Excluded Middle, Bivalence, and Disquotation

LEM: For every  p, p v ~p.

BV: Every proposition is either true or false.

These principles are obviously not identical.  Excluded Middle is syntactic principle, a law of logic, whereas Bivalence is a semantic principle. The first says nothing about truth or falsity. The second does. (See Michael Dummett, Truth and Other Enigmas, Harvard UP, 2nd ed. , 1980, p. xix; Paul Horwich, Truth, Oxford UP, 2nd ed., 1998, p. 79) Though not identical they might nonetheless be logically equivalent.  Two propositions are logically equivalent iff each entails the other.  Entailment is the necessitation of material implication. Can it be shown that (LEM) and (BV)  entail each other? Let's see.

The logical equivalence of the two principles can be demonstrated if we assume the disquotational schema:

DS: p is true iff p.

For example, snow is white is true iff snow is white. Or, if you insist, 'snow is white' is true iff snow is white. In the latter forrmulation, which does not involve reference to propositions, the truth predicate  — 'is true' — is merely a device of disquotation or of semantic descent. On either formulation, 'is true' adds no sentential/propositional content:  the sentential/propositional content is the same on both sides of the biconditional.  The content of my assertion is exactly the same whether I assert that snow is white or I assert that snow is white is true.  But if (DS) is granted, then so is:

DS-F: p is false iff ~p.

For example, snow is white is false iff ~(snow is white).    

Now if the disquotational schemata exhaust what it is to be true and what it is to be false, then (LEM) and (BV) are logically equivalent.

Given (DS) and (DS-F), we can rewrite (LEM) as

LEM-T: For every p, p is true v p is false.

Now (LEM-T) is simply a restatement of (BV). The principles are therefore logically equivalent given the disquotational schemata. 

But this works only if falsehood can be adequately explained in terms of the merely logical operation of negation.  This will NOT work if negation can only be explained in terms of falsehood.  For then we would enter  an explanatory circle of embarrassingly short diameter. 

Ask yourself: when is one proposition the negation of another? The negation of p is the proposition that is true iff p is false and false iff p is true.  To explain the logico-syntactic notion of negation we have to reach for the semantic notions of truth and falsehood.  But then falsehood cannot be exhaustively understood or reduced to negation.

It is telling that to explain negation and the other logical connectives we use TRUTH tables.  Such explanation is satisfactory.  But it would not be if the redundancy or disappearance or disquotational schemata gave the whole meaning of 'true' and 'false.'  (The point is made by M. Dummett, Truth and Other Enigmas, p. 7)

I take this explanatory circle to show that there is more to truth and falsehood than is captured in the above disquotational schemata.

Conclusion: if one's reason for accepting the logical equivalence of (LEM) and (BV) is (DS) then that is a bad reason.

Are there counterexamples to (DS)?  It seems to fail right-to-left if 'Sherlock Holmes is a detective' is plugged in for 'p' on the RHS of (DS).  Arguably, Holmes is a detective, but it is not true that Holmes is a detective.  For it to be true that Holmes is a detective, 'Holmes' would have to refer to something that exists.  But this requirement is not satisfied in the case of purely fictional items.  I am assuming that veritas sequitur esse, that truth 'follows' or supervenes upon being (existence):

VSE:  There are no true predications about what does not exist.

Since Holmes does not exist, 'Holmes is a detective' appears to express a proposition that is neither true nor false. Likewise for its negation, 'Holmes is not a detective.'  (LEM) is not violated since either Holmes is a detective or Holmes is not a detective. But (BV) is violated since the two Holmes propositions are neither true nor false.

It is worth noting that from 'Only propositions have truth-values' one cannot validly infer 'All propositions have truth-values.'  

Proof that I am a Native American

A while back a front page story in the  local rag of record, The Arizona Republic, implied  that one is either a native American, a black, or an Anglo. Now with my kind of surname, I am certainly no Anglo. And even though I am a 'person of color,' my color inclining toward a sort of tanned ruddiness, I am undoubtedly not black either.

It follows that I am a native American. This conclusion is independently supported by the following argument:

1. I am a native Californian.
2. California is in America.
3. If x is native to locality L, and L is within the boundaries of M, then x is a native M-er.
Therefore
4. I am a native American.

