B.C. Askins

The Man With the Golden Gun

Archive for the category “Philosophy”

Executive Summary of The Noetic Effects of Sin by Stephen K. Moroney


Does God Exist? A Debate (6): Atheist Conclusion, Dan Courtney

(Dan Courtney is the President of the Freethinkers of Upstate New York. He lives near Rochester, NY with his wife, and has been active in the atheist community for several years. Dan blogs at http://underminingchristianity.blogspot.com/)

Dan’s Closing Statement

First, I want to thank Ben for participating in this debate. He has intelligently and articulately presented his position, and done an admirable job of expressing difficult concepts. Despite our fundamentally different perspectives, I hope that he has found this exchange beneficial.

Burden of proof

The weak versus strong atheism distinction is used by Ben throughout the debate. However, in the conclusion Ben takes a turn deep into ad hominem territory, by concluding that those who characterize atheism, in the broader sense, as a lack of belief in a deity have somehow done a disservice to atheism because “…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.” This bit of sarcasm is apparently an attempt to embarrass me into accepting an unwarranted burden of proof.
Ben is at least in good company in this burden shifting, as apologists such as Dr. William Lane Craig also spend considerable effort trying to place the burden of proof on the atheist. While the theist does not usually deny their burden in establishing the existence of God, they have good rhetorical reasons to place the burden of establishing non-existence on the atheist’s shoulders. In short, once the atheist accepts the burden, the theist can engage in a series of retreats for which the atheist is obliged to pursue ad infinitum. Take, for example, the analogy I gave to a commenter on this blog earlier in this exchange:

A man comes up to us and tells us that he met a man that is over 200 years old, is over 10 feet tall, and can stop the wind with his thoughts. Do you believe him? Since this is well outside of our experience, I would want some evidence before I even entertain the idea. When I ask to see the 200 year old man I’m told that I can’t be taken to him, and in fact I can’t be told where he is.

Is my disbelief/unbelief/lack of belief (whatever you want to call it) reasonable? Do I need to demonstrate that such a man does not exist to reasonably reject the claim? How would I prove this man does not exist? No matter where I look, there will always be some place unexplored.

Also consider the scenario playing out in court rooms all over:

In a court of law the jury is charged with determining the guilt or innocence of the defendant, right? Wrong. The jury’s one and only task is to determine whether the prosecutor has presented sufficient evidence to establish guilt. The verdict is either guilty or not-guilty. The defense attorney does not need to establish Innocence, but only that the evidence to convict is insufficient. So the defense merely needs to show that the prosecutor’s conclusion of guilt does not reasonably follow from his argument. If the defense does this, then in every sense, they have won the case.

Anderson by proxy

I was glad to see that Ben sought clarification from Dr. Anderson about my claim that Dr. Anderson’s own line of reasoning led him to the conclusion that “sin is intrinsically irrational”. But far from refuting my claim, this clarification simply reinforces the gaping hole in the Calvinist conception of the first sin. We could sum up the Calvinist dilemma as follows:

Premise 1: A sinning agent is one that freely chooses sin.
Premise 2: Adam did not freely choose sin.
Conclusion: Adam is not a sinning agent.

The first premise seems obvious enough, and follows from the concept of an agent as one that initiates an action of their own accord. The second premise is directly from Dr. Anderson’s paper Calvisinism and the First Sin, in which Dr. Anderson excludes Adam from freely choosing sin, “Surely to say that God foreordained the fall goes no way toward explaining why unfallen Adam would freely choose to sin.” “At this point I must confess that further answers escape me.” The conclusion logically follows from these premises. If Dr. Anderson is to assert that the Calvinist doctrine of original sin is rational, then he is must show how either the above premises or the conclusion is flawed.

To be fair Dr. Anderson states that Adam did sin, but he is unable to establish that Adam chose to sin, much less that Adam should be morally culpable for that sin. Indeed, the only one to have had a choice in the matter was God, whom Dr. Anderson implicates when he writes, “Calvinists can affirm that there is a sufficient ultimate explanation for Adam’s sin: God decreed it.” But according to Calvinist doctrine God is incapable of sin, and thus He is excluded from moral culpability.

