Isn't it interesting how conversations are filled with tautologies? And I never knew it. There's absolutely nothing wrong with saying that sentence in casual conversation, but it might be frowned upon in formal writing.

I don't think people are expected to speak like they formally write. It would be boring and unexpresssive speech. People don't like to listen to dry logical speakers.

Thanks for this explanation, Yazata! So, a contradiction is a compound statement that is always false, and a tautology is a compound statement that is always true. Would an implication then be a hint of both? (a tautology and a contradiction) Can you help me to understand a contingency?

That's true. But, then there's this: Please Register or Log in to view the hidden image! I want to produce a truth table.

Yogi Bera was famous for these. "It's like Deja Vu all over again." "In theory, there is no difference between theory and practice. In practice, there is. https://www.pinterest.ca/sktz3131/yogi-bera-quotes/

Possibly, for a similar reason you’re fascinated by the paranormal. Different things arouse our curiosity, I guess. Please Register or Log in to view the hidden image!

You don't know that. But even if no one wishes to discuss it in my social circle (although, I can think of one or two nerds who might), **I** am interested in the topic.

That chart is identical to the truth table for programmatic AND. If A and B are true, then the result is true. If either A or B are true but not both, then the result is false.

True (for the tautology) or false (for the contradiction) for all interpretations, for all truth value assignments of the atomic propositions that go into the compound statement. Your illustration illustrates it very well. A contingent proposition is a proposition that's true in some interpretations and false in others. In other words, it's T for some combinations of truth values of its component parts, and F for others. As we already saw, 'and' is defined to be T if and only if both of the propositions it joins are T. Now look at the truth table (in your illustration) for (P and Q). There are four possible combinations of T and F for the atomic propositions P and Q: P Q (P & Q) T T........T F T........F T F........F F F........F It's not a tautology since it's false in three of the four interpretations. (To be a tautology it would have to be T for all of them.) And it's not a contradiction since it's true in one of them. (To be a contradiction, it would have to be F for all of them.) So it's contingent, meaning that it might sometimes be T and sometimes F, and which one it is will depend on the truth values of its component parts (and not just on its logical form). Please Register or Log in to view the hidden image! The 'If - Then' operation is subject to quite a bit of discussion in the philosophy of logic. Much of it is above my pay grade. (It's the kind of stuff that people write doctoral dissertations on.) A surprisingly understandable discussion is in the SEP. It considers at some length whether the truth-functional approach is really the right way to understand conditionals. https://plato.stanford.edu/entries/conditionals/ It's possible to give a truth-functional definition of the 'If - Then' relation. For various reasons, the one given in most of the beginning logic texts is: Please Register or Log in to view the hidden image! But this is unsatisfactory to many logicians. For one thing, basing everything on truth functions ignores the need for Q to be relevant to P when we want to say that P implies Q. This has motivated the development of a species of non-classical logic called Relevance Logic. A closely related problem is the problem of explosion, where anything whatsoever can be derived from a contradiction. Attempts to avoid that extremely unpalatable problem have led to another form of non-classical logics called Paraconsistent Logic. https://en.wikipedia.org/wiki/Relevance_logic https://en.wikipedia.org/wiki/Paraconsistent_logic

In language, as opposed to logic, tautologies are sometimes a sign of a poorly thought out explanation, but there are many times it is used by way of emphasis: A promise is a promise. Business is business. A man's got to do what a man's got to do. "If we don't succeed then we run the risk of failure." - Dan Quayle I am what I am. Have a look with your own eyes. "It isn't pollution that's harming the environment. It's the impurities in our air and water that are doing it." - Dan Quayle Que sera sera (bit topical given the recent passing of Doris Day) It is what it is Etc. Plenty of place names are tautological as well: Lake Tahoe (Tahoe means lake) Sahara desert (guess what Sahara means... Please Register or Log in to view the hidden image!) There's a place in Warwickshire that I've been to called Napton-on-the-Hill, even though Napton meant "settlement on the hill". Undoubtedly plenty of cases of "river river" or "lake lake" etc.

Those are great examples, Sarkus, thanks!! It's not a word I've been familiar with, so it's been fun learning about this. Please Register or Log in to view the hidden image!

As the Ringmaster said when the Human Cannonball resigned, "Where will we find another man of your caliber?"