B.C. Askins

The Man With the Golden Gun

Archive for the tag “covenantal apologetics”

Does God Exist? A Debate (5): Christian Conclusion, B.C. Askins

This post contains my final rebuttal and conclusion. Dan will have the last post.

Weak atheism
I pointed out in my initial rebuttal that Dan undermines his own credibility when he demonstrates that he doesn’t understand Christianity, such as when he conflates theological terms with their non-theological senses (i.e. equivocating between general uses of the term “incomprehensibility” and the specific definition of “divine incomprehensibility”). Ironically, Dan’s latest response reveals that he doesn’t really understand atheism either, thoroughly undermining himself and his views. He doesn’t seem to be familiar with the common distinction between “strong atheism” and “weak atheism.” Whether Dan realizes it or not, his opening statement represents negative/weak/soft atheism. Positive/strong/hard atheism would present an argument for the non-existence of God; Dan presents no such argument. To be clear, I referred to Dan’s position as “weak atheism” because that’s what his position is called within the taxonomy of various non-theistic viewpoints; however, I did not “imply that [his] position is consequently weak.” I explicitly stated that it is weak then demonstrated its numerous weaknesses.

[Note for readers: weak atheism is far more common than strong atheism these days, probably due in some part to the contributions of village atheist popularizers like Dick Dawkins and Chris Hitchens (among others), who characterize atheism as “the absence of belief” in divinity. They are well within their rights to define their own position, but this definition has the unfortunate consequence of downgrading atheists, in this regard, to the same noetic level as shellfish or a Chevy Lumina: they all lack a belief in God.]

Debate Topic: Does God Exist?
Dan asserts, “Not only is it not necessary, it is not possible to prove that such a God does not exist.” For whatever reason, Dan turns his guns on strong atheism here for a moment, asserting that position is neither necessary nor even possible (a rather strong modal claim which he does not even attempt to substantiate). After nonchalantly waving aside his half of the burden of proof, he also dismisses an entire group of his fellow atheists then moves ahead with the debate as though nothing happened. It reminds me of Monty Python’s famous Black Knight, except all of Dan’s wounds are self-inflicted in this instance.

Recall that the subject of the debate is the question: “Does God exist?” My answer is “yes,” and I presented a pair of arguments to support my affirmation along with two arguments against atheism; Dan’s answer is “no,” but he has not presented a single argument in defense of his denial. Instead, he has used an altogether-too-common tactic of trying to shift the burden of proof entirely to me. At a tactical level, Dan has not even entered the debate. Yet he seems utterly unaware of this. He doesn’t understand Christianity—he repeatedly argues with straw men, even after being corrected. He doesn’t understand atheism—even the most basic nomenclature associated with his own position eludes him. He could have saved himself a lot of time by just typing “Nuh uh” as his latest response and left it at that. He presents no arguments (meaning “premises implying conclusions”) and merely persists in assertively asserting his own assertions.

Since Dan hasn’t presented much new material in his response, rather than engaging in a painfully iterative summary of our exchange (i.e. I said x, then Dan said y, then I said z and critiqued y, then Dan re-asserted y, so I reiterate x and z and my critique of y, scratch, woof, yawn, etc.), I’ll just provide some criticisms not yet mentioned and briefly point out issues already addressed.

Russell’s teapot
Dan’s repeatedly referenced reason for adopting weak atheism is “Russell’s teapot.” This is a reference to a passing illustration in philosopher Bertrand Russell’s unpublished article “Is There a God?” For those interested, here is the salient section of that article:

“Many orthodox people speak as though it were the business of sceptics to disprove received dogmas rather than of dogmatists to prove them. This is, of course, a mistake. If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.”

First, all sides can acknowledge that the absence of evidence is not the evidence of absence. There is no evidence for Russell’s celestial teapot, but this alone does not disprove its existence. For someone to conclude that Russell’s teapot doesn’t exist merely because there isn’t evidence for its existence is to argue from ignorance (an informal fallacy). Rather, although Russell does not mention this, it is positive evidence for its non-existence which leads us to conclude the celestial teapot does not exist, such as that NASA (or the Russian space program) never sent a teapot into orbit, matter doesn’t self-organize into celestial ceramic china, etc. Either Russell argues from ignorance or he conveniently omits the positive evidence which leads him to believe in the teapot’s non-existence.

Second, Russell presents some category confusion in the analogy. The celestial teapot is causally, explanatorily, epistemically, morally, transcendentally irrelevant; on the other hand, God is posited as the necessary condition for each of those categories. This confuses the category distinctions between Creator and creature. The dilemma is that the atheist wants to say that God is just as irrelevant as the teapot—however, he must establish this point before the analogy holds. But if he could establish this independently then the analogy would be superfluous. It’s rhetorical sleight of hand. Russell’s illustration suggests that God is irrelevant by referring to an analogy which rests upon an unknown, unarticulated argument that God is irrelevant. In other words, he’s arguing for a conclusion without a premise or an inference via an imaginative fairy tale about a flying teapot.

Methodologically, this approach also commits what Greg Bahnsen referred to (in his debate with Gordon Stein) as the crackers in the pantry fallacy:

“We might ask, ‘Is there a box of crackers in the pantry?’ And we know how we would go about answering that question. But that is a far, far cry from the way we go about answering questions determining the reality of say, barometric pressure, quasars, gravitational attraction, elasticity, radioactivity, natural laws, names, grammar, numbers, the university itself that you’re now at, past events, categories, future contingencies, laws of thought, political obligations, individual identity over time, causation, memories, dreams, or even love or beauty. In such cases, one does not do anything like walk to the pantry and look inside for the crackers. There are thousands of existence or factual questions, and they are not at all answered in the same way in each case.”

Russell assumes (possibly due in some part to his “logical atomism”) that the methodology for discerning the existence of a celestial tea pot is the same as for discerning the existence of God. But, as I argued in my opening statement, the question of the existence of God has its own transcendental methodological concerns, analogous in many ways to proving the existence of space and time (note: actual space and time, not a mere model of space-time).

