Basic Logic Concepts

Readings

Texts

• Anthony Weston, "A Rulebook for Arguments", 2nd ed. (optional)

Notes

• Example Informal Arguments
• Valid Argument Forms
• Basic Logic Terminology
• Extracting Arguments

Synopsis

We began today with a reminder that our investigations have revealed that hard moral cases, aka moral dilemmas, are problematic because:

1. There are at least two and possibly more than two alternative courses of action;
2. The alternative courses of action are incompatible in the sense that one cannot take one of the courses of action by taking another--they are genuine forks in the road, as it were;
3. The alternative courses of action are consequential in the sense that lives, livelihoods, limbs, etc. are at stake;
4. The alternative courses of action are forced in the sense that one of them must be chosen--doing nothing is still a course of action;
5. There are seemingly equally good reasons for each of the alternative courses of action.

The problem is not just that of weighing the relative merits of reasons for and against a given course of action. It runs deeper than that. For we are inevitably led to asking about the reasons for the reasons. That is, we can only contrast and evaluate reasons pro and con once we fully understand the justification, in turn, for those reasons. What reasons, in other words, are there for and against the reasons themselves? How in a principled way to determine whether a reason is a good reason, and thus should count in our moral deliberations, or a bad reason, and thus should be discarded from our moral deliberations?

We face much the same challenge Socrates did in responding to the early charges he thought poisoned Athens against him.

Socrates starts out by suggesting that he is accused of impiety and corrupting the youth, which are the more recent charges. Much earlier Socrates was charged by popular opinion with i) busying himself with matters in heaven and under the earth and ii) making the weaker argument seem the stronger. The first of these earlier charges amounts to being accused of having interests we today would call scientific. The second charge amounts to the claim that he manipulates his audience to embrace arguments they really shouldn't. Socrates himself admits he can offer no response to this second charge. Why not?

You see, the only way he has to respond to this second charge is to give an argument in his defense that he does not make the weaker argument seem the stronger (nor, presumably, vice versa), but what then of the very argument he might mount 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, since that very argument would be yet another demonstration--confirmation, if you will--that he does indeed make the weaker argument seem the stronger!

Enter logic.

Aristotle, Socrates' student's student--Socrates was the teacher of Plato, who was the teacher of Aristotle--brilliantly discovered that we can reason about reason itself so as to develop tools for objectively evaluating reasons.

Now, 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 just one or two lectures; it's the best we can do in a course of this nature, nonetheless.

That is to say, I do not expect, require, demand, or even believe that you understand every concept from today's 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 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.

There are a few facts about arguments which are crucial. If you don't understand them at first, you should at least memorize them.

1. 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 white raven!)
2. In a valid deductive argument, the conclusion must be true if the premises are all true.
3. 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.
4. If the conclusion of a valid deductive argument is false, at least one of the premises must be false.
5. 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.
6. 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.
7. A deductive argument is valid if it has the form of a valid argument; validity is a formal or syntactic feature of arguments.
8. If a deductive argument is sound, then we know that its conclusion is true.
9. If a deductive argument is unsound, we know that it is either invalid, or it has at least one false premise.
10. 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.

Now for most students, this is a highly abstract and difficult discussion. It is, as I say, the most challenging material we encounter this semester (as one might well expect, given its foundational nature.) I will do my level best to connect all the dots while I develop as best I can the relevant conceptual apparatus we will be employing. At the same time, it is crucial that you i) do your best to follow the discussion and, simultaneously, ii) be patient with yourself as you struggle to understand it. Again, most--maybe all--students struggle. Being patient with yourself in part demands setting aside once and for all the common fear that everyone else in class understands while you alone do not. It also requires that you recognize some concepts take longer to grasp than others, but that eventually you can and will master this material.

Next time we will examine the nature of theory, both scientific and ethical, and we will develop standards of evaluation (using the facts of logic) which we can employ to determine whether a proposed ethical theory should be rejected.