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The book I got this question from is "logic, the laws of truth" by Nicholas j.j smith.

"Necessary truth preserving" (NTP in the book) is defined as the property that an argument has when it is impossible for the premises to be true and the conclusion false.

Now an argument is valid if and only if

  1. The premises cannot be true while the conclusion false (it is NTP).
  2. The form or structure of the argument guarantees that it is NTP.

the 2nd criterion for judging ( whether and argument is valid or not) does not make sense to me.

and the answers of the exercises ( on determining validity), imply that an argument being NTP is enough for being valid and I don't really see 2nd criterion for judging ( whether and argument is valid or not) being needed to get the correct answers.

the exercise:

1)All dogs are mammals. All mammals are animals.


All dogs are animals.

2)All dogs are mammals All dogs are animals.


All mammals are animals.

the first one is valid and second one isn't, but we can find the answers without knowing what validity is/ equating validity with NTP.

I hope I'm clear enough, I just read this from the book, so i couldn't articulate my thoughts very clearly.

  • The subtlety is in the nature of "necessity". It may be impossible for something to be red all over when it is green all over, but this necessity does not result from the form of the argument. On the other hand, it is impossible for something to be red and round without being red in particular, just in virtue of logical form. See three main conceptions of validity. – Conifold Apr 2 at 20:40
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The author gives an example (page 15) of an argument that is NTP but not valid:

  1. The glass on the table contains water.

    ∴ The glass on the table contains H2O.

He then says (page 17):

In the case of (7), to see that the premise cannot be true while the conclusion is false, we need specific scientific knowledge: we need to know that the chemical composition of water is H2O.

So, the argument is NTP: there is no way for the premise to be true and the conclusion false because water is necessarily H2O. But the argument is not NTP in virtue of its form. The form of the argument is just: 'A contains X. Therefore, A contains Y', which is not valid.

He says on the same page:

So, some arguments that are NTP are so by virtue of their form or structure [...] Other arguments that are NTP are not so by virtue of their form or structure: the way in which the argument is constructed does not guarantee that there is no way for the premises to be true and the conclusion false. Rather, the fact that there is no such way is underwritten by specific facts either about the meanings of the particular terms in the argument [...] or about the particular things in the world that these terms pick out (e.g., water—its chemical composition is H2O), or both.

Other examples can be constructed using mathematical statements. For instance: 1 + 1 = 3; therefore, 2 + 2 = 4. There is no possibility in which the premise is true and the conclusion false because the premise is never true. So, the argument is NTP. Nevertheless, this is not because of the form of the argument, but only because of the nature of mathematical statements. So, the argument is not valid in the sense defined here.

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I've just tried skimming over the book and I can see how it's confusing.

In many accounts being truth-preserving means that if the premises are true, then the conclusion must be true.

On such accounts, it is often a synonym for validity -- because validity means that if the premises are true, then the conclusion must be true.

Smith is trying to be more precise and spends quite a few pages working on a distinction between his NTP and validity. I think the easiest way to get it is this: NTP includes ways of being truth preserving that are non-formal.

By formal, I mean things that follow based on rules ( a AND b is TRUE when a is TRUE and b is TRUE and never otherwise).

But there are other things that are truth preserving:

Clark Kent is in Boston. Therefore, Superman is in Boston.

This is also 'truth-preserving' since we know Clark Kent = Superman, but it's not formally valid because we have not supplied this within any formal rule by adding a biconditional or something to that effect.

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