So Dr. Anderson’s conclusion, “sin is intrinsically irrational”, applies both to Adam (as Dr. Anderson asserts), and to the Calvinist concept of sin itself. For Adam, sinning would be irrational because, as Dr. Anderson argues, Adam would not “freely choose to sin.” And the concept is irrational because there is no logical bridge between a morally perfect God and Adams sin. Nor is there a logical connection between Adam sinning and his moral culpability, or to Mankind’s subsequent culpability.

Meaningless meanings

Ben contends that by pointing out contradictions in his definition of God, I am merely battling straw men. I am, according to Ben, “working without any familiarity with these terms in their theological senses.” This reminds me of an answer I received from a Catholic apologist when I asked him for evidence that the communion wafer transubstantiates into the body of Christ. He said that I wouldn’t find any physical evidence, but that there was theological evidence. How this is better than imaginary evidence isn’t clear.

Like theological evidence, “theological senses” or meanings apparently have a magical quality that make then indiscernible to non-theists. When I challenged Ben on “divine incomprehensibility”, it appeared that he was providing a translation of this theological term into non-theological language when he expressed it as “unknowable”. But perhaps this is not a translation, because Ben also disagrees with my understanding of “unknowable” as something that cannot be known. Maybe we could have both saved a lot of time if we had agreed to conduct the debate in English instead of some unfathomable theological variation thereof.

Getting personal

In repeating his definition of a person, “a rational, self-conscious entity”, Ben is being more than a little disingenuous. Ben is arguing for more than “a rational, self-conscious entity”; he’s arguing for a host of attributes wrapped up in an immaterial transcendent mind. It is these other attributes, which Ben insists belong to a “person”, that are not shared by our common understanding of the term. This minimalist definition of a person is akin to defining anything that is alive as a dog, and then insisting that the growth clinging to the underside of a rock is a dog. But just like “dog” conveys more information than just being alive, “person” conveys more information than simply “a rational, self-conscious entity”.

It’s perfectly understandable, however, that Christians would want to claim that God is “personal”. Humans are social animals, and we have evolved sophisticated means for interacting with other humans. In fact, human interactions have dominated our lives to the degree that we relate to non-humans in very human-like terms. Referring to God as “Him” or “Lord” or as a “person” may be a natural inclination, but it is simply a metaphor for reality itself. Calling God a “person” may have symbolic significance, but it is no more justified in real terms than calling Mother Nature or Father Time “persons”.

In Closing

As with any debate, changing the other person’s mind, or even getting them to acknowledge a contradiction in their position is not the goal. The goal is to present issues to readers on both sides (or no side) that challenges their current view and assists in furthering their understanding of the world. Whatever you, as the reader, take away from this debate, I hope that you have benefitted from contemplating these issues.

In reviewing our exchanges, it seems clear that I have established that the theist has the clear burden of proof when claiming that a god exists. Not only has this burden not been met, but the definition of God that was presented is laden with contradictions and meaningless assertions such that we have not even established what God is supposed to be, much less whether such a thing exists.

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 (4): Initial Atheist Rebuttal, Dan Courtney

(Dan Courtney is the President of the Freethinkers of Upstate New York. He lives near Rochester, NY with his wife, and has been active in the atheist community for several years. Dan blogs at http://underminingchristianity.blogspot.com/)

In my opening statement I pointed out that the burden of proof for the existence of the Christian conception of God falls squarely on the person making the positive claim. Not only is it not necessary, but it is not possible to prove that such a God does not exist. Ben refers to this position as “weak atheism”, and implies that my position is consequently weak. I prefer to let the reader decide which of us is in the stronger position.

In the famous “Russell’s teapot”, the philosopher Bertrand Russell points out that it is not possible to disprove the existence of a teapot orbiting between the Earth and Mars, but that accepting the idea without evidence is not rational. In this case the teapot is at least a coherent concept. But with Ben’s definition of God, he fails to meet the standard of coherence, and thus we are not even in a position to consider what might constitute evidence.

More importantly, in response to my contention that his belief in the Christian God is irrational, Ben writes, “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.” It seems the point of any debate is to show that your opponent’s position is not rationally supported, while your own is rationally sound. If Ben is not interested in demonstrating the “mere rational status” of his beliefs, then it’s hard to imagine why I, or anyone else, would take his arguments seriously.

