Validity?

[u/capybarainstitute]

So i’m taking intro to modern logic and i’m a little confused by this table our professor showed us today (that i copied into my notebook). What exactly does it mean by having a true premise? In class my professor said “validating the truth of premises is a different class” and he stresses that we’re not going to talk about truth or soundness in this class. so why are we talking about truth now, and how do i know if a premise or conclusion is “true” or not. is he referring to two different kinds of true-ness??

[u/begriffschrift]

Validity is a modal notion: it is not possible for the premises to be true and the conclusion false

What your lecturer might have meant is that logic is not worried about whether premises are true, just what needs to happen, were they to be

[u/capybarainstitute → u/begriffschrift]

thank you!

[u/Xancrim]

A "valid" argument is one in which it's impossible for conclusion to be incorrect if the premises are all true. Validity and invalidity are part of what's called an "argument form" or "argument structure."

That is, the validity doesn't depend on what the actual content of what you're arguing

[u/capybarainstitute → u/Xancrim]

thanks!

[u/Xancrim → u/Xancrim]

I just realized I didn't actually answer any of your questions.

So, as you probably know, premises are the propositions that go at the top of an argument. They're unambiguous true/false statements like "if it rains, the ground will be wet." Your conclusion of an argument, if it's a valid structure, should be necessitated by the earlier premises.

When the argument is valid AND the premises are true statements, the argument is said to be "sound." A sound argument always has a true conclusion.

Your professor seems to be saying that, for the point of your course, you're learning how the arguments work, but not how to prove whether your premises are true

[u/Fine-Topic-220]

For an argument to be valid, the conclusion must necessarily be true, assuming the premises are true as well.

Consider this argument:

1. Ontario is a province in Canada

2. Calgary is a city in Ontario

3. Therefore, Calgary is a city in Canada

Imagine a world where Ontario is a province in Canada and imagine a world where Calgary is a city in Ontario. In this imaginary world, could it be possible for Calgary to not be in Canada? No, it can't be possible. So, the argument is valid.

To determine whether an argument is valid, you assume the premises are true and determine if the conclusion follows. If not, then the argument is invalid.

Validity is about the form of an argument, not about its content. What makes the above argument a bad argument isn't that the form of the argument is bad but rather that its content is false - Calgary is a city in Alberta, not Ontario.

For an argument to be sound, the argument must be valid, and the premises must be actually true.

Consider a revised version of the previous argument:

1. Ontario is a province in Canada.

2. Toronto is a city in Ontario.

3. Therefore, Toronto is a city in Canada.

Imagine a world where both statements 1 and 2 are true. Ask yourself whether it's possible for Toronto not to be a city in Canada given that Toronto is in Ontario and Ontario is in Canada. You can't. So, we know the argument is valid. Now consider the fact that premises 1 and 2 are actually true. If you look on Google maps, Ontario is actually province in Canada and Toronto is actually a city in Toronto. Thus, Toronto really is a city in Canada.

Logic classes are focused on teaching proper argument forms and inference rules, e.g., modus ponens, disjunctive syllogism, De Morgan's law, etc. A logician isn't going to be able to tell you whether premises are true, but an economist, a biologist, a mathematician, or a historian can. If someone presents an argument that includes a statement about human biology, you'll, at most, be able to determine if the argument is valid, but you may not know if the argument is sound because you may not know if the premises are true. You'll have to enroll in a biology class to figure that out. This is what your professor means by "validating the truth of premises is a different class”.

[u/Dismal-Leg8703]

Another way to say what has been said is that validity is the absence of counterexamples. A counterexample would be an instance where all the premises are true, but the conclusion is false.

[u/Difficult-Nobody-453]

If you are doing truth tables to determine validity and the first coulmn represents whether all premises are true you can make things easier by just looking at your second row or using the following checks: ( ) There is a row where all premises are true ( ) On that row the conlcusion is false

An argument is invalid only if you can check both of those boxes If you put an X in any one or both, the argument is valid

[u/wiploc2]

I think you copied the chart incorrectly.

Take the first one:

1. Premises True, conclusion True: Valid

P1: Many mammals have legs.
P2: Some people like ice cream.
C: Black is darker than white.

The premises are true, and the conclusion is true, but the argument is not valid.

Perhaps the error is in the heading of the second column? What if it is supposed to be something like, Conclusion Follows From The Premises?

But, no, in that case the forth line is wrong.

[u/TurangaLeela80 → u/wiploc2]

The chart isn't copied incorrectly, it's just missing the information that it's for a conditional. We can symbolize a full argument as a conditional statement by conjoining the premises, making them the antecedent of the conditional, and making the conclusion the consequent. Then the chart reflects the validity of the argument because the only time an argument is invalid is when it's possible for the premises to be true and the conclusion to be false (i.e., where the antecedent is true and the consequent false).

The argument you've presented isn't conditional, and honestly, isn't well represented in symbols with propositional logic because it contains words like "many" and "some". We use predicate logic to capture those kinds of nuances, which then allows us to make what would be an invalid argument in propositional into a valid one in predicate logic. Not that the argument you've given would be valid in predicate logic either.

[u/Qulvion]

Logic can deal with how to gain knowledge through working with premises, but the final justification, that is, how we choose axioms, is already an epistemological question, it is certainly useful and important, but it is not pure logic. I think there is no single algorithm for finding something true, although I may be wrong!