Logical Errors in a Logic Textbook, Alas!

1. Early on in his Socratic Logic, Peter Kreeft offers what I’ll take to be two arguments in favor of a thesis that traditional, or Aristotelian, logic is superior to modern, or symbolic or mathematical, logic, that, indeed, modern logic is, as I’ll put it for him, a defective logic. The matter is of some importance in logical theory, for, if he is right, the past century and a half or so of progress in logic has been an illusion.

2. I will critique the first of the two arguments in the present post, leaving the second for a post to come. The first argument can be formulated as:

Any logic accepting an invalid argument as a valid argument is a defective logic.
Modern symbolic/mathematical logic is a logic accepting an invalid argument as a valid argument.
Therefore, modern symbolic/mathematical logic is a defective logic.

Kreeft and I can easily agree that the argument is a perfectly valid argument, in that, if its two premises are true (or were true), then the conclusion must be true (or would have to be true). But then the question arises of whether the argument is more than just a valid argument, but a sound argument, having both of its premises true. Now, though Kreeft leaves the first premise unexpressed, I am fully confident that he would take it as true, without any “ifs,” “ands,” or “buts.” We disagree, however, about the second premise, for while Kreeft holds that it is true, I hold that it is simply false.

3. To see that this is the case, let’s turn, then, to Kreeft’s formulation of the argument in question. It starts out well enough (p. 24).

A logically valid argument is one in which the conclusion necessarily follows from its premises. In a logically valid argument, if the premises are true, then the conclusion must be true. In an invalid argument this is not so. “All men are mortal, and Socrates is a man, therefore Socrates is mortal” is a valid argument. “Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog” is not a valid argument. The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. It does not “follow” from the premises.

So far, so good.

Kreeft continues (Ibid.).

Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is “implied” by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees.

Still, so far, so good.

But then the argument goes off the rails, for Kreeft goes on to claim in the next sentence:

However, modern symbolic logic disagrees.

That is, according to Kreeft, while Aristotelian logic and common sense agree that the argument about Lassie is not valid and that its premises do not prove its conclusion, “modern symbolic logic disagrees.” The disagreement is not over whether the argument about Lassie is an argument, but over whether it is valid. Kreeft is therefore committed to saying modern logic holds that the argument about Lassie is a valid argument and therefore that modern logic holds that some invalid argument about Lassie is a valid argument.

4. Kreeft could not be more wrong. In no way would the so-called “predicate calculus,” that branch of modern logic by which the argument at hand would be assessed, pronounce it valid. On the question of whether or not the argument about Lassie is a valid argument traditional logic and modern logic in full agreement.

5. Let me set the argument forth both as it would be presented in traditional logic and as it would be presented in the “predicate calculus.” In traditional logic, stating the argument even a bit more carefully than Kreeft does, the argument would read:

All dogs are animals having four legs.
Lassie is an animal having four legs.
Therefore, Lassie is a dog.

As, as we have seen, Kreeft has said:

The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. It does not “follow” from the premises.

And no logician will or even can come up with a sequence of inferences acceptable to traditional logic that would begin from the two premises and those two premises alone and logically arrive at the proffered conclusion. For, if all that we are given to know is what we know through the argument’s premises, it may well be, for all we know, that Lassie is, not a dog, but a turtle.

On the other hand, of course, we could introduce the premise that Lassie is a dog into the argument. The argument would then read:

All dogs are animals having four legs.
Lassie is an animal having four legs.
Lassie is a dog.
Therefore, Lassie is a dog.

Then, however, we would have a different argument, one in which the conclusion that Lassie is a dog would certainly follow from the premises. But this argument is precisely that, a different argument.

6. Now, in the modern logic, the argument would be stated as:

For any existent x, if x is a dog, then x is an animal having four legs.
Lassie is an animal having four legs.
Therefore, Lassie is a dog.

The judgment that Kreeft advanced about the Aristotelian formulation applies equally well here.:

The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. It does not “follow” from the premises.

And no logician will or even can come up with a sequence of inferences acceptable to modern, symbolic or mathematical logic, that would begin from the two premises and those two premises alone and logically arrive at the proffered conclusion. For, if all that we are given to know is what we know through the argument’s premises, it may well be, for all we know, that Lassie is, not a dog, but a turtle.

