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The first exercise is "Spot the valid argument(s)." The following are the arguments.

I think all of these arguments are valid. Am I right?

(i)

If abortion is permissible, infanticide is permissible.

Infanticide is not permissible.

Therfore, abortion is not permissible.

(ii)

It is wrong to experiment on a human subject without consent.

Dr. X experimented on Mr.Z.

Mr. Z consented to this experiment.

Therefore, it was not wrong for Dr. X to experiment on Mr. Z.

(iii)

I will not survive my death.

My body will survive my death.

Therefore, I am not my body.

(iv)

Geoffrey is a giraffe.

If X is a giraffe, then X's parents were giraffes.

Therefore, all of Geoffrey's ancestors were giraffes.

The second exercise is "The following arguments are not valid as they stand. Supply missing premises to make them valid."

I could not understand why the first argument is invalid. Is it because "the universe" is a member of "every event," and so the premise is TRUE and the conclusion is FALSE?

Besides, how could I make this argument valid by adding premises?

(i)

Every event has a cause.

No event causes itself.

Therefore, the universe has no beginning in time.
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  • If an argument has validity in Mathematical logic then there is an inference rules associated with the inference. If there is no inference rule associated then chances are not enough information is given to make the right connections between premises and the final conclusion. The content of the premises does not come into play with simple validity tests. Inference rules such as modus ponens or modus tollens should be familiar. Or perhaps conditional introduction & conditional elimination should ring a bell. – Logikal Sep 4 at 17:04
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    (iii) is a fascinating argument I've not seen before. – PeterJ Sep 4 at 17:11
  • yeah these were fun to read @PeterJ – another_name Sep 4 at 17:52
  • You already posted the exact same question on Mathematics SE. Please don't post the same question across multiple site in the network. – lemontree Sep 4 at 21:22
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Every event has a cause.

No event causes itself.

Therefore, the universe has no beginning in time."

For this to work you'd have to make explicit the connection between causation and time. It can only become a sound argument if the gaps in it are filled in. How about:

All events are effects having causes.

Causation is a process requiring time.

Therefore, the universe is an uncaused non-event with no beginning or end in time and Reality extends beyond the world of space-time, causation and events.

This seems to be an improvement. Because the logic is sound we end up where Parmenides did, with an unchanging Ultimate.

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  • The issue with the OP post and answers to the last problem is the same word is being equivocated. Causation and cause are not expressing the same idea. How cause is being used is not even clear. Every even has a CAUSE may express a Beginning or an origin. Causation does not imply origin but one force moving another force to behave a particular way. The example is just poor wording. This shows that almost anything is acceptable as a proposition for some people like the OP allegedly learning logic. There is a million people doing stuff like this mistake and call it logic. – Logikal Sep 5 at 1:59
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It is wrong to experiment on a human subject without consent.

Dr. X experimented on Mr.Z.

Mr. Z consented to this experiment.

Therefore, it was not wrong for Dr. X to experiment on Mr. Z.

This is an invalid argument, none of the premises say anything about experiments on consenting people. Consider this (clearly absurd) argument of the exact same form:

It is wrong to murder people younger than 10.

Adam murdered Beth.

Beth was not younger than 10.

Therefore, it was not wrong for Adam to kill Beth.

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  • You counter example is not identical form of the question. The example on experiments is very clear consent is in rule it is wrong to experiment on a human subject without consent. Then the second premise states consent as well: Mr Z consented to this experiment. Dr X has performed within the rule of consent. Your reasons why this is invalid is wrong. As the problem is written it is not invalid as the rule and the Dr X actions are consistent. If the rule is true and the Dr acts un accordance to the rule we have no issues. One could question the quality of the rule but that is not the point. – Logikal Sep 5 at 2:08
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Consider the one that requires a premise:

Every event has a cause.

No event causes itself.

Therefore, the universe has no beginning in time.

The conclusion is making a claim about time from two premises that do not mention time. Perhaps the implied premise would be Every cause precedes the caused event in time.

For the first four:

  1. This appears to be a valid use of modus tollens.
  2. The conclusion that it was not wrong for Dr. X to experiment on Mr. Z does not seem to follow. All one knows from the first premise are (some) sufficient conditions for when the experiment is wrong, not when it is not wrong. One may paraphrase the first premise as a conditional: If one experiments on a human and the human does not consent, then it is wrong. The antecedent of the first premise is false because Mr. Z consented. That false antecedent makes the first premise true. However, there may be a situation where all three premises are true, but the conclusion might not be true. That might happen if Dr. X did something not mentioned in the premises that would make experimenting on Mr. Z wrong.
  3. This seems valid by Leibniz law or the identity of indiscernibles. By assumption my body has a property of surviving death that is different from properties I have.
  4. This seems like a valid argument by induction. The first premise is the base case for the induction. The second is the induction step. Together they lead to the conclusion about all of Geoffrey's ancestors.
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