* Logic is about reasoning, i.e., about the way we infer one thing from another. * More specifically, logic deals with correct reasoning, and explains why certain forms of inference are correct while other forms are not. That is, it studies the abstract forms, the structures of reasoning that are used in argumentation. * More explicitly, logic evaluates arguments.
But what is an argument?
* In English, the terms 'argument' and 'arguing' are frequently used in a way that is slightly different from the one we'll be using in this class. * Generally we use the term 'argument' to refer to a dispute or disagreement and 'arguing' to refer to the activity of disagreeing. The two ways of using the terms, while different, are not entirely unrelated, for when we are involved in disagreement or dispute, we often try to show that our position is correct by stating evidence to support it. * In dealing with problems of logic and reasoning, the word 'argument' most commonly refers to a set of sentences related in such a way that some of the sentences purport to provide evidence for one of the sentences, without any suggestion of dispute or disagreement. * More specifically, an argument is a set of sentences consisting of one or more premises (the starting assumptions) and a conclusion, which is supposed to follow from the premises. * A sentence (or declarative sentence) is a statement that can be true or false. * Intuitively, a good argument gives the premises as reasons for believing the conclusion.
Varieties of arguments
* Rather artificially, arguments where the premise don't fully guarantee the conclusion, but make it likely or probable are called inductive (or even abductive) arguments. That is, inductive or abductive arguments only provide a partial degree of support for the conclusion (e.g., empirical sciences, etc.) * By contrast, arguments where the truth of the premises is supposed to provide full support for the truth of the conclusion is called a deductive argument. For a valid deductive argument, there's no way for the premises to be true and the conclusion false. Or: the premises strictly imply the conclusion. * In this course, we will be concerned only with deductive arguments.
Some examples of deductive arguments
* All men are mortal.
* Socrates is a man.
* Therefore, Socrates is a mortal.
* If I eat McDonald's for lunch, then I'll be sick.
* I ate McDonald's for lunch.
* Therefore, I will be sick.
When is an argument valid?
* When an argument has the property that the truth of the premises absolutely guarantees the truth of the conclusion, we say the argument is valid, i.e.: there is no possible way the premises could all be true but the conclusion be false. * An argument is valid if and only if it is an instance of a valid form.
When is an argument invalid?
* A deductive argument is invalid if it is possible for all its premises to be true and its conclusion false. * Note: Don't confuse the everyday meaning of validity with the technical notion. An argument is valid when it has the proper form, not when the argument is a "good" one or has intuitive force.
Given the premises:
* All fish are whales.
* Mr. Gloopgloop is a fish.
and the conclusion:
* Therefore, Mr. Gloopgloop is a whale.
This argument is valid, because there is no way for the conclusion to be false if the premises are true. The reason that all the previous arguments are valid is because they all follow the same form:
* All X are Y
* p is an X
* Therefore, p is a Y.
An argument is valid also if it is not sound
* The truth or plausibility of the premises does not matter regarding validity! * Why is it valid? Because there can't be any...