On the other hand, of course, we could introduce the premise that Lassie is a dog into the argument. The argument would then read:

For any existent x, if x is a dog, then x is an animal having four legs.
Lassie is an animal having four legs.
Lassie is a dog.
Therefore, Lassie is a dog.

Then, however, we would have a different argument, one in which the conclusion that Lassie is a dog would certainly follow from the premises. But this argument is precisely that, a different argument.

7. If the foregoing holds up, I have shown that the first of the two arguments that Kreeft has offered on behalf of the thesis that modern symbolic/mathematical logic is a defective logic, fails, in that he has not shown that that argument’s premise, that:

Modern symbolic/mathematical logic is a logic accepting an invalid argument as a valid argument.

is true.

In a post to come, I will offer a critique of the second of the two arguments Kreeft advances on behalf of the thesis that modern symbolic/mathematical logic is a defective logic.

Until next time.

Richard

* Peter Kreeft, Socratic Logic. A Logic Text Using Socratic Method, Platonic Questions, and Aristotelian Principles. Edited by Trent Dougherty (Edition 3.1; South Bend, Indiana: St Augustine’s Press, 2014 [2004])

If you wish, you may purchase a copy of Socratic Logic through Amazon.com by simply clicking on the following:

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Countering the Philosophical Skepticism of Former Secretary of the Treasury Robert Rubin

In an April 30, 2018, New York Times Opinion page article, “Philosophy Prepared Me for a Career in Finance and Government,” former Secretary of the Treasury Robert Rubin singled out his undergraduate Harvard University Professor Raphael Demos for special praise, telling us:

Professor Demos would use Plato and other great philosophers to demonstrate that proving any proposition to be true in the final and ultimate sense was impossible. His approach to critical thinking planted a seed in me that grew during my years at Harvard and throughout my life. The approach appealed to what was probably my natural but latent tendency toward questioning and skepticism.

Rubin then went on to say:

I concluded that you can’t prove anything in absolute terms, from which I extrapolated that all significant decisions are about probabilities. Internalizing the core tenet of Professor Demos’s teaching — weighing risk and analyzing odds and trade-offs — was central to everything I did professionally in the decades ahead in finance and government.

I myself have to admit to having a “tendency toward questioning and skepticism,” if, though natural, hardly latent. Here and now, for example, I cannot help doubting that Professor Demos was able to “use Plato and other great philosophers to demonstrate that proving any proposition to be true in the final and ultimate sense was impossible,” at least in “the final and ultimate sense.” Or, I’ll put it directly: There is no way to prove in absolute terms that it is impossible to prove anything in absolute terms.

On the other hand, one can prove that one can prove that at least some propositions are true in “the final and ultimate sense” by presenting the actual proofs that they are true, for whatever is actual must be possible. I have in fact presented such very genuine philosophical proofs or demonstrations in the pages of this very blog. I invite you to peruse the:

A Proof That at Least One Thing Can Be Proven in Philosophy,” of March 6, 2018;

Sathya Sai Baba. The Man Who Was God,” of February 20, 2018; and

A Diagram of the Trinity,” of February 8, 2018.

There are also some earlier posts related to the Trinity, links to which can be found in the three posts listed.

I’ll close by repeating the claim I made in the last of the aforementioned posts:

My arguments, I submit, are valid, in that their conclusions must be true if their premises are true. Moreover, they are not only valid, but sound, in that their premises, and therefore their conclusions, are true. Moreover still, they are not only sound, but apodictic or demonstrative, in that their premises, and therefore their conclusions, are not just true but necessarily true.

Until next time.

Richard

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A Suggestion for the New York Times. And for the Author of the Gospel According to John

The New York Times has launched a new advertisement campaign, one installment of which culminates in the propositions that:

The truth is hard.

The truth is hard to find.

The truth is hard to know.

The truth is more important now than ever.

I’m afraid that the campaign has gotten off on the wrong foot, for any proposition that begins with “The truth is” is, strictly speaking, false. But I will not allow myself to be but a critic and so, after pointing out how the propositions at hand are false, I will, with tongue not quite in cheek, point the Gray Lady in the direction of the logical tools she so evidently is in need of. I will then, albeit rather belatedly, do the same for the writer of the Gospel According to John.