This argument is impeccable in point of logical form, and sports manifestly true premises. What more do you want?

Note that (2) is true whether 'America' is taken to refer to the USA or to the continent of North America.

Let us also observe that since I am a native American, it cannot be the case that "we are all immigrants" as far too many 'liberal' knuckleheads like to claim.

We need more mockery of 'liberals.' There is little point in attempts to engage them on the plane of reason, for that is not the plane they inhabit.

Slavoj Zizek remarks (jokingly I think) that  ‘native Americans’ hate this term, mentioning one who preferred to be call an ‘Indian’ on the ground that ‘native’ American is racist. For it means that someone so denominated  is part of nature, and is therefore beneath the cultural American. The Indian in question prefers to be called an ‘Indian’ for this moniker implies the white man's stupidity.

Saturday Night at the Oldies: Metals and Mining

Springfields, Silver Threads and Golden Needles

Neil Young, Heart of Gold

Connie Francis, Oh My Darling Clementine

Lee Dorsey, Working in a Coal Mine

Marty Robbins, That Silver-Haired Daddy of Mine

Joan Baez, Silver Dagger

Miranda Lambert, Gunpowder and Lead

James Taylor, Copperline

Allman Bros., Silver Dollar

Bob Dylan, Cold Irons Bound

YouTuber comments:

There's something about not having a perfect voice that lends so much authenticity, sincerity and soul to a particular song. Dylan has it, Leonard Cohen, Tom Waits, Janis Joplin, Kris Kristofferson, Johnny Cash, Willie Nelson, John Prine, Shane McGowan, Billie Holiday and yeah — even Dean Martin….none are perfect — yet, they are legends. Ha. Because there's a thrill factor to it all. This is one of Dylan's best…this is rock and roll. Don't forget the word "roll" at the end. That guarantees it's the real thing. (There are other singers too…I can't list them all).

Amazing! The concentrated precision on their faces, every note delivered on time, These guys are so tight makes my teeth hurt. Accompanying the most enigmatic, musical artist on the planet, and doing it with grace and style. Of the hundred times I've watched this video masterpiece a percentage has been just for the ending. After the last chord stops reverberating (I can't help but read into the moment) a small but enthusiastic applause breaks out there is a look of enjoyment on their faces, an understated sense of accomplishment. Something has happened here. Something greater than the sum of it's parts.

READERS' RECOMMENDATIONS (2/3)

Keith Richards, You Got the Silver

Loretta Lynn, Coal Miner's Daughter.  This one goes out to Hillary Clinton.

Bill Mize, The Silverplume Waltz. Great solo acoustic guitar.

The Eagles, Silver Dagger

Joan Baez, Silver Dagger (live)

Is the Philosophical Life the Best?

This from a reader:
I have a concern about the philosophical life. While I do think philosophy is intrinsically valuable, and while I do deny that one is obligated to "do the most good" with one's life (I'm not a consequentialist), I wonder if there are better ways to live than to devote one's life to philosophy. Prima facie, devoting one's life to solving global poverty or curing cancer seems better than focusing on philosophy. If so, then even if one isn't obligated to solve global poverty or cure cancer, why not devote one's life to these causes instead?
 
Perhaps the philosophical life is better than these other options, but that isn't clear to me. It seems more plausible that, all things being equal, a life that saves countless lives is better lived than a life that doesn't save a single life. Again, I'm not saying we're obligated to save lives, I'm just making a comparative judgment.
I can't refute what you say, but I can offer an alternative point of view.  If you consider it, it may help you better understand your own point of view even if it does not motivate any modification of it.
 
One question concerns the best life humanly possible.  Aristotle discussed it in his Nicomachean Ethics. He considered lives devoted to pleasure, material acquisition, politics, and philosophy. I set forth his answer here.
 
But the best life possible for humans might not be the best life  for a particular human.  Whether or not the best life is the philosophical life, not everyone is 'philosophy material.'
 
Philosophy is a vocation, and only some are called to it. (I am speaking in ideal terms here: what passes for 'philosophy' in the 'universities' falls far short of the ideal.)
 
