Is this a modus ponens or a modus tollens? Is this argument considered invalid because of such?

Question

a situation as follows:

"If the alien spaceship landed, there should be a large circular depression in the field. There is a large circular depression in the field. So the alien spaceship must have landed."

I have figured, that it is an INVALID argument and must figure if it falls under modus ponens or modus tollens.

* Modus ponens states that if A (the antecedent) is true, then B (the consequent) is necessarily true.
But if A is false, that tells us nothing about B (except that if B happens to be true, it is for some reason other than A).
* Modus tollens states that if B (the consequent) is false, then A (the antecedent) is necessarily false.
But if B is true, that tells us nothing about A (because there might well be other causes of B).

I know that A (the antecedent) is false for the reason that the aliens themselves create a fallacy (correct me if I am wrong though) and that B could of been caused by something else than the alien.

thanks...

Answer 1

I would rather put this logic problem under rules of inference using dilemmas.

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Proof

For arguments that involve complex statements, or more than a few premises, even the short version of the truth-table method can be cumbersome. It is often easier and more natural to look for a proof by which the conclusion can be derived from the premises. Proof in logic is like proof in geometry. It is a series of small steps, each of which is itself a valid inference. If we can get from premises to conclusion by valid steps, then the argument as a whole is valid. Constructing a proof often takes some ingenuity, so the fact that you haven't found a proof in a given case does not establish that the argument is invalid. Perhaps you haven't looked hard enough.

Unlike the truth-table method, the method of proof won't establish that an argument is invalid. If an argument is valid, however, a proof will often reveal the connection between premises and conclusion more clearly than the truth-table method does.

Described below are several inference forms commonly used in propositional logic as building blocks from which proofs can be constructed. They can all be proven valid by the truth-table method, and you are already familiar with most of them. These inference rules can be grouped into three general categories:

* Rules of inference using disjunction and conjunction

* Rules of inference using hypothetical and disjunctive syllogisms (here is where Modus ponens and Modus tollens reside)

* Rules of inference using dilemmas

Answer 2

Typically whether or not the antecedent matches up with reality in the world as we know it doesn't figure into evaluating logic propositions. The antecedent is asserted to be true under some world, somewhere.

So you have the following Modus Ponens Proposition:
If A then B.
B then A.

As you've determined this is a fallacy, but it is not a fallacy because the antecedent is false in our world. It is false because, as you've stated, the circular depression could have been caused by something else, and the original Proposition does not exclude other depression causes.

Answer 3

They are both valid arguments. Modus Tollens simply denies the consequent. The first is simply If P then Q; P, therefore Q The second is If P then Q; Not Q, therefore Not P