Let’s, then, take the third of the four propositions, “The truth is hard to know,” as illustrative. Taken as it is given, it is equivalent to the conjunction (and here I’m making use of Bertrand Russell’s “theory of definite descriptions”)

There is at least one truth
and
any truth whatever is identical with that truth
and
that truth is hard to know.

Now, I’ll happily grant the truth of the first conjunct, “There is at least one truth”; for example, it is true that

At 10:00 am eastern standard time on March 8, 2018, Donald Trump was President of the United States of America.

And I’ll even, and still happily, grant the truth of the conjunction of the first and the last of the conjuncts, thus:

There is at least one truth
and
that truth is hard to know.

For example, it is either true that there exists extra-terrestrial intelligence or true that there does not exist extra-terrestrial intelligence. In either case, the truth is hard to know.

But I can’t grant that the conjunction of the first and second of the conjuncts

There is at least one truth
and
any truth whatever is identical with that truth.

is true. Take, once again, the above proposition, about Donald Trump, instantiating the first conjunct, “There is at least one truth.” It is just not the case that any truth whatever is identical with that truth. The following truth is a truth that is not identical with that one:

At 10:00 am eastern standard time on March 8, 2018, Michael Pence was Vice President of the United States of America.

There are, then, at least two truths. In fact, I’ll hasten to add, there are others, some, but only some, at least somewhat similar to the two about Messieurs Trump and Pence, e.g., those we all could generate about Messieurs Ryan and McConnell. Etc.

So, here’s my suggestion for the New York Times. Learn to distinguish between universal and particular propositions, as the introductory logic textbooks characterize them, and between affirmative and negative propositions. Applied to the case at hand, those distinctions enable us to distinguish between the universal affirmative proposition:

All truths are hard to know.

the universal negative proposition:

No truths are hard to know.

the particular affirmative proposition:

At least some truths are hard to know.

and the particular negative proposition:

At least some truths are not hard to know.

A moment’s reflection reveals that the Times’ proposition, “The truth is hard to know” implies the universal affirmative proposition, “All truths are hard to know.” As the latter is false, so too the former is false. I have already, in pointing to the truth of the answer to the question of the existence of extra-terrestrial intelligence as a truth that is hard to know, indicated that the universal negative proposition is false. The two particular propositions, on the other hand, are true.

I urge, then, that the writers and editors of the New York Times, in the case at hand and indeed in almost all others, content themselves with particular propositions, instead of, say, a sentence the beginning of which is “The position of the White House is….” But, as I said early on in this post, I am offering the same advice, albeit rather belatedly, to the writer of the Gospel According to John, for therein (14:6) we read Jesus saying

I am the way and the truth and the life.

There may be room for some question as to whether or not the statement “I am the way” is true and perhaps even as to whether or not the statement “I am the life” is. But the statement, “I am the truth,” is just false, for there are many truths, the vast majority of which have little to do with Jesus.

I leave the spelling out of the advice to be offered to the author of the gospel, were it possible to offer him advice, to the reader.

Until next time.

Richard

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A Proof That at Least One Thing Can Be Proven in Philosophy

1. There is a widely held opinion that, in contrast with, say, mathematics, there are no demonstrative arguments, or proofs, in philosophy. This opinion is held, not just by those not well acquainted with philosophy, but also by many or even most of those whom we all, including they themselves, would identify as accomplished philosophers. One member of the latter group is William (Bill) Vallicella, the famous or infamous, depending upon one’s political point of view, blogger publishing so prolifically at Maverick Philosopher. I offer as evidence that my inclusion of him in that group is justified the statement, made almost in passing, in his January 23, 2018, post, the “The Two Opposites of ‘Nothing’ and the Logical Irreducibility of Being (2018 Version).”

I won’t be able to prove my point because nothing in philosophy can be proven.

An obvious first reply, of course, is that our maverick philosopher offers no argument here for, much less any proof of, the thesis that “nothing in philosophy can be proven.” But, again of course, that observation invites the equally easy retort that neither is it itself an argument for or a proof of the thesis that “at least one thing in philosophy can be proven.” The aim of the present post is to prove that at least one thing in philosophy can be proven and to prove it by, well, proving at least one thing in philosophy.