The best life for you will depend on your aptitudes, values, and worldview.   Everyone has a worldview of sorts even if unexamined and unarticulated.  Suppose your outlook is broadly secular.   And suppose you find secularism obvious.  Then you will not be inclined to question it and will have no need for philosophy.  You have 'your truth,' a worldview you believe is true, and therefore feel no need to investigate whether it is true in whole or in part.  Doubt is the engine of inquiry, but you have no doubts. For you philosophical inquiry would be idle.  You would be left cold by the Socratic, "The unexamined life is not worth living."
 
And if the people you associate with share your tacit worldview, then you will have no need to articulate and defend it.  The existence of competing worldviews might trouble you or then again it might not. You might be the sort of person who is not disturbed or given pause by the disagreement of others.
 
For me, disagreement is a goad to inquiry. I have a consuming need to know. And a life lived without examination is definitely worth little or nothing. Such a life remains on the animal level. A human life, speaking normatively, is a transcending life, a life of self-transcendence and aspiration.
 
Primum vivere deinde philosophari.  I agree. We must live and live fully to gather the grapes of experience from which to press the wine of wisdom.  We don't gather grapes to gather grapes, but for the wine. The vita activa subserves the vita contemplativa.
 
You say it is not clear to you that the philosophical life is superior to, say, cancer research.  Then I say you should leave philosophy alone.  The quest for the ultimate truth about the ultimate matters is the highest calling and it demands total commitment.  I can argue for this conviction, but I can't prove it, and I will persuade only those who already sense its truth.
 
In the early '80s I heard a speech by the American politician, Mario Cuomo, in which he touted the political life as the highest life. I thought to myself: "He can't really believe that!"  But I soon concluded  that he did believe it.  I can give my reasons why Cuomo is wrong, but these reasons, which suffice for me, will make no impression on those who think the political life the highest. (To me, politics is like taking out the garbage or unplugging the toilet: it's a dirty job and it has to be done and done properly; in an ideal world, however, there would be no State and no need for politicians. As things are, our fallen predicament makes the State  practically necessary, a necessary evil, along with its agents.)
 
My advice is, first of all, know thyself.  Having honestly assessed your abilities, do with your life what you think is the best, and what you are fit to do.
 
I realize that this advice is of very little practical value.  Listen to others, but keep your own counsel, and follow the urgings vouchsafed to you in the highest moments of existential clarity and discernment.

Is the Unexamined Life Worth Living?

Written in October of 2004.

Norman PodhoretzI recently read Norman Podhoretz's Ex-Friends: Falling Out with Allen Ginsberg, Lionel and Diana Trilling, Lillian Hellman, Hannah Arendt, and Norman Mailer (The Free Press, 1999). It is an enjoyable and stimulating analysis of the breakdown of friendship in the crucible of political disagreement. I recommend it.

But an early passage inspired me to fire up the old Pentium II. Describing "most people," Podhoretz says that "The ideas that underlie their way of life are mostly taken for granted and remain unexamined – luckily for them, since the biggest lie ever propagated by a philosopher was Socrates’ self-aggrandizing assertion that the unexamined life is not worth living." (p. 4)

Can a philosopher let this passage pass unexamined? The first thing that raised my critical hackles is the irresponsible use of the word ‘lie,’ a use that is unfortunately widespread these days. Does Podhoretz really mean to suggest that Socrates was lying when he made his famous statement at his trial? Does he mean to imply that the great Athenian knew the truth, but was bent on deceiving us? Of course not. Podhoretz knows that one can utter a falsehood without lying, as when one says what one believes to be true but is not true, and I am sure that he appreciates that Socrates was sincere in his belief that the unexamined life is not worth living. Charitably interpreted, Podhoretz is opining that Socrates was wrong in his belief, not that he was lying.

A second thing to question is whether the Socratic assertion is "self-aggrandizing." If I praise a certain way of life that happens to be my way of life, it does not follow that I praise this way of life simply because it happens to be mine. For there is also the possibility that I praise this way of life because I have objective reasons to believe that it is a good way of life, and that I have chosen it for these objective reasons. In the second case, the life is mine because I have objective grounds for praising it, not praised because it is mine. Only in the first case would we speak of Socrates’ assertion as self-aggrandizing. Given that Podhoretz has provided no evaluation of the Socratic reasons for the Socratic assertion, he is not justified in describing the latter as "self-aggrandizing."

