So when I was reading through Tim’s WordPress site, and I came across his rant, or rather, his confusion about what a vacuous truth is, I would be the first to say why yes indeed – even now there are debates among scholarly mathematicians, logicians, metamathematicians, metalogicians, etc. about the validity of classical logic (the logic we are all used to, the two-valued logic – either being true or false). But don’t worry – I am going to attempt to list out all the basic terms of logic that one already knows in a more normal manner; but almost all will be listed in fancy Latin phrases, just to sound snazzier. Here are some of the basic and well-known logical terms:

1. Modus ponendo ponens (Latin: mode that affirms by affirming)
2. Modus tollendo tollens (Latin: mode that denies by denying)
3. Modus tollendo ponens (Latin: mode which, by denying, affirms)
4. Modus ponendo tollens (Latin: mode that affirms by denying)
5. Vacuous truth

Doesn’t this make it sound even more complicated? But don’t worry, I’ll go through each of these fun statements, and at the end of it, you can use these and recognize how much we use these concepts without even thinking about it! But I’ll leave these explanations for later; if you are very curious and want to know more about this now, now, NOW – Wikipedia gives a good enough explanation of these concepts.