2. The philosophical thesis which I will prove is that God does not exist, at least if he, she, or it is the cause of all and only those causes that do not cause themselves. Virtually all who have degrees in philosophy, and many others besides, will recognize in that thesis a precise analogue of the thesis, long ago proven by Bertrand Russell, that there is no class that is the class including all and only those classes that do not include themselves. That does not concern me, for my aim is, as I have said, to prove that something in philosophy can be proven and to prove it by proving something. It is not my aim to argue, much less to prove, that I am an original thinker.

3. The proof is very brief. It involves, first, an assumption that there is such a God, then an observation that such a assumption leads to a falsehood, and then the conclusion that that assumption is false; an argument of this sort goes by the name, reductio ad absurdum. First, then, the assumption: There is an existent, God, which is such that, for any existent y, God is the cause of y if and only if y is not self-caused, i.e., y is not the cause of y.

From that assumption, it follows, since God is, ex hypothesi, an existent, that God is the cause of God if and only if God is not the cause of God.

It cannot, however, be the case that God is the cause of God if and only if God is not the cause of God, just as it cannot be the case that it is 5:00 pm in Massachusetts if and only if it is not 5:00 pm in Massachusetts and as it cannot be the case that Donald Trump is a patriot if and only if Donald Trump is not a patriot.

Therefore, it cannot be the case that there is an existent, God, which is such that, for any existent y, God is the cause of y if and only if y is not self-caused, i.e., y is not the cause of y. Q.E.D.

4. It must be understood that, on the one hand, this proof is a proof that there is no such God in reality. It must also be understood, on the other, that it is not a proof that God as otherwise specified does not exist.

5. The foregoing proof is a philosophical proof. Therefore, at least one thing in philosophy can be proven. Q.E.D., once more.

Until next time.

Richard

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Sathya Sai Baba. The Man Who Was God

0. Reading today’s (February 20, 2018) post by James Chastek, “Sathya Sai Baba as Atheist argument trope,” in the blog, Just Thomism, I became aware of Sathya Sai Baba for the first time. This was perhaps a bit late, for with but a few clicks I found myself reading today’s Time Magazine on-line article, “Sathya Sai Baba. The Man Who Was God Is Dead.”

The article tells us that:

Believing in the Baba was easy. Devotees were not required to adhere to any particular set of beliefs or renounce worldly pleasures; non-Hindus did not need to change their religion. “I am God,” he would say. “You too are God. The only difference between you and me is that while I am aware of it, you are completely unaware.”

1. In reading him being described in the title as “the man who was God,” I am of course reminded of the classical Christian belief that Jesus of Nazareth was God (and indeed is God; the claim that any person was God should also, it would seem, entail the further claim that he or she is God). In reading the Baba’s statement:

I am God. You too are God. The only difference between you and me is that while I am aware of it, you are completely unaware.

I am also reminded of the logical incoherence of such doctrines. In my February 8, 2018, article, “A Diagram of the Trinity,” and, more thoroughly in my June 12, 2014, article, “Garrigou-Lagrange on Trinity and Triple Identity,” I presented what I take to be a definitive refutation of the Trinitarian doctrine. In the present post, I’d like to present a similar logical response to the doctrine offered by the Baba.

3. First, then, there are the logical principles (I’d rather call them the ontological principles, but I’ll let that matter go for now) of the symmetry and the transitivity of identity. The principle of the symmetry of identity is the principle that:

For any existent x and any existent y, if x is identical with y, then y is identical with x.

Now, if we let ourselves imagine that the Baba was addressing me when he said, “You too are God,” then he would have been saying:

Richard is God.

If, then, we apply the principle of the symmetry of identity to the case of Richard and God, we have:

If Richard is identical with God, then God is identical with Richard.

Given the last two propositions, we find ourselves with the following utterly valid argument, one in the form known by logicians as Modus Ponens:

If Richard is identical with God, then God is identical with Richard.
Richard is identical with God.
Therefore, God is identical with Richard.

4. Let’s turn now to the principle of the transitivity of identity, the principle that:

For any existent x, any existent y, and any existent z, if both x is identical with y and y is identical with z, then x is identical with z.

