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The Beauty and Utility of Logic
by Joel Marks
One of the joys of philosophy is logic. That there is such a structure underlying thought is as amazing and delightful to me as, I imagine, the amenability of the physical universe to mathematics is to a scientist. And that both realms can be codified with just a handful of symbols and formulae is but the surprising frosting on this most improbable cake. I will leave the technical side of the matter to the textbooks. Here I would like to highlight some of the remarkable properties of reasoning. I do distinguish reasoning from logic, by the way, the former being the more inclusive category. But the story of the one is also the story of the other.
Reasoning, as I comprehend it, is the providing of reasons for claims or beliefs. But of course not just any reasons will do; one seeks to provide good reasons. Extraordinary Fact Number 1 about reasoning is that the notion of a good reason can be fully explicated in the abstract, such that the potentially infinite number of good and bad reasons for anything whatsoever can be sorted definitively.
To explain this, it helps to employ the concept of an argument. The kind of argument I have in mind is not the one where two people are having a row. Rather, it is an instance of giving a reason for something, as in, “Why should I believe what you have just told me? What’s your argument?” Any argument contains two components: premise or premises, and conclusion. The former constitute the reason being given by somebody to believe the latter. “Most older women should not hesitate to undergo long-term hormone replacement therapy (HRT) for serious postmenopausal problems [that’s the conclusion] because [here are the premises] all available research suggests that such treatment often alleviates such problems and even enhances women’s health overall.” That is an argument.
Now we can pose the prior problem more precisely: What makes an argument a good one? Answer: The argument satisfies two conditions. One condition is that all of the premises are true. It wouldn’t be much of an argument if it were based on falsehoods, would it? Thus, if there were little evidence that HRT helped alleviate hot flashes and insomnia or helped preserve bone strength and mental acuity in the relevant group, then the reason given for undergoing HRT would be unsound.
But it is the second condition where logic proper enters the picture. For suppose the premise or premises of an argument are all true: Is the argument now a good one? Not necessarily. And that is perhaps the most important lesson logic has to teach us. In the language of logic: Does the conclusion follow from the premises(s)? For even if the premises of an argument were all true, its conclusion could be flat-out false. But reasoning is surely in the business of wanting to establish true conclusions.
In our example, let us suppose that the year is 2001 and a doctor and her client are considering the advisability of HRT. In 2001 the premises were true. But in fact – as became known in 2002 – the conclusion was and is false! Therefore (if I may reason about reasoning) it must be the case that the conclusion of the argument about HRT does not follow from the premises. As logicians says, the argument is invalid.
The general reason that justifies this conclusion about that argument is none other than the fundamental principle of logic, to wit: A false conclusion cannot follow logically from true premises. In other words, if all of the premises of an argument are true, then, if the argument is valid, the conclusion must also be true. That is the very meaning of validity, which is the central concept of logic.
In the particular argument under discussion, the invalidity can be accounted for in this way. Prior to the most recent large long-term experimental investigation of HRT, the women who had been studied were those who had undertaken HRT at their own initiative or their doctor’s recommendation [this being the so-called experimental group], and those who had failed to do so [this being the control group]. But this means that members of the former group were likely to be the more informed, hence likely wealthier, hence likely healthier (there being presumed correlations among those variables). Hence, as a sheer artefact of the selection process, the HRT group would turn out healthier than the non-HRT group!
The latest study confirmed this possibility by recruiting equally healthy volunteers for random assignments to the HRT and non- HRT groups. Unfortunately, this has now made one of the original premises false; for today it can truthfully be asserted that the available research shows that HRT does not have a benign influence on women’s health overall. In fact, it increases a woman’s chances of heart attack, stroke, breast cancer, and blood clots.
But to conclude my argument for the utility of logic: Even in 2001, when that premise was true, logic alone would have told us that the conclusion did not follow and hence ought not to have been relied upon as an established fact, suggesting that more research needed to be done (which is exactly what happened). Thus, logic can reveal to us what we do not know (and point us in the direction to resolve the question). That is just one way in which logic is useful. It also enables us to decide whether certain hypotheses are worth the bother to test in the first place … and to uncover assumptions … and to generate an infinity of new knowledge from already existing knowledge. It also applies equally to mathematics as to language. Each of these benefits deserves an essay (or a book) in its own right. But the long and the short of it is: Logic is great!
(By the way: The latest research findings re HRT do not establish that women should avoid it. Logically that simply would not follow! For example, the actual percentage increase of health risk for women in general who undergo HRT, while statistically significant, is still tiny. Each woman and her doctor should therefore assess the relative advantages and dangers.)
© Joel Marks 2003
Joel Marks is Professor of Philosophy at the University of New Haven in West Haven, Connecticut. www.moralmoments.com.