I also stated that according to the definition of God that Ben is using, “incomprehensible” stood out. It was stated that I was equivocating on this concept when I suggested that I could simply agree and claim victory. I don’t see how agreeing with this particular attribute is equivocating, but Ben provided a clarification of the term anyway; “divine incomprehensibility refers to the doctrine that God cannot be fully comprehended and is unknowable apart from self-revelation.” Assuming that Ben is not providing to us, through his argument, a “self-revelation”, then I am not dissuaded from agreeing with him that God is “unknowable”. Yet Christians of all stripes will continue to make arguments in an attempt to show that we can somehow know the unknowable. If, in Ben’s opinion, I’ve set the bar too low in this debate, then certainly he’s not only set the bar impossibly high, but he’s conceded that he cannot reach it.

If it isn’t obvious that “incomprehensible”, as a characteristic of the very thing that is being defined, doesn’t contradict the idea of a definition, then perhaps another example will help. Let’s take “forgiving iniquity” on one hand, and “who will by no means clear the guilty” on the other. If forgiveness is to mean anything, then clearly it must mean absolving one of guilt in some sense. Or how about “living’ and “immutable”? In what sense can a changeless entity said to be alive? If an entity does not grow, or learn, or age, or reproduce, then calling it ‘living’ becomes a meaningless assertion. And if it is thought that God is an immaterial mind such that growing, et al, doesn’t apply, then what about thoughts? What is the purpose of thoughts if not to conceptualize new relationships and thus increase knowledge? But new knowledge is a change in the state of one’s knowledge, which contradicts God’s supposed immutable nature, not to mention his supposed omniscience. As with virtually every proposed characteristic of God, the characteristic is immediately negated by a subsequent characteristic. The proposed definition of God is an impressive list of terms that says absolutely nothing.

As with other Transcendental Arguments for God (TAG), the TAG-M (mathematics) version relies on an intentional conflation of reality with the models used to represent reality. Whether it’s the use of mathematics or the traditional reference to the laws of logic, the error is the same. In Ben’s original argument he referred to the “mathematical universe”, and calls numbers “mental objects”. Mathematics is useful because it mirrors the consistency that we observe in reality. But we are not observing “mental objects” within some parallel “mathematical universe”. Numbers are not real, existent entities, but rather mental constructs used to model the behavior we observe in reality. The use of the term “object” is an equivocation designed to blur the distinction between an abstract concept and the reality to which it refers. Once the distinction is realized, the TAG (and TAG-M) argument collapses.

I was also accused of failing to substantiate my claim of reification on Ben’s part. As Ben points out, reification is the false assigning of concreteness to an abstraction. But this is exactly the point when Ben calls numbers mental objects. Ben wishes to confer independent existence (real, existent entities) to mental abstractions. In this sense, concepts are granted existence status equivalent to physical objects, and the only remaining question is in what kind of mind to store them. This is reification in broad daylight.

To see how Ben continues to confuse the abstract from the real, consider this question he poses in his first response; “If everything with a brain woke up dead tomorrow, how much would 2+2 equal?” The key here is that Ben is asking the question today, when brains are available to ask and answer the question. He and the reader can conceive of the question and the numbers involved. However, if tomorrow there are no brains, neither the question, or the numbers involved, would be conceptualized. The answer is, as far as we know, that the underlying reality which we model with numbers will survive the death of all brains, but the mathematical model that we use to represent that reality will cease with our brains.

The Anderson-Welty argument (TAG meets Ontological), commits the same error as TAG-M. The arguments states that “propositions are real entities”, but then fails to distinguish propositions from the reality to which they refer. The error is only compounded by trying to bridge the flawed TAG argument, as the premise, to the ontological argument, which has problems of its own.

I’m happy to clarify my use of the term axiom in my opening statement. I am using the term to mean a necessary truth foundational to subsequent knowledge claims. So when I refer to Einstein’s use of axioms, I am not referring to the mathematical principles used to derive his equations, but the foundations of rational thought.

