Logically Valid Arguments Flashcards
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What is a logically valid argument?
An argument is logically valid just if there’s no possible situation where the premises are true and the conclusion false.
What is an argument?
For our purposes, an argument is just a sequence of sentences where zero or more are identified as premises and exactly one is identified as the conclusion.
What is a premise?
A premise is just a sentence that we say is a premise. (That’s all there is to being a premise.)
What is a conclusion?
Likewise, a conclusion is just a sentence that we say is a conclusion. How simple is that?
What do we mean by a “possible situations”?
A possibile situation is just a way that the world is or could be. So consider the situation which is as similar to the actual situation as possible except that you are in Havana smoking a fat cigar rather than attending my lecture. This is a possible situation.
Now possible situations are huge things; in specifying a possible situation, you are specifying something as big as the actual situation, with all the trees, leaves, insects and everything. It is helpful to have a proxy for possible situations, something much simpler than a real possible situation.
For our purposes, a good proxy is often an arrangement of shapes in two dimensional space. For evaluating the argument about John and Ayesha, we can pretend that possible situations are just shapes in space. Thinking of possible situations in this way is simpler, and doesn’t ignore anything relevant to this particular argument.
What depends on whether a premise is true or false in our definition of logically valid arguments?
Note that whether a sentence is true or false depends on which possible situation we are talking about. In this possible situation, the first premise is true, the second premise is false and the conclusion is false.
