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Consider arguments of the following form for some proposition P:

If P were the case, I would know that P.

But I don't know that P.

Therefore, it is not the case that P.

I am wondering what kind of propositions P will make the first premise true.

For example, in the below argument it is true.

If I am infected with coronavirus (and tested for it), then I would know that I am infected with coronavirus.

But I do not know whether I am infected with coronavirus.

Therefore, it is not the case that I am infected with coronavirus.

However, in the next argument the first premise is false.

If aliens exist, then I would know that aliens exist.

But I do not know whether aliens exist.

Therefore, it is not the case that aliens exist.

What kind of P will make this type of premise false?

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    Re your first example's premise "If I am infected with coronavirus, then I would know that I am infected with coronavirus.", are you sure it's valid? Many people were never aware of they're infected with Covid if not tested positive...
    – Double Knot
    Sep 24 at 5:40
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    Williamson calls propositions whose truth makes them known to us "luminous", see IEP. For example, propositions about our own phenomenal (felt) mental states (like "I am cold", "I am thinking", etc.) are traditionally considered luminous, although Williamson himself disputes it. In all other cases, there is room for doubt, covid tests do return false negatives, for example, anything we observe can be an illusion, and any reasoning can contain subtle errors we overlooked.
    – Conifold
    Sep 24 at 11:03
  • Your title question asks about it being true, but the last sentence asks about it being false. (Monty Python sound of man being flung through the air)
    – Scott Rowe
    Sep 24 at 14:16

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In logic, validity concerns merely the formal structure of an argument where, if the premises were true, the conclusion must also be true (or, an argument is invalid if it was possible for the premises to be true yet the conclusion to still be false).

Your first argument is of the form:

  • If P then Q
  • ¬Q
  • Thus, ¬P

Which is simply modus tollens, and is a valid argument, regardless of what is plugged in as P and Q. The issues with the second and third arguments are not in their validity but in their soundness. That is, at least one of the premises are false, therefore the argument fails or is unsound. In the case of the third argument, premise one is false (aliens might exist in a manner where we are unable to know about them with modern technology), thus the argument fails despite being valid (it is unsound).

Validity concerns merely the formal structure of an argument, whereas sound deductive arguments are both valid and have true premises (and thus, we then are able to state that the conclusion is also true).

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