The Non-sequitur

Or, The End of All Logic as We Know It!

posted by SES

In the world of fallacious argumentation, the non-sequitur is the father of all fallacies. It simply means “it does not follow.”¹ That is, the conclusion does not follow from the preceding premises or reasoning. Given this broad scope, you might think, every invalid argument should fall under this. Indeed, it is popularly used for just about any fallacious argument. Some logic textbooks do not even mention it.

However, I remember my logic teacher warning us about this. Sometimes if a student can’t figure out what is wrong with an argument, the temptation is to just write “non-sequitur” for the answer. But technically, and especially on your logic exam, this is incorrect. It should only be applied to or used for arguments that commit a certain informal fallacy. This helps distinguish it from other informal fallacies that may exist as well as formal fallacies that may be present. What is the difference? Informal fallacies are errors in clarity or soundness of the reasoning process. Formal fallacies are errors in the way an argument is put together, especially the terms.

Consider the following:

1) Angels are immortal.

2) Christians are immortal.

3) Therefore, Christians are angels.

This argument does not follow, but commits a formal fallacy. Among other problems this is an Illicit or Undistributed Middle. That is, the middle term is not distributed. . . . I need to stop here since this blog series only concerns informal fallacies. Don’t worry; you might not be able to identify these until you take the whole course on Logic that covers formal argumentation and corresponding fallacies.

But consider this one:

1) Angels don’t sleep.

2) I can’t fall asleep.

3) Therefore, angels are keeping me awake.

Yes, this is a non-sequitur. That is the conclusion does not follow from the premises.

How about this one:

All churches are buildings.

Therefore, all buildings are churches.

No sorry, this commits a formal fallacy . . .

Again, consider this one:

I hate going to church.

Therefore, God does not love me.

Yes, that does not follow and is a non-sequitur.

You might be thinking, “We could do this all day, right?” You are right. “Is there anything else to this non-sequitur?” Yes, how about what some have suggested is the destruction of all logic and reasoning as we know it! And for that matter all the subjects of study that rely upon it. Got your attention? Maybe you won’t need to take that final exam after all.

Is the Non-Sequitur Fallacy the End of Logic?

Consider the following valid formal argument:

1) All men are mortal.

2) Socrates is a man.

3) Therefore, Socrates is mortal.

Does this argument commit a fallacy? John Stewart Mill (1806-1873) would point out that this argument either commits petitio principii or is a non-sequitur. What?! Yes, Mill would ask, “How can anyone assert all men are mortal without already knowing about Socrates (being mortal)?” Hence the proposition “all men are mortal” presupposes a knowledge of the particular instance (Socrates) asserted. It tells us in the conclusion what we must already know for the first premise to be true. So, it is circular. I have to admit I have never met Socrates.

But even if somehow I could get over the circular problem, I am faced with this: I (and probably you) have not met or do not know every man, that is, human being that has ever existed past, present, and future. How could anyone assert the statement “all men are mortal” without knowing about every individual man? Therefore, it does not possess sufficient knowledge of all instances (including Socrates) to assert the conclusion: “Socrates is mortal.” Therefore, it is a non-sequitur. Either way, this argument, call the fallacy what you want, is invalid. Or is it?

As I would say to my students at this point, “If you can’t answer this, all logic and learning is pointless. Close your textbooks and go home.” All jesting aside, this is a dilemma that plagued not only logicians but philosophers of other disciplines especially science. What do we say to Mill?

Realism to the Rescue

Not so fast. Sit down and open the textbook!² In short, Mill has invoked nominalism to cause this dilemma. Nominalism is the view that universals (for example, ‘man’) are the mere arbitrary groupings of particulars that are then just given a name. That is, nominalism says particulars do not share in the same universal nature or essence. Hence, to answer this we must arrive at a right understanding of universals. Only then can logic, as well as everyone relying on it, be back in the business of correctly knowing and reasoning.

One problem with nominalism is that it has no explanation as to how we can call something the same thing without depending upon universals in the explanation of things. For example, when Mill uses the term ‘man’ in his objection (see above), he secretly relies on knowing a universal nature or essence. Otherwise, he could not even issue the objection using terms we universally understand. In short, it is self-defeating since his objection is using the very universal that his philosophical system denies.

We must emphasize two points that we should not lose. First, logic applies to reality. This is an undeniable truth. If you try to deny it, you will be affirming it. If someone says, “logic does not apply to reality,” it is self-defeating since it is relying on the very kind of application or correspondence it is denying. Human beings or persons, not just my thinking mind, really do exist.

Second, things in reality have natures or essences that can be shared by like particulars and known to us. And as Aristotle’s famous dictum reminds us, you can know the universal without necessarily knowing all the particulars that fall under it. Therefore, the syllogism is not committing a non-sequitur. Realism removes the mental mud from Mill’s criticism. If we can know the universal from the particular without having to know all particulars, then I can know all men are mortal without having to know Socrates. This obtains because things in the world have knowable natures or essences.

So yes, if you are in a logic class or some other class, rest assured you will still have a final exam.

  1. Peter Kreeft, Socratic Logic: A Logic Text Using Socratic Method, Platonic Questions, and Aristotelian Principles, 3.1 ed., ed. Trent Dougherty (South Bend, IN: St. Augustine’s Press, 2010), 92.
  2. For an in-depth analysis of this problem and its solution, see Francis H. Parker and Henry B. Veatch, Logic as a Human Instrument (New York: Harper & Row, 1959), chaps, 17-18.

The views and opinions expressed in this article are those of the author and do not necessarily reflect the position of Southern Evangelical Seminary.

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