Convincingness, Truth, and Validity



Our definition of an argument:
An argument is a string of declarative sentences intended to convince someone of something.
So: to be a good argument is to be a convincing argument (for a typical rational person).




The two ingredients for being a convincing argument:
1. The premise(s) must be true (or at least: accepted as true).
2. The argument (as a whole) must be valid.



A valid argument is an argument such that, in any possible situation where the premises are true, the conclusion is also true.




In other words: a valid argument is an argument where:
  • true premises are always accompanied by a true conclusion
  • true premises guarantee a true conclusion
  • it's impossible to have true premises without having a true conclusion
(These are all just different ways of saying the same thing; so pick whichever definition of "valid argument" you like best.)


Validity (being valid) is just a more formal version of the ordinary concepts of following from or having sufficient grounds for a claim. If an argument is valid, the conclusion follows from the premises. Likewise, if an argument is valid, the premises provide sufficient grounds to establish the conclusion.



If it's even possible for an argument to have true premises without having a true conclusion, then that argument is not valid – it’s invalid.

So a possible situation where the argument has true premises but a false conclusion is all it takes to show that the argument is invalid. We call such a situation is called a validity counterexample.




Validity counterexample: a possible situation where the premises of an argument are true, but the conclusion is false.



So a validity counterexample is a possible situation which reveals the invalidity of the argument.




Keep in mind: a valid argument is valid always and everywhere.  An invalid argument is invalid always and everywhere.  It makes no sense to say that an argument is invalid in one situation, but valid in another – if it's valid, it's always valid, and if it's invalid, it's always invalid.

On the other hand,, the truth of some sentence (in the argument) can change from one situation to another. A sentence like "Today is Thursday" or "It's raining" can be true in one situation (a Thursday, or a rainy day), but false in some other situation (a Friday, or a rainless day).

And remember: an argument is valid or invalid, not true or false.

A sentence is true or false (in a given situation), not valid or invalid.




beakley > 1900 > informal logic
 
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