier if I try to think like a robot who knows the rules, and not like an English speaker. For example, if P models the statement "it's snowing in Miami right now" and Q models the statement "I am the Pope", then the truth values of P and Q are false and false respectively, so according to the definition of ->, the truth value of the symbolic sentence "P -> Q" is true. It's just how -> is defined. Similarly, "~(P -> Q)" is just "P and (~Q)".

Anyway, in translating between symbols and English, I find it helps to do all of the thinking/reasoning/rearrangement on the "symbols side" if that makes any sense. Hope this helped.
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