So Dan’s reason for abdicating his half of the burden of proof in our debate is (at worst) based upon an argument from ignorance or (at best) category confusion and a flawed methodology.

Coherent Definitions
Dan has asserted and re-asserted that the definition of God “fails to meet the standard of coherence.” When given the opportunity to substantiate his claims, he roasts a straw man to the ground. Our debate (and Dan’s YouTube channel) is covered with a thick layer of the burnt remains of straw men. Here’s a humble suggestion for how Dan might increase the credibility of his position in the future: read, properly interpret, then cite a reputable systematic theology text’s definition of one of these terms, then imply a contradiction from that definition—rather than supplying your own blatantly self-contradictory definition then implying a contradiction from it just by repeating it sarcastically. All of Dan’s purported contradictions in Christian theology are pre-empted by an introductory familiarity with Christian doctrine. When he persists in his equivocal use of “incomprehensibility” he does so to the further detriment of his own credibility.

Then he raises other purported examples of contradictions in Christianity, such as that God “not clearing the guilty” contradicts “forgiving iniquity.” A cursory familiarity with doctrines such as penal substitutionary atonement, double imputation, and union with Christ preempt such simplistic contradiction proposals. He gives a series of rhetorical questions on why “living” and “immutable” are incompatible attributes, but all he demonstrates is that he’s working without any familiarity with these terms in their theological senses. Until Dan decides to become familiar with Christian theology his critiques will remain a superficial example of anti-preaching to the a-theological choir.

Dan’s “Axioms”
Dan happily clarified that he uses the term “axiom” to refer to “a necessary truth foundational to subsequent knowledge claims.” Since this definition was already criticized in my initial response, I won’t say much here. As I said before, when someone calls a philosophical proposition an “axiom” he is usually deceptively attempting to borrow credibility from mathematical terminology while persuading someone to accept his beliefs as necessarily true without any argument for doing so. It’s more of the same equivocation and rhetorical sleight of hand already discussed.

Reification Reiterated
I’ve decided to coin a term for Dan’s particular approach to criticism: reificatomania. As I’ve already said, Dan sees fallacious reification everywhere. When I refer to an abstraction, such as a number or logical rule, as a mental object Dan believes this is “reification in broad daylight.” I’m not attributing anything other than mere existence to abstract ideas; ideas exist as ideas, thoughts as thoughts, abstractions as abstractions. Existence isn’t a concrete quality like color or density.

Dan says, “Numbers are not real, existent entities, but rather mental constructs used to model the behavior we observe in reality.” Do “mental constructs” exist? If so, then he commits his own idiosyncratic version of the reification fallacy. If these “mental constructs” do not exist, then what could they be and what’s the point in referencing them?

Existence could only be a concrete attribute according to a particular sort of materialism; but Dan will need to justify his materialism (if he is a materialist) before he can establish his peculiar application of the reification fallacy. But Dan hasn’t even made it clear if he is a materialist, much less whether he can justify that position. This is just another example of the question-begging which I mentioned in my initial response. You can’t refute immaterialism by reference to materialism; it is fallaciously circular.

Definition of Personality
My definition of person is “a rational, self-conscious entity.” Dan objects and says that human beings are “in virtually every sense, not persons per Ben’s definition.” While Dan may have placed his own status as a “rational, self-conscious entity” into some doubt by his performance in this debate, human beings as a class clearly fit well within my definition.

My definition doesn’t include physicality as an essential aspect of personality. Dan disagrees. Pointing to the fact of his disagreement could be the basis for proposing a debate like the one we’re already having, but it does not provide any substance to the debate we’re currently conducting. Again, Dan would need to substantiate his reasons for disagreement to even begin to enter this debate—but it’s a little late in the game for that, I’m afraid.

Self-Dissolving Solvents
I’ve already pointed out some of the absurdities entailed by Dan’s position regarding the non-existence of numbers and truth and logic apart from the existence of human brains. Simply, a proposition about the future can’t be true today, but non-true at the point in the future to which the proposition refers; that is completely absurd—as demonstrated by the global brain death reductio.

It’s also noteworthy that his position begs the question against mine. He asserts, “However, if tomorrow there are no brains, neither the question, or the numbers involved, would be conceptualized.” This assumes that God’s mind does not exist in order to assert that God’s mind does not exist. Dan’s position on the existence of God, numbers, logic, and truth is a philosophical solvent which dissolves itself.

I raised the question of how Dan proposes to bridge the subject-object gap. He wants to treat logic, math, and truth (at least) as purely subjective matters, but still wishes to maintain that there is some objective reality out there—math and logic and truth are just models of this reality, but by what does Dan transcend both subject and object in order to even draw this distinction in the first place? We don’t know because, apparently, Dan doesn’t know.

He weakly asserts, “It’s not a contradiction to have an objective reality exist while only being able to experience it subjectively.” But how does Dan know this is not a contradiction? He asserts there is an objective reality out there, but that all of math, science, reasoning, and experience are locked up in a purely subjective realm, with no bridge between the two. He doesn’t provide any answers, but does lamely footnote himself as having “debunked [the core of presuppositionalist argument] at some length in other writings.” If it’s anything like the so-called “debunking” we’ve observed in this debate, you’ll have to pardon me if I find this form of self-referential footnoting unpersuasive.

The Metaphor of Misinterpretation
I pointed out that Dan clearly misinterpreted James Anderson’s paper “Calvinism and the First Sin.” Again, Dan asserts I am mistaken. Unfortunately, his interpretation is remarkably wrong. I can’t even begin to understand how he draws his conclusions on this point. This interaction could be spread out metaphorically across our entire debate. I argue for a point—Dan declares that he disagrees—I demonstrate Dan is wrong—Dan reiterates his disagreement.