But the main issue is this: Is an unexamined life worth living? If my way of life happens to be good, then one might argue that it is good whether I examine it or not, whether I can give objective reasons for its goodness or not. (Compare: if my roof is in good condition, it is so whether I examine it or not. It is no part of my roof’s being in good condition that it, or someone, know that it is in good condition or that it, or someone, raise the question of its condition.) In this sense, an unexamined life could very well be worth living. But a human life is not merely a biological process, but essentially involves the exercise of (not merely the capacity for) emotion, will, and reason. Thus no ‘fully human life’ (an unabashedly normative phrase used unabashedly!) is possible without the exercise of reason upon the ultimate objects, among which is one’s own life, its whence, whither, and wherefore. A fully human life, as a life necessarily involving the exercise of reason, requires the examination of such questions as how we should live. To live thoughtlessly, uncritically, without consideration of ultimates and without consideration of alternative ways of living – there is indeed something  contemptible about this,assuming that the person is in a position to conduct the examination. To that extent, Socrates was surely right, and Podhoretz is surely wrong.

But Socratic self-examination implies no rejection of traditional ways of life. Perhaps lurking in the background of Podhoretz’s mind is some such argument as this: (1) Socratic self-examination leads to the rejection of traditional mores; (2) traditional mores are sound; ergo, (3) Socratic self-examination is a mistake. I hope this is not the way Podhoretz is thinking, given the falsity of (1). Socratic examination may lead to the rejection of traditional mores, but it might also lead to their rational defense.

Excluded Middle, Bivalence, and Tertium Non Datur

Dave Gudeman comments:

I was surprised to see you distinguishing between bivalence and the LEM. As far as I can tell, in the traditional and most common formulations, they are identical.

Here is the way I understand it.  They are not identical.  Excluded Middle is a law of logic, whereas Bivalence is a semantic principle. (See Michael Dummett, Truth and Other Enigmas, Harvard UP, 2nd ed. , 1980, p. xix; Paul Horwich, Truth, Oxford UP, 2nd ed., 1998, p. 79) If 'p' is a place-holder for a proposition, any proposition, then Excluded Middle is:

LEM. p v ~p.

If 'p' is a propositional variable, and we quantify over propositions, then we have the universal quantification

LEM*. For all p, p v ~p.

It is understood that the wedge in the above formulae signifies exclusive disjunction. Why is that understood? Because both p and not-p is excluded by the Law of Non-Contradiction:

LNC. ~(p & ~p).  

If I may be permitted parenthetically to wax poetic in these aseptic precincts, (LNC) possesses a 'dignity' in excess of that possessed by (LEM). What I mean is that there are some fairly plausible counterexamples to (LEM), but none that are very plausible to (LNC).  Few philosophers are dialetheists; many more accept truth-value gaps.

The laws of logic are purely formal: they abstract from content or meaning. They are syntactic principles. Bivalence, by contrast, is a semantic principle. It goes like this:

BV. Every proposition is either true or false.

Tertium non datur means that a third is not given: there is no third truth value.  (TND) is also a semantic principle:

TND. No proposition is neither true nor false.

So the difference between (LEM) and (BV) is that the first is a syntactic principle and the second a semantic principle. But is this a difference that makes a difference? Is there a conceivable case where (LEM) is true but (BV) false?  I don't know the answers to these questions. Either that or I forgot them.

But if you conflate the two principles,  then you are in good company. W. V. O. Quine, Mathematical Logic, Harvard UP, 8th ed., 1976, p. 51: ". . . the law of excluded middle, which is commonly phrased as saying that every statement is either true or false . . . ."

Of E-Mail and Doing Nothing

Dolce far nienteI do appreciate e-mail, and I consider it rude not to respond; but lack of time and energy in synergy with congenital inefficiency conspire to make it difficult for me to answer everything. I am also temperamentally disinclined to acquiesce in mindless American hyper-kineticism, in accordance with the Italian saying:

Dolce far niente

Sweet to do nothing

which saying, were it not for the inefficiency lately mentioned, would have been by now inscribed above my stoa. My paternal grandfather had it emblazoned on his pergola, and more 'nothing' transpires on my stoa than ever did beneath his pergola.

