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Self-Referential Unsound Modus Ponens 


[Image Source Credit: TeX]

An argument is sound if and only if it is valid and the premises are true. If those conditions are met, the conclusion must be true.

Consider the following argument:

P1. If God does not exists, this argument is unsound.
P2. God does not exist.
C. Therefore, this argument is unsound.

The argument is valid (Modus Ponens), so it is sound if the premises are true. But, if both premises are true, the conclusion is would have to be true, and the argument would both be sound and unsound. So consistency demands that we deny the soundness of the argument. At lease one of the premises must be false.  
Consider whether P1 is false. It is a material conditional, and so it is false when the antecedent is true (it is true that God does not exist) and when the consequent is false (it is false that this argument is unsound).[1] So P1 is false only if the argument is sound, which means that the falsity of P1 leads to a contradiction, since the soundness of the argument entails P1 is true. So, P1 cannot be false.  

P2 is the only premise that can be false. So given that the argument must be unsound, we must conclude that it is false that God does not exist.

So this unsound modus ponens proves the contradictory of the minor premise, whatever it might be!

I am probably not the first to note this, but it is new to me.

[1]The truth-table for the Material Conditional is as follows:

    p  q | p → q
1. T  T        T
2. T  F        F*
3. F  T        T
4. F  F        T
*The material conditional is only false on line 2.

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On the Death of my Mother

Wedding098

[A Personal Reflection] My mother died on April 7, 2013.  It’s a plain and ugly fact that can only be said with plain and ugly words.  And since that day I have hoped for the solace that many have reported.  I am speaking of the inexplicable experience of feeling the presence of a departed loved one.  I can’t say that I have had such an incident.  I have not felt as though she were with me — watching me.  I have not felt as though she is embracing me from beyond.  No.  Rather, since the  passing of my mother, in the tiny moments of joy and grief that punctuate each day, I can only say that I have strongly felt an impulse to reach out to her, to call her, to call for her.  And occasionally I will try writing to her.  But when I am finished, I experience only the lack of a response.  I have felt nothing but the absence of her presence.

The absence of the presence of a person is unlike any other absence one can experience.  When I lose my keys, I experience frustration.  The same is true of any other material object that I value.  When those objects go missing, or break,  I feel anger, frustration, sadness, etc.  But with a person, it’s profoundly different.  Yes, I have felt anger; I have felt frustrated, and sad too.  But in addition to these emotions, I have also, in a very real sense, felt the presence of her absence.  It’s a big void that I can nearly touch, and  it is an abyss into which I have occasionally stumbled.  I have felt it strongly.  In fact, just hours ago, when I entered the school library, there it was.  My mind drifted to my mother as I walked by the endless stacks of books.  She loved books.  And I realized that she wasn’t here, nor was she there at home.  She wasn’t sitting in her chair reading a book on healing prayer, or faithfully reciting Psalm 91 from her Bible.  She wasn’t sipping from a big frosted glass of iced tea, nor was she chatting with her sister.  My mind turned to the grave and to the dirt.

As I left the library, it occurred to me how palpably I had felt this void.  It was a disturbing presence–her absence.  But my mother was always keen on exorcising such disturbing presences.  So, I’ve reflect on this paradox for a moment and have decided to turn it on its head.  For the death of my mother entails the absurdity that the absence of her presence could become the presence of her absence—an absence that can transmute itself into a presence, a presence-that-is-not-a-presence.  And yet, it is as truly felt as any sensation I have ever felt.  But that paradox, that absurdity, can only lead me to conclude that death is itself an absurdity—a contradiction that dares to entail further contradictions.  My existential experience of her absence (her death) leads me to the reductio ad absurdum of death itself.  And so with all reductios, and as any good logician should do, I must reject the premise. Though my mother is dead, she yet lives.  Because absences and presences are rectified in the Christian mystery–the beautiful promise that declares: “Therefore we are always confident, knowing that, whilst we are at home in the body, we are absent from the Lord: (For we walk by faith, not by sight:) We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord” (2 Cor 5:6-8).

So I trust in this promise, and dispel the presence of my mother’s absence to the foot of the cross.  Because there, “…Death is swallowed up in victory” (1 Corinthians 15:54).

I love you mom!  I can’t hear you, but I know.

Paradox of Omnipotence

It is sometime alleged that the concept of omnipotence is logically self-defeating and therefore impossible.  If omnipotence is an essential attribute of God and impossible, then God cannot exist.  But are these paradoxes any real threat to orthodox theistic belief, or is the threat overblown?

Perhaps the most common example of the paradox of omnipotence is posed in the following dilemma: Either God can create a stone so heavy that he cannot lift, or God cannot create a stone so heavy that he cannot lift it.  If God can create such a stone, then there is something an omnipotent being cannot do—namely, lift the stone.  If God cannot create the stone, then once again an omnipotent being lacks the ability to do something.  So, no matter what, it seems omnipotence is impossible.