I emailed Dr. Anderson and asked him to adjudicate between our interpretations of his paper. He replied to me, “You’re basically correct about what I said. My point is that from the perspective of the sinning agent, the act of sin is irrational. It cannot be rational to sin. Thus one cannot identify reasons for which Adam sinned. That this is what I meant can be confirmed from the references in the footnote. I’m certainly not claiming that the Christian doctrine of sin is intrinsically irrational (or any other Christian doctrine for that matter)… Dan apparently thinks that I’ve openly conceded that Calvinism is irrational, which couldn’t be further from the truth… He seems to assume that any appeal to mystery is irrational. But he doesn’t argue the point. And as you know, I wrote an entire book arguing the very opposite!” [Note for readers: James’ book, which I hyperlinked, is one of my absolute favorite works of philosophical theology. For what it’s worth, I don’t recommend many books without reservation, but this is one exception.]

Hopefully this clarifies things for Dan and he will openly forsake his misreading of Anderson’s paper (and correct or retract his errant YouTube video which is based upon the same error).

I’d like to thank Dan for taking the time to engage in this debate and I wish him the best in the future. (To be clear, by “I wish him the best” I mean I hope he someday repents of his atheism and turns to Christ to redeem him, epistemology and all.)

As I said in my opening statement, my belief in God is basic and intuitive. Dan simply hasn’t given me any reasons to doubt my intuitions on this subject (or any subject, for that matter).

I also stated in my opener, “On the question of the existence of God, either atheists are radically self-deceived or theists are… One of us is colossally wrong.”  I suggest Dan’s half of our exchange has convincingly demonstrated my assertion to be true:

Dan believes proving the non-existence of God is impossible—yet persists in believing in God’s non-existence; he refuses to accept standard theological definitions, even when corrected; he’s unfamiliar with the basic taxonomy of his own position; he equivocated frequently; he engaged in fallacious reasoning, including ipse dixitism and petitio principii; his position on abstract objects entails absurdity and self-contradiction; he places himself on the horns of a dilemma with his idiosyncratic application of the reification fallacy; when questioned, he doesn’t even attempt to provide an answer to a fundamental epistemic issue, i.e. the subject-object problem; his philosophy is difficult to discern, but it resembles a sort of diluted logical positivism—a thoroughly debunked view, left on the philosophical ash heap by Karl Popper, Thomas Kuhn, and P.F. Strawson (among others) some fifty years ago; finally, he has refused correction on his tortuously obtuse reading of Dr. Anderson’s paper.

In other words, he is “colossally wrong.”

Dan, the last word is yours. Use it wisely. With great power there must also come—great  responsibility!


Does God Exist? A Debate: (3) Initial Christian Rebuttal, B.C. Askins

Thank you, Dan, for your opening statement. Here is my initial response.

Strong vs. weak atheism
I’ll ask readers to note that in Dan’s first paragraph he chooses to defend weak atheism, rather than assume any burden of proof for his answer to the question “Does God exist?” This seems appropriate, given the rather weak responses in his opening statement. He immediately lowered the bar for his side of the debate, then failed to even meet that standard.

He states, “I do not claim, nor is it necessary, to prove that the Christian God does not exist… demonstrating that Ben’s arguments for the Christian God are fatally flawed is sufficient to conclude that such beliefs are irrational.” Recall that we are debating about the existence of God, not the mere rational status of my beliefs. All of my beliefs in this regard could be “fatally flawed” and that would not prove anything with respect to the subject of the debate. I am arguing, “God exists,” while Dan is merely arguing, “Some of Ben’s beliefs are irrational.” Let’s investigate now whether or not he has satisfied the significantly reduced burden of proof which he has placed upon himself.

Defining the term “God”
Dan alleges that there are many contradictions in the definition of God which I referenced in my opening statement. He doesn’t show that there are any contradictions, he merely alleges as much. He chooses divine incomprehensibility as noteworthy, then demonstrates that he hasn’t been taking good notes.

Equivocation is the misleading use of terms which have multiple definitions. When Dan says of divine incomprehensibility, “It would be a simple matter for me to agree with this part of the definition and claim victory,” he equivocates (an informal fallacy). “Incomprehensible” is synonymous with “non-intelligibility” in most contexts; however, divine incomprehensibility refers to the doctrine that God cannot be fully comprehended and is unknowable apart from self-revelation. This standard definition is referred to as a “common retort” by Dan, which makes him seem less credible. It’s not a retort; it’s a standard definition in Christian theology which has been maintained across many cultures and centuries.

If he can demonstrate a contradiction in the doctrine of divine incomprehensibility (or the definition of God), then he should simply do so—rather than equivocating and obfuscating. When one desires to refute another’s position, it would behoove him to be familiar with the standard definitions associated with that position before attempting refutation. A bare familiarity with some standard work in systematic theology would prevent these sorts of unfortunate errors. Before one can effectively “undermine Christianity” one must correctly understand Christianity.

Actual vs. potential infinite
Dan also seems to be unfamiliar with the common distinction (tracing its roots all the way back to Aristotle) between actual and potential infinity. This is evidenced by the scare quotes around “actual” in statements such as, “We’ll see later how Ben attempts to make the concept of infinite ‘actual’, and then tie ‘God’ to the ‘actual’ infinite, and why this doesn’t work.” He also asserts twice that “infinite means without limits,” which is simply a reference to potential infinity (e.g. limits in calculus). Actual infinity is a set with infinite members, such as the set of all positive integers {1, 2, 3, 4,…}. These are non-controversial, introductory matters in set theory which are important to even understanding, much less refuting, the Transcendental Argument for God from Mathematics (TAG-M).

Dan has also made a couple of unsubstantiated assertions about what he calls “axioms,” e.g. Einstein’s work depends upon “deeper axioms” than a belief in space-time, I’m relying upon certain axioms to conclude that God exists, etc. I’m confused by Dan’s use of this term and I’d ask him to clarify what sense of “axiom” he is using, please. If he’s referring to, say, axioms in geometry used to derive theorems, then I fail to see the relevance of his statements. These axioms are simply stipulations used for mathematical modeling (as in Einstein’s physics). However, if he means the term in a more philosophical sense, as referring to necessary or self-evident truths, then he has again equivocated in explicitly referencing Einstein’s axioms in this other sense. Logic and math share many similarities but they are not mutually reducible to each other.