So time each day must be devoted to 'doing nothing': meditating, traipsing around in the local mountains, contemplating sunrises and moonsets, sunsets and moonrises, and taking naps, naps punctuated on one end by bed-reading and on the other by yet more coffee-drinking.

Without a sizeable admixture of such 'nothing' I cannot see how a life would be worth living.

Two Senses of ‘Presupposition’ in Van Til and in General

Cornelius Van Til, The Defense of the Faith, 4th ed., p. 279: "Thus the truth of Christianity appears to be the immediately indispensable presupposition of the fruitful study of nature." My gloss:

The fruitful study of nature presupposes the truth of Christianity.  It is a fact that we study nature, and it is a fact that our natural-scientific procedures are successful in many ways and in many areas of inquiry.  Now what is factual is actual, and what is actual is possible. But how is it possible? What are the conditions of the possibility of our successful understanding of nature and (some of) her laws? We are being told by Van Til that an indispensable and thus necessary condition is the truth of Christianity.

This illustrates one legitimate use of  'presupposition.' Presupposition in this sense relates an activity or procedure to a proposition.  To say that activity A presupposes proposition p is to say that A could not be undertaken with the hope of success  were p not true. 

For example, the procedures of natural science presuppose the intelligibility of nature.  We would not seek the laws of planetary motion, for example, if we did not antecedently believe that the motion of the planets was regular and law-like and understandable by us. But IS nature intrinsically intelligible, intelligible an sich? We have  good reason to think so given the success of our physics as shown by its technological implementation.

The presupposition of the intelligibility of nature is therefore well-grounded .

We can push our transcendental regress a step further by asking: what does the intelligibility of nature itself presuppose? What are the conditions of the possibility of nature's being understandable by us?  What would have to be the case for nature to be intelligible to us?  Here are some candidate answers:

A. The intelligibility of nature presupposes the truth of Christianity. (Van Til)

B. The intelligibility of nature presupposes the existence of God. (It is only because a supreme Intelligence created the world that it is intelligible.)

C. The intelligibility of nature presupposes the truth of Kant's transcendental idealism according to which "The understanding is the law-giver of nature." 

D. The intelligibility of nature presupposes an immanent order and teleology along the lines of Thomas Nagel's Mind and Cosmos. On Nagel's view, the rational order is self-explanatory, a necessary feature of anything that could count as a cosmos. Nagel views the intelligibility of the world as "itself part of the deepest explanation why things are as they are." (17).  Now part of the way things are is that they are understandable by us.  Given that the way things are is intelligible, it follows that the intelligibility of the world is self-explanatory or self-grounding. "The intelligibility of the world is no accident." (17)   "nature is such as to give rise to conscious beings with minds; and it is such as to be comprehensible to such beings." (17) See my Nagel category for much more on Nagel's book and other works of his.

I myself incline toward (B).  (A) entails (B), but I see no reason to accept (A).  The sort of bottom-up reasoning that can plausibly justify us in positing God cannot plausibly justify us in positing the God of orthodox Christian theism with all the Reformed add-ons.

The other sense of 'presuppose' is in play here: "I therefore presuppose the Reformed system of doctrine." (Van Til, p. 27) A presupposition in this sense is an assumption that is accepted unconditionally, uncritically, without question. 

Bottom-Up and Top-Down

The first sense of presupposition fits with a bottom-up approach. We start with various features of the world we experience and we then ask what makes them possible.  We attempt  a regress from the given to the hidden. We start with the world, not with God, and we aim to arrive at God.  But if we arrive at God in this way, then the properties we will be justified in attributing to God will  only be those needed for our explanatory purposes.   Those properties are in a certain sense tied to our starting points.  For example, one might reason along these lines: the universe is contingent, but its existence is not a brute fact; so it must have a cause external to it.  In this way we get to God as First Cause.  Or we start from the intelligibility of nature and arrive at God as the supremely intelligent source of the intelligibility we find here below.  Supposing we can get to the true God in this way, a God that needn't have caused anything, or sourced the intelligibility of anything distinct from himself,  it nonetheless remains the case that the properties of this God will reflect the facts we start with and our need to explain them. 

