Wednesday 9/4

Basic Logic Concepts





By way of review, I pointed out today that our investigations last week revealed that hard moral cases, aka moral dilemmas, are problematic because:

  1. In a moral dilemma we find apparently equally good reasons for alternative, incompatible, and consequential courses of action.
  2. The existence of such competing reasons makes us unsure how to proceed, particularly when the stakes are high.
  3. Competing reasons raises the difficult question of how we should go about adjudicating between them.
  4. The challenge of assessing competing reasons in an unbiased, principled way can even make us wonder whether there really is a morally right course of action in the first place!

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 are the arguments, in other words, for and against the reasons themselves? Presumably, reasons pro or con will have merit to the extent that we can give good arguments for them. How, though, do we evaluate these arguments?

Enter 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 one or two lectures; 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 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 crow!)
  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.

To be sure, this is conceptually challenging material. The distinction between the factual correctness of an argument and its formal correctness is particularly difficult. We're so accustomed to thinking in terms of factual correctness (truth of the premises) versus factual incorrectness (falsity of the premises) that the discovery that arguments can also fail in being formally incorrect&emdash;in that the conclusion does not follow from, deductively, the premises regardless of their truth&emdash;blindsides us. Before despairing, however, please recognize that this is likely the most conceptually challenging material you will encounter this semester&emdash;challenging, but necessary. It gets easier as we move forward and see these distinctions applied over and over again.

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.