1. In my immediately previous post, the “First Thoughts on the First Principles” of January 19, 2018, I offered statements of the principles, of non-contradiction and excluded middle, recognized as “first principles” by classical philosophical thought. I further pointed to a passage in Plato’s Apology and a couple of passages in Peter Kreeft’s Socrates Meets Jesus* where at least the principle of non-contradiction makes an appearance. In the present post I will first restate the two principles. I will next take note of the passage in Socrates Meets Jesus, also noted in the preceding post, where Kreeft has Socrates claim that one cannot conceive of an exception to the principle of non-contradiction. I will then proceed to the point of the present post and to the conceiving of exceptions, not to just the one, but to both of the principles, in a most direct way, that of simply negating them.

2. First, then, the principle of non-contradiction is the principle that, quite simply:

No beings can both be and not be (in the same respect and at the same time).

The principle of excluded middle is the principle that, equally as simply:

All beings must either be or not be (in the same respect and at the same time).

Two notes should perhaps be added here. First, the qualification, “(in the same respect and at the same time),” is inserted simply to ward off possible equivocation. A person can be, in different respects, but at one and the same time, both off, because not working, and not off, because his mind is functioning well; the word “off” needs to have the same meaning in its two occurrences. And a person can be, in the same respect, but at different times, both off, because not working, and not off, because working.

Second, I offered some illustrations of the application of the two principles in the aforementioned “First Thoughts on the First Principles.”

3. On now to the passage in Kreeft’s Socrates Meets Jesus where he has his Socrates claim that one cannot conceive of an exception to the principle of non-contradiction. Closely repeating what I said in “First Thoughts on the First Principles,” the background to the story has Socrates, finding himself, much to his astonishment, alive and well and a student at Have It University in Camp Rich, Massachusetts. In the passage at hand, he is defending the possibility of miracles in a conversation with a Professor Flatland. One part of the conversation reads as follows:

Socrates: Let’s try it another way. You can’t even conceive of an exception of the laws of logic or math, but you can conceive of exceptions to the laws of nature.
Flatland: How’s that? Give an example.
Socrates: All right. You can’t conceive of a man both walking through a wall and not walking through a wall at the same time, can you?
Flatland: No.
Socrates: But you can conceive of a man walking through a wall, can’t you?

4. To make sure that my most direct way of conceiving of exceptions to both of the principles, that of simply negating them, is well understood, I will now illustrate that act of simple negation with a pair of propositions less imposing than our two principles. First, reversing the order in which they usually are presented, let us note that the principle of excluded middle is both a universal proposition, bearing on all beings, and, let us be careful to notice, an affirmative proposition, affirming that they must either be or not be. So too the less imposing proposition:

All humans must be animals.

is both a universal proposition, bearing on all humans, and an affirmative proposition, affirming that all humans must be animals.

Similarly, let us note that the principle of non-contradiction is both a universal proposition, bearing on all beings, and, let us be careful to notice, a negative proposition, denying that they can both be or not be. So too the less imposing proposition, the obverse, as logicians would identify it, of the proposition just reviewed and logically equivalent to it:

No humans can be non-animals.

is both a universal proposition, bearing on all humans, and a negative proposition, denying that they can be non-animals.

5. Now let me go on to deny first the less imposing universal affirmative proposition and then the less imposing universal negative proposition. The denial of the former is:

It is not the case that all humans must be animals.

This, a few moments’ thought will tell you, is equivalent to:

At least one human can not be an animal.

(Note that this is very different from “At least one human cannot be an animal.).

The denial of the less imposing universal negative proposition, of course, is:

It is not the case that no humans can be non-animals.

This, a few moments’ thought will tell you, is equivalent to:

At least one human can be a non-animal.

6. The negations of the more imposing universal affirmative proposition, the principle of excluded middle, and of the more imposing universal negative proposition, the principle of non-contradiction, now beckon. The negation of the principle of excluded middle has to be:

It is not the case that all beings must either be or not be (in the same respect and at the same time).

This is equivalent to:

At least one being can not either be or not be (in the same respect and at the same time).

The negation of the principle of non-contradiction has to be:

It is not the case that no beings can both be and not be (in the same respect and at the same time).

This is equivalent to:

At least one being can both be and not be (in the same respect and at the same time).

7. That’s how easy it is for one, even one who is sure, as I am, that they are without exception, to conceive of exceptions to the principles of non-contradiction and of excluded middle. Actually, it seems to be even easier than that, for I cannot recall an introductory philosophy course that I have taught in which no student advanced the thesis that God, at least, was not bound by the two principles; at least two of my students in the introductory course I am teaching this semester have thought that this might be so.

And, returning to the thesis put forward by Kreeft’s Socrates, that “You can’t conceive of a man both walking through a wall and not walking through a wall at the same time,” I can conceive both that:

There is at least one man who can both be walking through a wall and not be walking through a wall (in the same respect and at the same time).

and even that:

There is at least one man who both is walking through a wall and not walking through a wall (in the same respect and at the same time).

In brief, I can very easily conceive that which I do not believe.

8. Let me go a bit further and enter an area that may be somewhat, shall I say, controversial by affirming that I, along with at least some others, can conceive both that:

There is at least one person who can both be identical with his father and not be identical with his father (in the same respect and at the same time).

and even that:

There is at least one person who both is identical with his father and not identical with his father (in the same respect and at the same time).

(I deal more definitely with the matter here brought up in a post published some time ago (April 4, 2014), “The Inconsistency of the Doctrine of (the Distinction of Divine Persons and so That of) the Trinity with Monotheism.”)

9. A final observation: Let us, at least for present purposes, adopt the name, “rationalism,” as that of the theory for which both the principle of non-contradiction and that of excluded middle are true. Let us then adopt the name, “irrationalism,” as that of the theory which negates them. Next let us note that the negations in question are both particular propositions, i.e., not universal propositions. Finally, let us adopt the phrase, “universalist irrationalism,” as the name of the theory that asserts the universal propositions corresponding to the two particular propositions. The one thesis of the theory, then, is:

All beings can not either be or not be (in the same respect and at the same time).

The other is:

All beings can both be and not be (in the same respect and at the same time).

We have here two more theses contrary to the first principles that you and I can easily conceive, even if we cannot believe them.

Until next time.

Richard

*Peter Kreeft, Socrates Meets Jesus. History’s Greatest Questioner Confronts the Claims of Christ (2nd edition; Downers Grove, Illinois: Intervarsity Press, 2002 [1987])

Should you wish to purchase a copy of Socrates Meets Jesus, you may do so quite easily by clicking on the following image.