The second sense of presupposition fits with a top-down approach.  We start with God, or at least we try to start with God, and then, instead of regressing from the given to the hidden conditions of the possibility of the given, we progress from the hidden to the given.  This is possible if the God who is hidden to the natural man with his natural intellect has revealed himself.   I understand Van Til to be saying that we know the true God, the God of Abraham, Isaac, and Jacob only because he has revealed himself to us.  The revelation that Van Till accepts is the final truth, not only about God, but also about man, and the universe.  Since it the revelation of God, it cannot be questioned.   We can say that for Van Til, God and his revelation understood along Reformed lines constitute the Absolute Presupposition.

Interim Conclusion

Van Til's bottom-up  transcendental argumentation appears to be a sham. Despite appearances, he is not trying to justify belief in the God of orthodox Christian theism by argumentation from given facts (the existence of nature, its order, beauty, and intelligibility) to that which must be presupposed if they are to be so much as possible; he is not trying to justify belief in the Christian God at all.  For he just assumes the existence of the Christian God as something that needs no justification and cannot be questioned since it is that without which there would be no questioning or proving or anything else.

With that absolute presupposition in place as his unquestionable starting point, he can then advance, but not justify, claims like (A) above: 

A. The intelligibility of nature presupposes the truth of Christianity.

What Van Til is doing in effect is simply presupposing the truth of (A)! What he ought to be doing, however, is giving us a reason to accept (A). It comes as no surprise, then, that Van Til claims that all reasoning is circular reasoning. (123) We will have to examine that claim and Oliphint's defense of it in a separate post.

Van Til just assumes the truth of his worldview and then in effect says: See! I can explain everything, including why there is no neutral ground for the assessment of worldviews, and why people who reject the particulars of my worldview reject them.  But this is of no help to someone who sees no reason to accept his worldview  in the first place.

Suppose I grant that that sin has noetic consequences. I grant the thesis.  But that leaves open the question as what exactly the noetic consequences are. Is it a noetic consequence of sin that I do not accept Van Til's worldview?  Or is rather a noetic consequence of sin that Van Til denies that there is a neutral ground for the assessment of worldviews?

Fascinating! More later. And thanks again to Dave Bagwill for inspiring me to get going on this.

Just Getting Started at 70

A valued correspondent offers,

I'm 70 years old, but I feel like I'm just getting started. Maybe that's a common experience.

I follow not far behind, and I can relate to the sentiment. I am just getting started as I near the end of the trail. The clock is running and I feel like a chess player in time trouble.  I am working on a book that I hope will sum it all up for me and bring my life to a rounded completion.  Will I have time before the flag falls?

Death is the muse of philosophy and one of her great themes. Now death is Janus-faced. One of her faces is that of the Grim Reaper, the other that of the Benign Releaser. 

JanusHow bad can death be if it releases us from this obviously unsatisfactory and bewildering predicament? Only the spiritually insensate could be blind to the horror of this life, a horror mitigated but not outweighed by the beauty in the world and goodness in some people. 

You live in a charnel house that is on fire and you pronounce it a wonderful abode?  How could escape from it not be good? On the other side of the question, that persons cease to exist utterly seems to be a very great evil, something intolerable barely conceivable. To appreciate this one must not think abstractly and objectively — one dies, all men are mortal — but concretely and subjectively: I will die. You, dear heart, will die.

When we think concretely and personally about death, our own death, and the deaths of those we love, we find ourselves agreeing with Arthur Schopenhauer: "The heart rebels against this, and feels that it cannot be true." ("The Vanity of Existence" in The Will to Live, ed. R. Taylor, p. 229)  Let us assume that you love and cherish your wife. Your loving her has conferred upon her uniqueness, at least relative to you. (Josiah Royce) Now imagine her lovable and loving unique personality blotted out of existence forever.  Or consider your own case. You have devoted a lifetime to becoming who you are. You have worked steadily at the task of self-individuation. Only to become nothing? Could things be arranged so badly for us? But then the whole thing would be a bad joke.

Is death evil or not?  No one knows. That we remain in the dark on a question so close to the heart and mind is yet another reason why our condition is a predicament. Should we therefore conclude that the good of escaping it outweighs the bad of personal cessation? No one knows.

The Epicurean reasoning strikes many as sophistical.  And maybe it is, though it is not obvious that it is. "When I am, death is not; when death is; I am not."