If we apply the principle of the transitivity of identity to the case at hand, we have:

If both the Baba is identical with God and God is identical with Richard, then the Baba is identical with Richard.

5. Now a third principle becomes pertinent, the principle of the indiscernibility of identicals, according to which, as I’ll word it:

For any existent x and any existent y, if x is identical with y, then, for any attribute φ, x has φ as an attribute if and only if y has φ as an attribute.

Applying this principle to the case at hand and recalling that the Baba has claimed that he is aware of his identity with God, we have:

If the Baba is identical with Richard, then the Baba has an awareness, that he is identical with God, as an attribute if and only if Richard has an awareness, that he is identical with God, as an attribute.

Let me assure you, however, that:

Richard has no awareness, that he is identical with God, as an attribute.

From these two statements, however, it follows that:

The Baba is not identical with Richard.

6. That was as expected, I suppose. But let us now recall that, above, an application of the principle of the transitivity of identity to the case at hand led to the proposition that:

If both the Baba is identical with God and God is identical with Richard, then the Baba is identical with Richard.

We have just determined, however, that

The Baba is not identical with Richard.

Given the last two propositions, we find ourselves with another utterly valid argument, this one in the form known by logicians as Modus Tollens:

If both the Baba is identical with God and God is identical with Richard, then the Baba is identical with Richard.
The Baba is not identical with Richard.
Therefore, the Baba is not identical with God or God is not identical with Richard.

7. I dare to say that the first proposition, that the Baba is not identical with God, has to be true, for it can be shown to be so by appealing once more to the principle of the indiscernibility of identicals. First, however, given that the Baba has died, we can safely assert:

The Baba is subject to death.

Accordingly:

If the Baba is identical with God, then the Baba is subject to death if and only if God is subject to death.

Unless Nietzsche is right, however, God is not subject to death; I am, moreover, confident that my assumption that the Baba himself believed, or at least consistently professed to believe, that God is not subject to death is secure. It follows then that:

The Baba is not identical with God.

An exactly parallel argument starting from the premise that:

Richard is subject to death.

would lead to the conclusion that:

Richard is not identical with God.

8. I can imagine that at least some readers have had the patience not only to follow my reasoning this far, but also to accept the conclusions it has reached related to the Baba and Richard, specifically, their non-identity with God. But would not exactly parallel reasoning apply to Jesus of Nazareth?

Until next time.

Richard

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A Diagram of the Trinity

Today my eyes fell on a diagram, the Scutum Fidei or “Shield of Faith,” the purpose of which is to set forth the relationships which classical Christianity believes to exist between and among the three persons of the Trinity, God the Father, God the Son, and God the Holy Spirit.

Before my retirement from Merrimack College in North Andover, Massachusetts, a few years back, I often had occasion to ponder an essentially similar diagram on a stained-glass window in the Church of Christ the Teacher at the college. What gave rise to the pondering, of course, is the evident impossibility that the Trinitarian relationships all hold. That impossibility is a primary reason why I have to count myself as a pagan Aristotelian, or neo-Aristotelian, and not a Christian Thomist.

That is, the conjunction of the theses that God the Father is God and that God the Son is God is quite simply inconsistent with the thesis that God the Father is not God the Son. Ditto for the set of theses coming with the introduction of God the Holy Spirit.

I have dealt with the Trinitarian doctrine at length in two previous posts, posts you may wish to subject to your most critical reading. One is that of April 4, 2014, “The Inconsistency of the Doctrine of (the Distinction of Divine Persons and so That of) the Trinity with Monotheism.” (I apologize for the length and complexity of the title and I resolve to never again try to express more than one thesis in the title of a post. At least in that manner.)

Another post you may wish to subject to your most critical reading is that of June 12, 2014, “Garrigou-Lagrange on Trinity and Triple Identity.”

My arguments, I submit, are valid, in that their conclusions must be true if their premises are true. Moreover, they are not only valid, but sound, in that their premises, and therefore their conclusions, are true. Moreover still, they are not only sound, but apodictic or demonstrative, in that their premises, and therefore their conclusions, are not just true but necessarily true.

I invite you, after you have completed your critical readings, to do your best to show that the arguments are invalid, unsound, or merely non-demonstrative.

Until next time.

Richard

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Conceiving of Exceptions to the First Principles

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.

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