Using the term “axiom” to refer to a necessary truth is just a wishful assertion—“wishful” in the sense that most often when one refers to a philosophical principle as an “axiom” he is just attempting to convince an audience, without argument, that the principle is indeed a self-evident and necessary truth. This was a common conflation among the ancient Greeks, however, most today would grant that our math and philosophy have advanced some since then (terminologically, at the very least!). Unfortunately for Dan, in both math and philosophy you sometimes need to substantiate your axioms with proofs and arguments, respectively.

Ipse dixitism
Dan is quite fond of alleging his opponents have committed various logical fallacies. However, the mere allegation of fallacious reasoning is insufficient to establish that a fallacy has actually been committed. Ironically, merely asserting something is the case without substantiation is an informal fallacy known as ipse dixit or the “bare assertion fallacy.” Dan will need to get his hands dirty demonstrating that I’ve committed the various fallacies he’s alleged, rather than the mere hand-waving and just-so assertions he’s given thus far. Dan tells us, on his bare authority, that numbers, propositions, persons, etc. are all just what he says they are. No need for argument, that’s just the way it is. God just doesn’t exist. QED.

Calling something a fallacy and demonstrating it is a fallacy are two very different things; and bare assertions don’t rise to the level of reasoned argumentation, no matter how often they are repeated or rephrased.

Everywhere Dan looks he seems to see somebody fallaciously reifying something. He sees it in the first three of my four arguments. I’m sure if he looks long enough, he could find it in the fourth as well. He may need to check his sources on this one, however. First, reification is not always fallacious; it is particularly common in rhetoric and literature, through the use of metaphor. Second, and more importantly, fallacious reification attributes concrete characteristics to abstractions. Referring to numbers as mental objects simply does not attribute any concrete characteristics to them at all. At the risk of stating the obvious, an abstraction is a mental object—an idea. If arguing that a number is an idea commits the fallacy of misplaced concreteness, then anything goes. Up so floating many bells down. I argued that numbers are mental objects; Dan says, no, they are metaphors. But what is a metaphor, if not (at least) a mental object as well? I’d suggest Dan may want to holster this fallacy until he figures out which end fires the bullets (*note the non-fallacious reification*).

Numbers and Logic
Dan says, “Numbers do not exist, as Ben asserts, independent of our brains that conceive of them.” So, if everything with a brain woke up dead tomorrow, how much would 2+2 equal? If you answered 4, according to Dan, you’d be wrong. All the numbers would have died with our brains. If you were riding in a car with me when all the brains in the world died, then there wouldn’t be two of us there afterward. We can project right now that there would be two of us in the car after the sudden global brain death (because we still have working brains), but after it happens there will not be two dead bodies in the car anymore. The dead bodies would be there and there would be two of them, but there couldn’t actually be two of them because there aren’t any numbers anymore. The clocks will keep running, but there won’t be any numbers to correspond with the passage of time. The billions of stars will still be there, but there won’t be billions of them anymore. Dan’s view is an absurd groupthink-meets-metaphysical-solipsism. Meanwhile, it remains painfully obvious that numbers and mathematics transcend our brains as demonstrated by the existence of actual infinite sets of mental objects, as I argued.

The same problem exists for Dan’s response to Anderson/Welty’s argument from logic. Does the principle of non-contradiction cease to apply the moment after global brain death? Did it apply during the timeline of evolution, before brains existed? Of course it did, but that means it transcends our brains. And if laws of logic are absolute mental entities, they must inhere in an absolute mind, i.e. the mind of God. Denying this principle produces the sorts of absurdities already discussed. Further, to say that the laws of logic are merely descriptive while repeatedly accusing me of committing logical fallacies is problematic. This is just Hume’s classic “is-ought problem;” but you can’t derive a prescription from a description without committing a category error.

Question-begging assertions
Many of Dan’s criticisms are simply question-begging. He believes one thing, and I believe something different. On the basis of the fact of this difference, Dan declares me wrong. He assumes his own position to be correct, without argument, then declares mine incorrect for not matching his. This is viciously circular.

An example: “Ben’s minimalist definition of personal, ‘rational, self-conscious entity’ is an equivocation. Ben wants the attribute of a person without the physical baggage that comes with it.” To assert that a “person” can only be physical begs the question against immaterialism. He’ll need to refute immaterialism on its own terms, rather than by direct appeal to physicalism. More examples could be adduced in this regard.

Subjectivism incompatible with realism
Dan has asserted that “numbers are metaphors,” “propositions are symbolic representations,” and “theories of truth… are simply our subjective understanding of what the word truth means.”
He has also stated that math “model[s] reality, but is not reality itself,” numbers and propositions “are symbolic representations of some aspect of reality,” that “we perceive some aspect of reality,” etc.

On the one hand, Dan wishes to say that all these things are subjective, reducible to our perceptions—to the point that if our collective consciousness dies, math and logic and truth die with it.

On the other hand he wishes to say that there is an objective reality which corresponds with those perceptions. (Unless he’s using the term “reality” as synonymous with “our perceptions,” which would make his statements consistent with subjectivism, but uselessly tautological.)

But one can’t be a subjectivist-realist any more than he can be an atheist-polytheist. So how does Dan propose to bridge the gap between subject and object? I’ll predict that whatever answer he proposes will be self-refuting apart from acknowledging the role of divine self-revelation in epistemology.

A Minor Point of Clarification
In Dan’s closing statement he quotes Dr. James Anderson’s article “Calvinism and the First Sin.” I think Dan has misunderstood James, for when he states “sin is intrinsically irrational” James means that the act of disobeying God (i.e. sinning) is irrational, not that the Christian doctrine of sin per se is irrational. I think if Dan re-reads this section of the paper he’ll see his mistake.

…speaking of sin
Finally, I’ll point out that these intellectual discussions connect directly with flesh-and-bone in that, if my position is correct then Dan’s position is not merely mistaken, it is sinful. One of the noetic effects of sin is turning rational creatures made in God’s image into irrational God-haters. I ask Dan to repent of using the intellect which God has given him in order to argue against the truth, and I ask him to become a thinker free from sin, embracing reason in Jesus Christ, in whom are hidden all the treasures of wisdom and knowledge. (Colossians 2:3)

I look forward to reading Dan’s next response, assuming no global brain death occurs before then.