The traditional theistic response has been to embrace one of horns of the dilemma while denying that the horn leads one to the conclusion that omnipotence is impossible.  To understand this, we first must understand what “omnipotence” means.  Most traditional theists define “omnipotence” as the ability to do anything logically possible.  So an omnipotent being could create stars, black holes, and even unicorns.  But such a being could not draw a round square, since roundness and squareness cannot cohere in the same object at the same time and in the same way.  But what about a really heavy stone, what is so logically incoherent about it?  Notice that the stone is attributed not with merely being super heavy, but with being so heavy that an omnipotent being cannot lift it.  We might put it this way: a being that can create anything and lift anything is tasked with creating something that a being that can lift anything cannot lift.  If there is no weight that is too heavy for an omnipotent being to lift, then it is simply not possible for an omnipotent being to create such a stone.  No such stone can exist.

There have been some other interesting examples of omnipotence paradoxes.  For instance, it appears that an omnipotent being cannot create legal U.S. currency.  Why?  Because in order for currency to be legally made, it must be minted at one of the dozen or so authorized mints around the United States.  So, if God were to just bring a dollar into existence, having not been minted legally, God would be guilty of counterfeiting the bill.  A clever theist might come up with a way around this, i.e. God could incarnate himself as man and then apply for employment at the U.S. mint.  Then he could be said to have at least been a part of the process of minting real money.  Still another theist might say something like, since God is the creator of all matter and energy, God is the remote cause of U.S. currency—though not the proximate cause.  Really the legal currency example really boils down to a logical incoherency.  An omnipotent being cannot create something that is defined as not having been created by an omnipotent being.  So if legal U.S. currency is, by definition, currency not created by omnipotent beings, there is little God could do, short of becoming the building, the printing machine, the employees, and the U.S. treasurer, so that God could be said to have fully created the dollar bill all by himself.  And even if he did all those things, there would still be some question as to whether the minted bill was really created by a genuine U.S. mint of a counterfeited one.

My interest in this puzzle is with those who might find this first solution dissatisfying.  They might insist that omnipotence is the ability to do anything, including the logically impossible.  So, if God cannot make a stone so big that even God cannot lift it, then omnipotence is impossible and so is God.  So rather than insist that the previous definition of omnipotence is the only one on the table, I would like to offer the following counter-dilemma to those who might think that these paradoxes are real defeaters for theism.  The dilemma is as follows:

Either omnipotence is the ability to do anything but the logically impossible or omnipotence is the ability to do anything including the logically impossible.  If omnipotence is limited to doing the logically possible, then God cannot make a stone so heavy that he cannot lift it simply for the reasons stated above.  If omnipotence is not limited by the logically impossible, then God CAN make a stone so heavy that he cannot lift it.  But this is not very problematic either.  For if one insists that omnipotence ought to include the ability to break the laws of logic, then it must be reassessed as to whether the inability to lift a stone qualifies as something which precludes an entity from being omnipotent.  I argue that we have no logical footing from which to make such an assessment.  If there is a logically impossible world where omnipotent beings can create objects so heavy that they cannot be lifted, then we are just as likely to infer that an omnipotent being is unlimited in action as we are to say that such a being is limited in action.  The laws of logic no longer apply to such a being, right?  So, if an omnipotent being could make a stone so heavy that a being that can lift anything cannot lift it, then the same omnipotent being certainly would have the power to stipulate the definition of omnipotence around any objections.  If one were to object to such a move as illogical it’s just too bad, for the objector has already insisted that an omnipotent being can do that which is illogical.

Is the ability to do the logically impossible logically impossible?  Squared-circles cannot exist because squareness and circularity are contrary attributes that cannot cohere in the same object at the same time.  But, is the ability to make squared-circles itself logically impossible?  So it might not be the case that the ability to do the logically impossible it itself logically impossible.

These questions aside, the theist is perfectly within her right to insist that omnipotence means only that God can do the logically possible.  If the atheologian insists that omnipotence requires the ability to do the logically impossible, then it is the atheologian who has walked through the dialethistic door of admitting the possible impossible.  And if the only reason for insisting that omnipotence means the ability to do the logically impossible is to conclude that omnipotence is itself logically incoherent and cannot exist, then one has merely begged the question through stipulating omnipotence in this manner.  That is, one has stipulated omnipotence to be defined as an impossible attribute which cannot exist.  That is not a very compelling reason to think omnipotence doesn’t exist, especially since there are competing definitions out there.  So I think a theist is perfectly within his or her rational right to think omnipotence can and does exist.

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