identifying an argument

Question

If topaz is harder than quartz, then it will scratch quartz and also feldspar. Topas is harder than quartz and it is also harder than calcite. Therfore, either topaz will scratch quartz or it will scratch corundum. 

identifying an argument

- is it valid, invalid, strong, weak or not an argument

Answer 1

When identifying logical validity and strength, we can notate it using formal logical symbols:

1. IF "T is harder than Q" (P), THEN "T scratches Q + F" (Q').
2. "T is harder than Q" (P) + "T is harder than Cal" (R).
3. THEREFORE, EITHER "T scratches Q" (Q1) OR "T scratches Cor" (S).

or simplified:

1. IF (P), THEN (Q').
2. (P) + (R).
3. THEREFORE, EITHER (Q1) OR (S).

This can be tough to figure out since there are a lot of different moving parts. The first thing to note is that we can isolate the different propositions into (P), (Q), (Q1), (R), and (S). Secondly, I wrote it as Q1 because it is a sub-proposition of (Q). Another way to think about this is that Premise 1 can be written out as

IF "T is harder than than Q" (P), THEN "T scratches Q" (Q1) + "T scratches F" (Q2).

Just remember that when you put (Q1) and (Q2) together it becomes (Q') or Q prime.

So first we need to figure out whether or not this is an argument. Because there are premises and a conclusion, it is indeed an argument.

The next step is to ask "Is it valid?" By valid, we mean that we assume that all of the premises are true, and if they are all true, does the conclusion necessarily follow? In other words, if all of the premises are true, is there any way for the conclusion to be false? With the argument as given, it is not valid. While we could deduce based off of what we are given more premises that could make the argument valid, such as a premise that says "T is harder than Q" (P), that premise is not given, and so the argument as it is right now is not valid. Depending on how much you have learned in your logic classes, a professor might be asking for logical proofs, or ways to make the argument valid based off of the premises given. However, your question makes it seem like this is not what is being asked of you, so while it is an argument, it is not valid.

If the argument were valid, meaning the conclusion follows necessarily from the premises, then we would ask "Is it sound?", meaning is it strong or weak? Soundness in logic asks whether or not the premises are actually true. In order to find out if the premises are true, you would need to do scratch tests, for example, to see if Topaz actually is harder than Quartz. In order for an argument to be sound, all of the premises need to actually be true. If all of the propositions within Premise 1 were true, but the propositions in Premise 2 were false, then the whole argument would be not sound, or weak.

Hopefully this answers your question, and if you would like me to explain more or in a different way, please let me know!