The Liar Paradox and Presuppositional Apologetics 4: Defending Classical Logic

This post will be an overly-brief thumbnail sketch of a response to a broad and complex philosophical topic: dialetheism. From SEP: “A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true… dialetheism opposes the so-called Law of Non-Contradiction (LNC),” (i.e. for any A, it is impossible for both A and not-A to be true).

The Liar Sentence (“This sentence is false.”), considered as a semantic paradox, is the most common example of a proposed dialetheia, and has been the subject of my most recent blog series. A notional objection to presuppositional apologetics was proposed by atheist philosopher Patrick Mefford, roughly stating that the Liar Paradox presents a problem for the presuppositional apologist’s use of the LNC in arguing for the existence of God. Mefford proposed that the adoption of a multi-valued logic (rather than the classical binary logic) might blunt the force of the apologist’s reliance on the LNC in his argumentation. (Or possibly the objection was that if there are true dialetheias then God must believe falsehoods or create contradictions or some other such untrustworthy or nefarious thing… as I said, the objection wasn’t clearly stated).

In response to the objection, I proposed that the adoption of a multi-valued logic wouldn’t be as problematic as Mefford supposed (and I criticized his proposed solution as well).

However, there seems to have been some confusion surrounding what a multi-valued logic actually is. (This seems to have been due to Mefford’s recent familiarity with the subject, as evidenced by his acknowledged unfamiliarity with dialetheism and paraconsistency.) So, to be clear:

A classical binary logic has two truth-values: true and false.

A multi-valued logic (MVL) contains multiple truth-values: true, false, and at least one other value – such as “both,” “neither,” “undefined,” “unknown,” etc.

There are also infinite-valued logics, such as fuzzy logic, with truth-degrees between 0 and 1.

There are many different multi-valued logics and I have neither the time, desire, nor the expertise to discuss them all at length here. I would simply note that even Asenjo’s Logic of Paradox (promulgated by the foremost dialetheist Graham Priest) doesn’t deny the LNC outright, but seeks to outline a logic which incorporates the LNC with sentences that are inconsistent with it (i.e. dialetheias). To attempt to put it more simply, a classical, binary logic seeks to maintain logical consistency in light of the LNC, while certain multi-valued logics seek to maintain a kind of logical consistency (paraconsistency) which takes into consideration the LNC and certain, specific dialetheias – while not succumbing to the problem of trivialism (the undesirable view that all contradictions are true) through logical explosion (when the truth blows up and gets everywhere).

Dialetheism is an extreme minority position in the history of Western philosophy, but in its more robust forms it is a difficult theory to overturn. There are many complex and thorny philosophical issues in this regard which, again, go beyond the scope of a blog post. While there are many motives proposed for adopting dialetheism, it would not be inaccurate to say that the Liar Paradox is the central reason proffered for the position.

The most common (and misbegotten) objection to dialetheism is that it entails trivialism via logical explosion – that any sentence can be materially implied from a contradiction via disjunctive syllogism.

An example:

Assume that (A) “All cats go to hell” and (¬A) “All cats do not go to hell” are both true. From this we can validly infer anything, such as (B) “David Hume is David Bowie.”

(P1) Either all cats go to hell or David Hume is David Bowie (A v B)

(P2) All cats do not go to hell (¬A)

(C) Therefore, David Hume is David Bowie. (B by DS)

If dialetheism produces these sorts of logical conclusions then it would appear to be deeply flawed. However, paraconsistent logics are constructed purposefully to avoid triviality. So the argument that dialetheism entails triviality fails because paraconsistent logics are non-explosive (though the details in this regard can be quite technical and are not entirely uncontested).

A stronger response to paradoxes of self-reference is the proposal of MVLs which can account for sentences which appear to be both true and false (or neither true nor false, by intersubstitutivity). So a sentence like the Liar is accounted for by giving it a third truth-value (as described above). However, these MVLs all ostensibly fall prey to various “Revenge Paradoxes,” such as the “Strengthened Liar.”

The Strengthened Liar accepts the truth-values of whatever multi-valued logic may be proposed, but then reproduces the paradox of self-reference within the truth-values of that logic (i.e. “This sentence is not true” or “This sentence is neither true nor false nor both,” etc.). So even the adoption of MVLs with truth-value gaps (neither true nor false) or gluts (both true and false) falls prey to various Strengthened Liars. Whatever truth-values a given logic may contain, a Liar Sentence can be produced for those values. These sentences have been called “Revenge Paradoxes,” in that they respond to proposed solutions to the semantic paradoxes with a reformulation of the original paradox, seeking semantic vengeance on their objectors. (“Semantic Vengeance” would be a pretty good band name for a progressive metal group, don’t you think?)

To summarize, semantic paradoxes (such as the Liar) provide evidence for the dialetheistic cornerstone position that there are true contradictions. The paradoxical characteristics of sentences like the Strengthened Liar(s) are due to the ordinary features of natural language, such as self-reference and the presence of truth predicates (i.e. “is true”). Various proposed solutions fail, such as Tarskian metalinguistic hierarchies, since they only produce languages that are expressively weaker than English. MVLs are non-explosive but still fall prey to Strengthened Liars. Several other solutions have been proposed, but most simply beg the question in favor of classical logic. As I said, dialetheism is a difficult theory to overturn.

So what recourse is there for the defender of classical binary logic in the face of the Liar Paradox?

Recently, a defense of monaletheism has been advocated by Benjamin Burgis, in his doctoral dissertation (HT: Paul Manata). The essence of Burgis’ argument, as I understand it, is that sentences with truth-value ascriptions are meaningless unless they are “grounded-out” in sentences which contain no truth predicate (p. 112f., esp. n. 101).

