Basic Logic Concepts

Basic Logic Concepts

Basic Logic Concepts

Readings

Texts

Notes

Synopsis

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

  1. 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.
  2. 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.
  3. 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. This is the conundrum in which Socrates finds himself.

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. It is also, not coincidentally, a solution to Socrates' conundrum.

Today we defined arguments, discussed conclusion markers and premise markers (and their importance!), and we distinguished between inductive arguments, on the one hand, and deductive arguments, on the other.

Although inductive arguments are not our central focus this semester, we took time today to characterize both Induction to a Generalization (IG) and Induction to a Particular (IP). There are other kinds of inductive arguments, but these two highlight the crucial feature of inductive arguments and what distinguishes them from deductive arguments: In an inductive argument the truth of the conclusion is always underdetermined by the truth of the premises taken together because there is information in the conclusion not contained in or determined by the premises. Hence the best we can do is assign probabilities to determine the likelihood (never certainty!) of the conclusion being true given the premises, and it is the job of the mathematical field of statistics to provide tests for these probabilities.

Deductive arguments are otherwise: In a good deductive argument the truth of the conclusion is overdetermined by the truth of the premises taken together. In a manner of speaking, the information expressed by the conclusion is determined by, or contained in, the information the premises propose. Thus, deductive arguments provide the proof or certainty of conclusion inductive arguments necessarily lack.

Next time we will start by characterizing the kinds of deductive arguments, just as we did with the kinds (weak and strong) of inductive arguments, and I'll give you the least bit of modern logic which is still useful and, as it happens, interesting in its own right.