Jacinto asked:

"An argument is based on the principle of inferential necessity." Discuss.

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The first question you have to ask is what are arguments for. An argument is not just a structure
made of sentences or strings of symbols. We make use of these structures. They have a point.Text
books on logic often forget this rather elementary observation. They tend to assume — or at least
give the reader the impression — that we all know what an argument is for, and the only question is
what is the difference between a good argument and a bad one.

We have to narrow this discussion somewhat. It is not true that all 'arguments' are based on the
principle of inferential necessity. Some arguments are probabilistic, representing the conclusion as
the most plausible inference to draw, rather than an inference that one cannot fail to acknowledge
when it's pointed out to you, on pain of irrationality.

The purpose of an argument is to persuade.Persuading someone involves finding something that
they accept, or are prepared to accept, and then showing that, if they accept that, then they have no
choice but to accept the thing you want them to accept. There's the 'necessity'.

I can be wrong in thinking that the conclusion follows from the premisses. In that case, I was wrong to
allow myself to be persuaded. I made an error of judgement. The argument was invalid. To
deliberately use an argument which looks valid but you know is invalid in order to persuade someone
is sophistry.

In terms of logic, a valid argument is one where it is impossible for the premisses to be true and the
conclusion false. If you are the person doing the persuading, you don't have to believe the premisses.
Or you might be unsure whether the premisses are true or not. (It is perfectly acceptable to point out
to someone the logical consequences of their beliefs, even if you do not hold those beliefs yourself.)
The only thing that matters is that anyone who does believe those premisses has got to accept the
conclusion. In every possible world in which the premisses are true, the conclusion is also true. If, on
the other hand, you are the person looking to be persuaded, it is still valuable information to know
what you would be committed to believing, if you ever came to believe the truth of the premisses.

That is only half of it. The question to raise now is how a string of sentences or symbols can possibly
perform this seemingly magical feat. In order for it to be the case that 'every possible world in which
the premisses are true, the conclusion is also true', there must be something that accounts for this,
either in the structureof the argument or the contentof the propositions expressed. Logic text books
will tell you all about the structure of logically valid arguments. A logically valid argument is valid in
virtue of its formalone. No matter what terms you substitute consistenly for the non-logical parts, you
will never get a case where the premisses are true but the conclusion is false. Arguments which are
valid in virtue of content are more problematic. This is where you will find virtually all of the arguments
of philosophy.

Geoffrey Klempner