The problem for the Liar is that this semantic paradox doesn’t ground its truth attributions in extra-semantic reality. Burgis alternatingly (and somewhat confusingly) calls this the “meaningfulness solution” or the “meaninglessness solution.” He states it more explicitly as the “Kripke/Tarski Thesis: We are making some sort of mistake when we attribute truth or falsity to a sentence that isn’t (directly or indirectly) about something other than truth” (p. 116). He argues that sentences like the Liar are actually meaningless (and thus not true dialetheias), though they give an initially plausible appearance of meaningfulness because they contain many of the characteristics of meaningful sentences, such as being grammatically well-formed, self-referential, truth-ascribing, etc.

The argumentation he presents is extensive and I would commend it to any with the time and interest in reading it. He seems to have a good case for a non-question-begging response to dialetheism, which is easier stated than demonstrated. Given our discussion above, it seems best then to briefly consider whether or not Burgis’ defense of monaletheism falls prey to any sort of Revenge Paradoxes.

A Revenge Paradox to Burgis’ meaningfulness solution could be formulated as: “It would be a mistake of some sort to call this sentence true.” If we say the sentence is true, we are mistaken – since it’s meaningless (per Burgis’ solution). If we say it is false, then we commit no mistake when we say it is true – but that’s exactly what the sentence says is a mistake. We make one kind of mistake in ascribing truth to a meaningless sentence, and another kind of mistake in ascribing falsehood to a true sentence. If it’s true, then we’re mistaken, if it’s false, then it’s true (and we’re mistaken), and if it’s meaningless then it’s true (and we’re still mistaken). There doesn’t appear to be a non-mistaken way to refer to the truth-value associated with this Revenge Paradox sentence.

So, given this analysis, a way of reformulating this sentence would be “This sentence is either false or meaningless.” It’s this disjunction which allows Burgis’ meaningfulness solution to escape the Revenge Paradox, since the first disjunct (“This sentence is false”) is meaningless and a disjunction must have two meaningful disjuncts in order to ascribe truth-value to it (per the meaningfulness solution). So if the disjunct is meaningless and it is saying the same thing as the Revenge Paradox above, then this Revenge Paradox is also meaningless (or begs the question against the meaningfulness solution).

So if the strongest candidate for a proposed dialetheia, the Liar Paradox, is meaningless, then one (the?) major objection to classical logic has been de-fanged.

In my limited and humble estimation, Burgis’ proposals give the strongest non-question-begging, non-ad hoc, intuitively plausible defense of monaletheism (and concomitant critique of dialetheism) available for pursuing a defense of classical binary logic in the face of semantic paradoxes such as the Liar.

So, to conclude this series, Mefford’s original objection can be answered by the presuppositional apologist through (1) demonstrating his dilemma is hornless by adopting a multi-valued logic (maintaining the same thesis-antithesis approach which incorporates the LNC but adopting an MVL as concerning the semantic paradoxes where necessary) – this is not problematic since the presuppositionalist in particular understands the relationship between divine and human logic as analogical; (2) criticizing his proposed solution in the Tarskian hierarchy; and (3) by defending classical logic, arguing that the semantic paradoxes like the Liar are meaningless.

In any case, it would hardly seem that the presuppositional apologist (or any apologist in general, I think) need fear anything from a consideration of the Liar Paradox.

The Liar Paradox and Presuppositional Apologetics 3: A “Final” Reply to Patrick Mefford

A good link-history of the recent discussion surrounding the Liar Paradox and presuppositional apologetics can be found at the beginning of Chris Bolt’s latest post. So I won’t re-tread any of that here.

It appears that Patrick Mefford has decided to take his ball and go home. Entirely his prerogative. We salute your service, Mr. Mefford, and wish you a happy new year.

In his final post to Chris Bolt, he did respond to me as well – so I’ll give some final thoughts in return. ‘Tis the season for giving and all…

Misreading Paul?

There was a bit of exegetical back-and-forth between Chris and Patrick over Titus 1:12-13a, specifically regarding whether or not Paul presents a case of the Liar Paradox when he quotes a Cretan prophet stating, “Cretans are always liars.”

Given that the broader context of Titus 1 has to do with the careful selection of church leaders according to certain character qualities, it makes the best sense to understand Paul’s quotation of Epimenides as proving his point – that close evaluation of men from Crete would be necessary in choosing church leaders. Cretans were notorious scoundrels, and even their own prophets (whom one might expect to evaluate their own heritage and culture patriotically) can be called as witnesses to the fact – “we’re all liars, gluttons and monsters.” This seems more in line with the whole letter to Titus – rather than the introduction of dialetheism without further commentary of any sort from the author.

However, I don’t think Patrick intended to get into an extended exegetical debate over the issue. His point seems to me to have been an attempt at providing a stronger reason for a Christian apologist to want to resolve the Liar Paradox – “look, it’s even in the Bible.” I’ll give Patrick credit for trying to bring some further rhetorical force to his objection, but his conclusion (unfortunately) requires a rather forced interpretation of Titus – which Chris, to his credit, resisted.

Regardless of the exegesis of Titus, the Liar Paradox remains an issue for both parties, since Chris desires to maintain a classical binary logic and there’s a few problems with Tarski’s position (which Mefford has proposed).

Misreading me?

Patrick quotes a section of this post, where I’m attempting to summarize Tarski’s semantic hierarchy as relevant to the issue of the Liar Paradox. He quotes me summarizing Tarski, then points out that “this does not accurately describe what I laid out.” Nor was it meant to. It’s a summary of Tarski, not Mefford.

Admittedly, my summary borders on an oversimplification of Tarski, but it was an attempt to break things down to laymen’s terms (as much as I might be able); but to criticize it for not being something it was never intended to be is hardly appropriate. So he misread me.

Misreading me… or Tarski… or himself?

Regarding his own formulation, Mefford states: “There is no bottom level object language that does not contains (sic) words like ‘true’ or ‘false’. This is made explicit.”

