Basic Logic Concepts
I began today by revisiting Plato's Apology, because there is a feature of Socrates' defense which raises an important question for us.
Socrates, you may recall from last time, is in a bind. His friend returns from asking the Oracle at Delphi, "who is the wisest man in Athens" with an astonishingly un-oracular, straightfoward answer: "Socrates is the wisest man in Athens". Yet Socrates, a humble stone-mason who enjoys discussing various issues with friends, cannot picture himself the wisest man in Athens. It is preposterous. It is unbelievable. It is, to his mind, absurd.
So Socrates sets out to prove the Oracle wrong. He searches out all the wisest men of Athens--the politicians, the poets, and the craftsmen--to determine once and for all who is the wisest man of Athens. In questioning each of these wise men, Socrates discovers, much to his dismay, that
- Those who think they are wise, the politicians, don't really have the wisdom to which they claim. Upon examination Socrates learns that their supposed wisdom was a kind of conceit, wherein they deceived even themselves into thinking they had wisdom they really didn't.
- Those who produce wise and insightful things, like the poets, aren't in any better a position to understand the wisdom of what they've done than anyone else. Indeed, they themselves will frequently disavow any special wisdom about their own work.
- Those who make things that require wisdom--the craftsmen--do possess wisdom appropriate to their trade or craft, but then make the mistake of pretending that that wisdom carries over to everything else. So they end up being almost as much the pretenders to wisdom as the politicians.
To be sure, those who believe themselves wise but who are not, in fact, wise, are not lying, exactly. A lie you must know to be false, even as you tell others it. No, all of these people actually believe they know much more than they do not, in fact, know.
It dawns on Socrates, after much thought, that this is what the Oracle of Delphi meant: Socrates was the wisest man of Athens not because he knew more than anyone else, but because unlike everyone else, he alone knew that he did not know.
The start of wisdom, then, is understanding that what you think you know, you may not, in fact, know. It is this sense of grasping that you do not know what you think you know which is characteristic of philosophy. Philosophy starts in wonder. The ancient Greek would call it aporia, which is frequently translated as 'perplexity'.
Philosophy, if it is done well, sets us back on our heels. It startles us into recognizing that what we take for granted we know may not, or sometimes could not, be the case. It unsettles us and makes us take stock and work hard to gain what we think we lost, but never really had in the first place: Genuine understanding.
The upshot, then, is that we should welcome perplexity and recognize that it is not the end of wisdom: It is the beginning.
Thus far review: Recall, however, that Socrates starts out by suggesting the the charges by Meletus (impiety and corrupting the youth) are the more recent charges. Much earlier Socrates was charged by popular opinion with i) busying himself with matters in heaven and the earth and ii) making the stronger argument seem the weaker, and the weaker seem the stronger. We already discussed the first of these earlier charges when we took up the presocratic transition to naturalism. We said nothing about the second of the earlier charges, except to point out that Socrates is really in a bind with this one.
The only way he has to respond is to give an argument in his defense that he does not make the weaker argument seem the stronger (nor vice versa), but what then of the very argument in his defense? Put another way, if you suspected Socrates on this score, you wouldn't trust any argument he gave--particularly an argument that he does not make the weaker argument seem the stronger.
Given the resources that were available at the time, there's not much he could say. Plato's pupil Aristotle, however, would come to recognize the importance of developing a theory of arguments by which their strength may be objectively established. We call this theory logic.
I proceeded today, then, to introduce the foundation for the course - logic. Logic is foundational in the sense that virtually everything we do in the course involves the presentation and critical assessment of arguments. Of course, it is completely unfair to expect students to understand logic after a single lecture; it's the best we can do in a course of this nature, nonetheless.
I do not expect, require, demand, or even believe that you understand every concept from this lecture. At best, the terminology of arguments is "in the air", as it were, and definitions are available for your repeated review. What I have discovered from previous classes is that once I start using the terminology on a regular basis, students steadily catch on to what is meant. If you feel completely lost, take heart: There are many, many others feeling the same way at this point.
Eventually you will be able (I promise!) to
- Explain the distinction between Truth-Tropic and Truth-Phobic Language.
- Explain the distinction between inductive and deductive arguments.
- Explain the distinction between a weak and a strong inductive argument.
- Explain the distinction between invalid, valid, and sound deductive arguments.
As we saw, validity and soundness are particularly slippery concepts, so this last will definitely take some work.
In any case, there are a few facts about arguments which are crucial. If you don't understand them at first, you should at least memorize them.
- It is always possible for the conclusion of an inductive argument to be false, even when all the premises of the argument are true. (Remember the silly white raven!)
- In a valid deductive argument, the conclusion must be true if the premises are all true.
- If one or more of the premises in a valid deductive argument are false, it does not follow that the conclusion is false. The conclusion may still be true; the argument just doesn't give us any reason for thinking that it is true.
- If the conclusion of a valid deductive argument is false, at least one of the premises must be false.
- A valid argument may have all true premises and (necessarily) a true conclusion, a false conclusion and (necessarily) one or more false premises, false premises and a false conclusion, or false premises and a true conclusion.
- The only situation in which the actual truth or falsity of the propositions in a deductive argument tell us anything at all about the validity of the argument is when the premises are all true but the conclusion is false: we then know that the argument is invalid. The validity of an argument is completely independent of the actual truth or falsity of the propositions in the argument in the sense that one can never find out whether the argument is valid based on the actual truth or falsity of the propositions in the argument.
- A deductive argument is valid if it has the form of a valid argument; validity is a formal or syntactic feature of arguments.
- If a deductive argument is sound, then we know that its conclusion is true.
- If a deductive argument is unsound, we know that it is either invalid, or it has at least one false premise.
- Critically assessing deductive arguments requires that we first find out whether or not the argument is valid and then find out whether or not the premises are all true. If the argument is invalid or has at least one false premise, then it follows that we have no reason to think that the conclusion is true; it does not follow that we have any reason for thinking that the conclusion is false.
There are other facts, of course, but these are the most important ones for you to grasp from this lecture.