Speakpigeon said:
Here is the definition you claim as the correct one:
To be more precise, I claim it is
a correct one. There are equivalent, also correct definitions. But let's go with that one - or with your preferred definition; it still works.
Speakpigeon said:
What is the justification given by mathematicians, logicians, philosophers etc. that would support your claim that this definition of logical validity is the correct one.
That is very ambiguous, but I will try to address that:
First of all, I did not claim that mathematicians or logicians or philosophers generally give a justification for a claim that this definition is the correct one. But we need to back up a little bit. First, what is for a definition to be correct? It is to match usage, right?
But surely, the definition is correct for for mathematics, logic, philosophy, and science, because it matches the way "valid" is used in those fields (nearly always, at least; for example, for the case of philosophy; there are more specialized fields of philosophy, logic or math in which a number of different definitions are used, so as to study different types of logic, in some sense of the word). I claimed that it is correct for those fields. Is
that what you want me to provide evidence of? I can do it if you like. For example, for logic, I already provided the link to the Wikipedia article on that, but I can find sources for math, more for logic, sources for philosophy, etc., though I'd rather not do that until you tell me that this is what you are asking, because otherwise there is a risk I spend time finding the evidence and then you will tell me that it is off-topic.
Now, I did provide an argument for why the property of arguments consisting in
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false is very important in mathematics, logic, science and philosophy. When a property of arguments is very important, it is often useful to give it a name. In this case, the property in question is named validity.
Speakpigeon said:
And if you already provided this justification, please remind me in which of your posts you did.
I will remind you that in
this post I provided a good justification as to why the property of
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false is so important in mathematics. I also briefly explained
here why that property is also important in science and philosophy, but let me elaborate: Since science uses mathematics extensively, and validity so defined is so important in mathematics, it is so in science. For example, physics papers are usually full of math, and the same points I made
here for math papers, hold for the vast majority of physics papers as well.
What about philosophy?
Well, philosophers are concerned about finding truth in different settings, and generally, knowing whether an argument has a form such that it is impossible for the premises to be true and the conclusion nevertheless to be false, is very useful indeed. As a matter of fact, and just as in the case of mathematics, a philosophy paper would be rejected if it has a deductive argument that
fails to have the property of
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, whereas at least in the vast majority of philosophical contexts, an argument that does have the property of
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false will only face objections to one or more of the premises - or directly to the conclusion, but
implying that at least one of the premises is false -, but there will not be an objection as to the acceptability of deducing the conclusions from the premises.
Similar reasons hold for logic.
In sum, in the fields of mathematics, logic, philosophy and science, the property of arguments consisting in
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false is very important. Now, when a property is very important in a context, it it often the case that the property in question is giving a name. There are good practical reasons for this; for example, in the specific case of the property of arguments consisting in
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, it is far shorter and less cumbersome to talk about valid arguments and the validity property.
So, in sum, that provides good grounds for giving the property of arguments consisting in
taking a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (or trivially equivalent properties) a name. As it happens, the name in English is "validity" - as you can see by looking at obviously equivalent definitions given in books specialized on those fields -, at least leaving aside some smaller subsets of philosophy, logic or math where other, non-standard forms of logic are studied.
Now, what else do you want? Are you asking whether that definition of validity matches common usage among English speakers with no formal training?
That is more difficult to say, but it seems that validity - like other technical concepts - is one of those concepts in which lay speakers yield to experts in the relevant fields for the definition. But before we get to that, I would like to know what your objections to my previous points in this post are, if any.
If you have objections, I will address them first, before I give more arguments on the matter.
If you do not object to the above, then please let me know, and also let me know what it is that you want me to justify. Is it a claim that the colloquial usage of "valid" matches the concept used in math, logic, philosophy and science? Is it something else?