However, quoting Mefford’s original post, he formulates the Liar Sentence within the hierarchy as:

(A1b) “P2 is false” [ln] is true [Tn+1] if and only if P2 is false [ln]

He explains, “The liar paradox cannot be stated in this hierarchy, because any language it is written in will not have the proper truth predicate.”

So, on the one hand, he says: (X) the bottom-level object language (ln-1) does not contain the proper truth predicate (i.e. words like ‘true’ or ‘false’), which is how the hierarchy eludes the paradox.

Or, on the other hand, he says: (Y) “there is no bottom level object language that does not contains (sic) words like ‘true’ or ‘false’.” So which is it, (X) or (Y)?

These propositions exist. They are a contradiction. How do they stand in relation to Patrick Mefford?

Well, most likely, he has either misread me or Tarski (or himself?) or some combination thereof. I don’t know which.

(Let me make the point more explicitly: if Mefford’s object language contains a truth predicate then it is susceptible to the Liar Paradox; if it does not contain the relevant truth predicate then he has no basis for his objection to my summary.)

Misreading me again?

Mefford goes on to quote my point regarding the infinite nature of Tarski’s hierarchy. But for some reason he thinks I’m raising this as a “mistake or problem.” He says, “…asking me where the hierarchy stops is to assume to (sic) the collection is finite instead of infinite.” But I never asked where the hierarchy stops. I didn’t ask, because that’s a dumb question. I was merely pointing out that Tarski’s hierarchy is infinite. I agree with Mefford when he says, “An infinite regress isn’t a mistake or a problem. Infinite regression is fine n dandy in mathematics…” So, I’m not sure why he disagrees with me, unless it’s due to the jocular reference to “turtles all the way down.”

It’s my understanding that the phrase “turtles all the way down” has specific historical reference to the infinite regress problem within the domain of cosmology – but when used outside of that domain it can refer to an infinite regress of whatever kind (in this case a non-problematic infinite regress). Since we weren’t at all discussing cosmology, I assumed Mefford would know that I was merely referencing a colorful illustration of the infinite recourse within Tarski’s hierarchy.

However, if Mefford objects that I shouldn’t have borrowed a term from cosmology for illustrative purposes, then I’ll simply point out (in good fun) that his illustration from Tristram Shandy is a pure cock and bull story.

Bottom line

Unfortunately, Mefford chose not to interact with any of my actual criticisms of Tarski’s hierarchy (such as that the semantic hierarchy is incapable of useful self-reference, it relies on natural language in a problematic way, and that it doesn’t resolve the Liar Paradox for natural languages). Rather, it would appear that his engagement with presuppositional apologetics in general could be characterized by the sorts of misreadings outlined above.

Since C.L. Bolt was kind enough to “leave the rest” to me, I’ll be following this post with a (brief) defense of classical logic, Lord willing.

The Liar Paradox and Presuppositional Apologetics 2: A Critique

English: The Pinocchio paradox. When Pinocchio...

The Pinocchio paradox. When Pinocchio says “My nose grows now” it creates a Liar sentence and makes Pinocchio’s nose to grow if and only if it does not grow. (Photo credit: Wikipedia)

Pat Mefford has said that “conventional notions of truth and falsity in our natural language and in our everyday discourse are what I consider to be a useful fiction.” He proposes the adoption of Alfred Tarski’s semantic conception of truth, an artificial hierarchy of languages whereby the truth predicate for an initial “object-language” is only found in a “meta-language” (neatly escaping the Liar Paradox, i.e. “This sentence is false.”). However, as we’ll see momentarily, if the intuitively appealing use of “true” and “false” in our natural language is a “useful fiction,” as Mefford put it, then Tarski’s hierarchy could be considered a “useless fiction” in contrast.

Tarski’s proposal is that we can save consistency in the face of the Liar Paradox, not for natural languages, but for restricted and regimented artificial languages, wherein no language contains its own truth predicate. At the bottom level, we have the “object language,” which does not contain words like “true” or “false” at all. Above that we have the “meta-language,” which contains such words, but where they can only be applied to object language sentences. It really is a very clever way of avoiding the Liar, since no self-referential, truth-value-ascribing sentences are possible within any given language.

However, if we want to contend with the truth-value of an assertion made in the meta-language, we would need further recourse to a meta-meta-language to consider whether or not the truth predication of the meta-language (regarding the object-language) is correct. What if there’s a question regarding the truth ascribed in the meta-meta-language? Well, we need a meta-meta-meta-language. See the pattern? It’s turtles all the way down.

Consider the following example:

(1) All dogs go to heaven.

(2) It is true that “all dogs go to heaven.”

(3) It is false that “all dogs go to heaven.”

Sentence (1) is written in the object-language while (2) and (3) are in the meta-language. How do we express the disagreement between (2) and (3)? If we were allowed to do that in the meta-language, then the meta-language would contain its own truth predicate, and we could construct a meta-language sentence like (1), but the problem of the Liar wouldn’t have been avoided. So we have to step up into a meta-meta-language to make a statement like:

(4) It is false that “it is true that ‘all dogs go to heaven.’”

Note that most explanations of Tarski’s linguistic hierarchy are commonly made in our natural language, not within the hierarchy itself. This isn’t clearly self-refuting, since such a project appears possible, but it would seem awkward and impractical to parse out each sentence’s place within the hierarchy while explaining the hierarchy itself; consistency would require such a task though. So, while this hierarchy of languages presents a resolution for the special case of the semantics associated with the Liar Paradox it makes the semantics associated with the rest of discourse cumbersome and unnatural.

Further, there are statements which seem intuitively true and which would be useful in discussing Tarski’s hierarchy but which simply can’t be said in any of his artificial languages. For instance:

(5) No sentence anywhere in the hierarchy says of itself that it is false.

(6) No sentence anywhere in the hierarchy is both true and false.

Sentences like (5) and (6) are commonly used in persuading someone to employ Tarski’s hierarchy, but have no place within the hierarchy itself. There is no “ultimate-meta-language” or “trans-meta-language” which can use a truth predicate in reference to itself (much less to the entire hierarchy). This is a severe problem for the theory, since the principle which helps it to escape the Liar Paradox also prevents it from being useful in broader discourse, especially when attempting to demonstrate the value of its proposed solution.