Dying is the end of trail, the last step on the via dolorosa.  It is indisputably evil, the only good thing about it being that it will force jokers finally to become serious. Will you be cracking jokes as you gasp for breath and feel yourself helplessly sliding into the abyss? Death, however, is not the last step; it is beyond the trail and its trials and beyond dying, a transcendent  'state' shrouded in mystery, or maybe not even a state: just mystery.

Companion post: On the 'Inconceivability' of Death

Van Til on an Absolutely Certain Proof of Christianity

Cornelius Van Til, The Defense of the Faith, 4th ed., p. 381:

The best, the only, the absolutely certain proof of the truth of Christianity is that unless its truth be presupposed,there is no proof of anything.

Van Til's  claim, to employ some Kantian jargon, is that the truth of Christianity is a condition of the possibility of proving anything. That's quite a claim. Let's put it to the test.

One can prove that the null set is unique by reductio ad absurdum. We begin the reductio by assuming that the null set is not unique, that there are two or more null sets. By the Axiom of Extensionality, two sets differ numerically only if one has a member the other doesn't have, or vice versa. But the null set, by definition, has no members. So the assumption leads to a contradiction. Therefore there cannot be two or more null sets. Hence the null set is unique. 

The proof presupposes the Law of Non-Contradiction (LNC), and I am willing to grant that LNC and the other laws of logic can be argued to presuppose in their turn the existence of an omniscient necessary being. One argument to this conclusion is the Anderson-Welty argument which I critically examine here. I conclude that, while the argument is not rationally compelling, it does contribute to the rationality of belief in God.  In other words, the Anderson-Welty argument is a good reason to believe in the existence of God. It does not, however, establish the existence of God in a definitive manner. It does not show that the existence of God is absolutely certain.

Van Til Cornelius At the very most, then, one can plausibly argue to, but not prove, the existence of an omniscient necessary being whose existence is a presupposition of our rational operations in accordance with the laws of logic.  But this is a far cry from what Van Til asserts above, namely, that the truth of Christianity with all its very specific claims is a condition of the possibility of proving anything. Trinity and Incarnation are among these specific claims. How are these doctrines supposed to bear upon the laws of logic?  Perhaps the Van Tilians have an answer to this. If they do, I would like to know what it is. But not only is Van Til's conception of God Christian, it is also Calvinist so that all the characteristic claims of Calvinism are also packed into the conception of a God that is supposed to be a condition of the possibility of all  proof.  How does predestination, for example, bear upon the laws of logic?

A New and Improved Argument for the Necessity of Something

Previous versions were long-winded.  Herewith, an approach to the lapidary.

1) If nothing exists, then something exists.
2) If something exists, then something exists.
3) Either nothing exists or something exists.
Therefore
4) Necessarily, something exists.

The argument is valid. The second two premises are tautologies. The conclusion is interesting, to put it mildly: it is equivalent to the proposition that it is impossible that there be nothing at all.  But why accept (1)?

Argument for (1)

5) If p, then the proposition expressed by 'p' is true.
Therefore
6) If nothing exists, then nothing exists is true.
7) The consequent of (6) commits us to the existence of at least one proposition.
Therefore
1) If nothing exists, then something exists.

Surely (5) is unproblematic, being one half of the disquotational schema,

DS. P iff the proposition expressed by 'p' is true.

For example, snow is white if and only if snow is white is true. The semantic ascent on the right-hand side of the biconditional involves the application of the predicate 'true' to a proposition. So it is not the case that the left and right hand sides of the biconditional say the same thing or express the same proposition. The LHS says that snow is white; the RHS says something different, namely, that the proposition expressed by 'snow is white' is true. The RHS has an ontological commitment that the LHS does not have: the RHS commits us to a proposition. Since the RHS is true, the proposition exists. (Cf. Colin McGinn, Logical Properties, Oxford UP 2000, 92-93. I am taking from McGinn only the insight that the LHS and RHS of (DS) do not say the same thing.)

But what about the inference from (5) to (6)? Can it be questioned? Yes, if we are willing to countenance counterexamples to (5) and thereby call into question Bivalence, the semantic principle that every proposition is either true or false, but not both. I'll pursue this in a later post. If, however, one accepts Bivalence and its syntactic counterpart, Excluded Middle, then it looks as if I've got me a rigorous a priori argument for the necessity of something and the impossibility of there being nothing at all.