I thought I would attempt the first draft of a college-level textbook, writing it directly into my blog, bit by bit. Feedback and recommendations in the thread comments are welcome, either encouraging or critical. The first chapter would be a mini-course in critical thinking for writers. To have a look at Concept 1.5, click here; for Concept 1.4, click here; for 1.3 here; 1.2 here; 1.1 here.
Lesson 1.6. Distinguishing the logically possible from the actual. As the three laws of logic suggest—and the early Wittgenstein observed—what we can say meaningfully about the world consists of an infinite number of logically possible sentences, but never impossible ones. The penguin flew to the moon is a logically coherent and meaningful sentence. Whether it is actually true or not is another matter. The penguin flew over and under the moon at the same time, however, is not a logically coherent sentence. It violates the law of non-contradiction, and you can’t even visualize it. The penguin sort of flew to the moon and sort of didn’t is also not a logically coherent sentence. It cannot be visualized. It violates the law of the excluded middle. The car is in the garage and on the street is also not a coherent sentence. I’m a married bachelor is not a coherent sentence. You cannot visualize, let alone think, such sentences. Thus, when we say that something is not, strictly speaking, logical, or not logically possible, we are speaking of words in relation. If the words make no sense in relation, then they cannot correspond to any actual state of affairs in the world itself.
Making distinctions is often central to reasoning, and so one way to think about the merely meaningful sentence in contrast with the factual sentence is to distinguish the logically possible from the physically possible, the technologically possible, and the actual. Something might be logically possible–a penguin flying to the moon–but not physically possible. When we test penguins’ ability to fly, we find that, though they are birds, they in fact can’t actually fly at all, let alone to the moon. It may one day, however, be technologically possible to put rockets on the backs of penguins that are powerful enough to propel them to the moon. We might also one day engineer bionic or robotic penguins that can fly over an survive on the moon. One day, perhaps, the moon might be terraformed (made earth-like, with an atmosphere). You may thus judge that it may be plausible—or even probable—that technology will one day make it possible for biological penguins to fly around and live on the moon. But that still doesn’t mean it will actually happen. What is plausible, possible, or probable does not always become actual. And if you put rockets on the backs of bionic penguins, we run into disputes over definition: is a bionic penguin with a jet pack and capable of surviving on the moon still a penguin?
We also might distinguish the logically possible from the actual in a still more fine-grained way, holding up a logically possible proposition for scrutiny from the vantage of a continuum, gray-scaling it. Bacterial life on Mars may thus be deemed:
possessing even odds
probable (possessing better than even odds)
Another example: someone might claim—“On the dark side of the moon is an advanced alien civilization from another galaxy, hiding”—which is logically possible, but how plausible is this? One might also make other distinctions. Observe, for instance, this claim: There has been the evolution of another planet in the observable universe that looks almost exactly like our own. It’s logically possible, but it would seem to be highly improbable. Yet, because of the vast extent of time and space involved, it may nevertheless be deemed likely–or even inevitable. If the universe is infinite in space and time, it might even seem to make such a claim logically necessary.
Deductions, inductions, and abductions. With logical possibility and the three laws of thought or logic stabilizing our words in their definitions and our sentences in their coherences, we can move further over the bridge of logical possibility (the many things contending for the truth concerning a matter) to truth (that one thing that is actually the case). We can do this by evaluating sentences (claims) through deduction, induction, and abduction. Two of these methods for getting at the truth of matters are ancient, going back to Plato and Aristotle, and the third (abduction) is more recent, going back to the mathematician and philosopher Charles Sanders Peirce (1839-1914).
Deduction and induction are grounded in the syllogism, which is two premises supporting a conclusion. Abduction is grounded in criteria and data evaluation, reasoning one’s way to the best explanation concerning a matter via experience or the scientific method. All three–deduction, induction, and abduction–are easy to learn and easy to remember, both as to what they are and what distinguishes them. The classic example of a deduction is the following:
[First premise] Socrates is a man. [Second premise] All men are mortal. [Conclusion] Therefore, Socrates is mortal.
In other words, if the two premises in a deductive syllogism are true, the conclusion is 100% certain. Socrates is indeed a man; all men are indeed mortal; therefore it’s 100% certain that Socrates is mortal. It must be the case.
By contrast, induction concerns conclusions that are less than 100% certain:
Socrates has a runny nose this morning. It’s allergy season. Socrates may have an allergy.
Again, induction deals with conclusions that have some degree of plausibility or probability attached to them, and so is distinguished from deduction, which deals with 100% certainties. And abduction takes induction further, brainstorming possibilities and ranking them:
Some logically possible theories that might account for Socrates’s runny nose are the following: allergy; a cold virus; psychosomatic illness; the devil; a side effect of medication; an invisible gremlin tickling Socrates’s nose with a tiny, invisible feather. For a variety of good reasons, I dismiss some of these as ludicrous, others as unlikely, and therefore choose allergy as the most likely, best explanation.
In other words, abduction is reasoning to the very best thesis or explanation. In trying to get at the truth of a matter, you don’t want just any logically possible induction or hypothesis that accounts for the facts surrounding it. Instead, you want to lay out your options and reason your way, both logically and empirically (that is, experientially), to what appears to be the best hypothesis. Abduction is attentive to new data, seeking to reconcile it to what one already thinks one knows (one’s background knowledge).
Writing 1.6.1. Describe in your journal a state of affairs that is logically possible, but not yet actual, and appraise how plausible you think it is that it will come to pass or be. (For example, the end of war over the next century; the prospect for an alternative energy economy to evolve over the next three decades, etc.)
Writing 1.6.2. Write a deductive syllogism and an inductive syllogism (two premises accompanied by a conclusion). Recall that, with a deductive syllogism, if the premises are true, then the conclusion is 100% certain, but with an inductive syllogism, there is only a possibility that the conclusion is true. (Socrates will die vs. Socrates probably has a cold).
Writing 1.6.3. Generate a list of plausible inductions surrounding a question (either an imaginative question or a factual one), and reason your way to what you regard as the best or most important induction about it. In a paragraph, discuss your conclusion, and why you see it as the best answer to the question. Question examples: Why are dogs preferred to birds as pets? How might my life turn out if I change my major from biology to art? If we ever detect a radio signal from an alien intelligence, what will most likely be the chief consequence for the course of the human decade after the discovery?
Writing 1.6.4. Write some sentences that clearly violate the laws of logic and think about what it is, exactly, that makes them either impossible to visualize or to think.
Writing 1.6.5. Write a paragraph in which you describe something that might be logically possible, but which you take to be physically impossible or technologically impossible, and explain why. For instance, imagining a person moving from one side of our galaxy to the other side of our galaxy within a single second is logically possible, but is neither physically nor technologically possible because to do so would violate the speed of light, the fastest thing in the cosmos (light travels at 186,000 miles per second; no human can travel faster than the speed of light).
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