To add insult to injury, the Liar Paradox may not be predicable in Tarski’s hierarchy, but it is still present in English – and Tarski’s solution says nothing about that.

In fact, some* interpret Tarski to be a “proto-dialetheist” of sorts, in that he believed semantic paradoxes of self-reference within natural languages were inescapable (he famously, and controversially, stated that natural languages were “inconsistent”). This may be why he was willing to abandon natural languages to preserve logical consistency (albeit of an artificial sort). (*See The Law of Non-Contradiction: New Philosophical Essays by Graham Priest, et al, p. 118f.)

So, with regard to Mefford’s proposed solution to the Liar Paradox (which he raised as an objection to Chris Bolt’s presuppositional/covenantal apologetic) there are some severe problems which leave him in the regrettable position of having no answer for his own objection.

As I said in my last post, (if I get the time and people seem interested) I’ll propose a solution to the Liar Paradox, as well as some ethical considerations on the whole issue.

The Liar Paradox and Presuppositional Apologetics

So Pat Mefford has raised an objection (here, here, and here) to Chris Bolt’s presentation of VanTilian Presuppositional (sometimes voguely referred to as Covenantal) Apologetics. Chris asked Pat for clarification, then responded here and here. Pat raises the “Liar Paradox” as an objection to Chris’ account of logic, specifically the Law of Non-Contradiction (LNC), as grounded analogically in the divine thoughts.

(His original objection was that Chris was “smuggling” classical binary logic into his account of logical laws – something which Chris’ opponent may not be willing to grant. Instead, Mefford proposed the adoption of Kleene’s ternary logic, which is paracomplete (it denies the Law of the Excluded Middle (LEM), not the LNC). Then he presented the Simple Liar Paradox (i.e. “This sentence is false.”) as the basis for adopting a (presumably paraconsistent) multi-valued logic (MVL). Initially, it was unclear which objection Mefford was proposing: the adoption of Kleene’s MVL (denying the LEM) or the acceptance of the Liar Paradox (denying the LNC). His follow-up posts have focused exclusively on the Liar Paradox, possibly because I pointed out that Mefford’s original argument was self-refuting, since he argued for denying the LEM via disjunction – a philosophical solvent which dissolves itself.)

Laying all of that to the side, I must admit that (despite Mefford’s clarifications) I’m still not sure what the substance of the objection is. To quote Mefford:

In what way does Chris’ simulacrum of God’s divine system answer this paradox? In what way are we thinking God’s thoughts after him when think (sic) of this scriptural passage that was at the top of my original post?… This proposition exists. It is a contradiction. How does it stand in relation to the Triune God? How is this proposition grounded in Almighty God? How does Chris account for it?

To my reading, it seems that Mefford is merely asking for an account of the Liar Paradox from the perspective of the Presuppositionalist (specifically one who holds to a classical, binary logic as Chris does). I don’t see how this is a very significant objection, but that may be a reflection of my poor reading skills rather than Mefford’s argumentation.

For example, Mefford believes Tarski’s semantic conception of truth solves the Liar Paradox. So Chris might say (arguendo, at the very least) that Tarski’s hierarchy more closely reflects God’s thinking with respect to the Liar. (I might suggest to both of them that Saul Kripke’s partial predicate T-schema seems to be a less problematic resolution. Kripke’s construction seeks to maintain classical binary logic with the Liar falling into a “truth-gap,” rather than outside of Tarski’s overly-restrictive semantic hierarchy.) Does this result in some wholesale denial of classical logic? Hardly. It simply provides a semantic “extension” of classical logic which “subsumes the binary apparatus into the new system” (to use Mefford’s own terms). Whether Tarski’s or Kripke’s or some other account is best is irrelevant to answering Mefford’s objection, since the Presuppositional Apologist is only committed to viewing human logics as analogs of divine “Logic” anyway.

Further points to consider:

Mefford’s treatment of Titus 1:12-13 is superficial. To prove this is a biblical example of affirming the Liar Paradox would require Mefford to establish that Paul intends to say that “absolutely every Cretan lies every time he speaks.” It seems much more natural to interpret Paul as hyperbolically generalizing about Cretans, citing one of their own poets as an authoritative source. Chris made this point quite clearly.

For the sake of argument, however, let’s assume Mefford’s interpretation. So Paul says the Liar Paradox is true. This would simply be a proto-affirmation of Graham Priest’s contention that there are true dialethias. This interpretation would put Christians in the minority in the history of Western philosophy, but dialetheism is not as easily refuted as some might like to think. So the Christian might just say that a paraconsistent, non-explosive logic is the most accurate way of thinking God’s thoughts after him. Mefford’s objection is again refuted.

Mefford seems to think that the adoption of a non-classical logic would dull the sharpness of the Classical Presuppositionalist’s double-edged Thesis-Antithesis approach to apologetics. However, he’s never demonstrated why this must be the case, and I’m not interested in doing the heavy lifting for him. To the contrary, the adoption of a classical-logic-with-truth-value-gaps may serve to strengthen the Presuppositionalist’s case in certain ways, a la Peter Strawson‘s conception of presupposition.

However, my intent is not to elaborate on that point right now, but rather to show that Mefford’s dilemma is hornless. Chris could defend classical, binary logic (hardly a losing proposition in my mind) or adopt a non-classical, multi-valued logic without losing any ground to his interlocutor. In my estimation, a VanTilian apologetic could comport with the more classical monaletheism or with a robust form of dialetheism, having a well-formulated paraconsistent logic.

If I get the time, I may attempt to present a reasoned defense of classical logic in this context – or Chris may beat me to the punch; I’d be willing to give it a shot, if others would find such an endeavor useful.

Finally, I find it interesting that Mefford sees the Liar Paradox as “rooted in epistemology and metaphysics,” but does not mention ethics. Being a good tri-perspectivalist, I think there must be some ethical aspects to any explanation for the Liar, which I may also consider at a later date. Remember, lying is a sin…

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