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  1. All cats are animals.

  2. TV's did not exist before the 20th century.

  3. All bachelors who are married are both married and unmarried.

What I think is the classification of each statement:

  1. Necessarily true.

  2. Empirically true. (not sure about this one)

  3. Necessarily false.

  • Is there a text or link you are using to provide context? This would help someone provide an answer. Welcome. – Frank Hubeny Sep 9 '18 at 2:47
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    Part of the difficulty in answering this question is that 'necessarily true' and 'necessarily false' involve the troublesome notion of necessity. Not all philosophers would grant that there are necessary truths; and those who do accept necessary truth approach it differently : a necessary truth is a tautology, some say, or a necessary truth is a proposition that is true in all possible worlds. Your classification - no fault of yours - is not sensitive to these philosophical issues. It treats the notion of necessary truth as unproblematic, which is the last thing it is. Best : GT – Geoffrey Thomas Sep 10 '18 at 17:25
  • 1 is empirical. It's true for a human. If you're a cat. you're a god. Humans are animals you keep around as pets and to operate the can opener. The Egyptians regarded cats as gods. Or at least they worshipped cat gods. It's an interesting question. Certainly regarding humans as animals is historically contingent. For most of our existence we regarded ourselves as separate from the animals. If you think that "we're right and the pre-Darwins were wrong," how do you know we won't have a different idea in the future? Where does absolute truth lie? I could make the case for contingency. – user4894 Sep 15 '18 at 3:46
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A cat by definition is an animal. It is necessarily true.

When TVs were invented can be checked, but it didn't have to happen. It is empirically true.

A ^ ~A > B is by definition true. It is necessarily true.

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  • I made some edits. You are welcome to roll these back or continue editing. Make sure I didn't misrepresent you. You can see the versions by clicking on the "edited" link above. You might want to expand the third one. What does "A" stand for. This will avoid any ambiguity in the answer. Welcome to this SE! – Frank Hubeny Sep 15 '18 at 1:17
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As Geoffrey points out, in order to be able to obtain a correct answer, your "terminology" has to be clearly defined.

In order to be able to say that a cat is necessarily an animal, one must: 1)define the characteristics of "animal", 2) define the characteristics of "cat", and 3)determine that all the characteristics of "cat" are found in the description of "animal". If this is true, then the statement "all cats are animals" would necessarily be true.

Your second statement is "empirically true" by your choice. You could look up the historical record and determine the exact date a fully functioning TV was built, and then you would be certain that TVs did not exist prior to that date, which would then make your statement "necessarily true."

Your third statement is "non-sense."
By definition, a "bachelor" is an unmarried person. So the set of "all bachelors who are married" is zero (empty). Also, the set of all (persons) married and unmarried, is zero (m v ~m) = 0

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  • Rather than "non-sense" I would have called it "undefined." It's in the same general category as "divide by zero." The result is undefined, and so cannot be used to generate anything except more undefined terms. Comparison of an undefined thing with anything, even another undefined thing, produces an undefined thing. – user34017 Sep 13 '18 at 18:13

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