Ben accuses me of viciously circular question begging when I state that he “wants the attribute of a person without the physical baggage that comes with it.” Ben is claiming an immaterial transcendent mind as a person. I’m fine if he wants to define persons this way, but what are we going to call the 7 billion or so people here on earth? We are physical, temporal, imperfect animals. We are, in virtually every sense, not persons per Ben’s definition. If Ben did not want the association of God with the hominids formerly known as persons, then I apologize.

Under the heading of “Subjectivism incompatible with realism” Ben wonders out loud how I can be a “subjectivist-realist”, which he states is a contradiction. I think Ben would agree that there is an objective reality that we engage through our subjective experience. It’s not a contradiction to have an objective reality exist while only being able to experience it subjectively. The implied question here is “How can we justify our knowledge of objective reality?” Positing a “divine self-revelation” as some way of justifying the objective reality is the core of the Presuppositionalist argument, and one that I have debunked at some length in other writings. But suffice it to say that positing objective knowledge of an objective reality through the subjective experience of “self-revelation” doesn’t get you there.

On Ben’s point of clarification about Dr. Anderson’s paper Calvinism and the First Sin, he is mistaken in asserting that Dr. Anderson’s conclusion that “sin is intrinsically irrational” only referred to the act of sinning as being irrational. I’ve just finished a video review of Dr. Anderson’s paper (http://www.youtube.com/watch?v=h5hrTkrd1JI&feature=share&list=UUiVyaC3sQ1puw3Qj9Ccx2xw – where you can also find a link to the full paper in the notes) and his conclusion is in the context of trying, and failing, to find a rational path to explain why Adam sinned without God being morally culpable. The conclusion “sin is intrinsically irrational” refers directly to Dr. Anderson’s inability to provide a rational explanation for the Calvinist doctrine of original sin, and not to any individual act of “sinning”.

On the subject of sin, I’m provided with a small sermon at the end of Ben’s response, in which he implies that I’m a sinful, “irrational God-hater”. No doubt I’m not completely rational in all my pursuits, but I’ve tried to use my best understanding of logic to construct a view of reality that is as accurate as possible. As we see with Dr. Anderson’s paper noted above, some do not constrain their views of reality to the same standard, and indeed even embrace the “mystery” of irrationality. If Ben’s embracing of “reason in Jesus Christ” means jettisoning reason when it conflicts with his religious doctrine, then I think I’ll stick with my “sinful” ways.

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.

Does God Exist? A Debate: (1) Christian Opening Statement, B.C. Askins

“God exists” is an intuitive, basic belief of mine. (To be clear, by the term “God” I do not mean a metaphor for the nature of reality—rather, I am referring to the classical Christian conception of God drawn from the Old and New Testaments. See the Westminster Confession of Faith Ch. 2 for a condensed statement on the subject.) Unfortunately, when confronted with opposition to some of our most basic intuitive beliefs, it is often difficult to provide evidence or arguments in favor of those beliefs—because they are the beliefs by which we evaluate evidence and formulate arguments. If I challenge you to prove the existence of your right hand, you might wave it in my face or touch me with it. But if I ask you to prove that space and time exist, you might just scratch your head in confusion. The existence of space and time is something which we often assume for the purpose of providing evidence or argumentation regarding other subjects. It can be difficult to explain and defend one’s intuitions inferentially. How would you respond to someone who stands before you, using the air she is breathing to deny the existence of both air and her own voice?

By analogy, arguing for the existence of the Creator of space and time is no less difficult than defending one’s belief in space and time itself, since—if God exists—his existence is even more foundational than the existence of his creation. So, on the question of the existence of God, either atheists are radically self-deceived or theists are. Either I believe in an “imaginary friend in the sky” or atheists, like Mr. Courtney, are assuming the existence of God in order to argue against the existence of God. One of us is colossally wrong.

There are many ways that people have responded to skepticism regarding a belief in God. I’ll provide four brief arguments in this regard. The first two will be arguments for the existence of God; the second pair will be arguments against atheism. These arguments aren’t original to me, though I will take responsibility for their particular presentation in this debate. I am indebted to the writings of Cornelius Van Til, Alvin Plantinga, Greg Bahnsen, John Frame, Gordon Clark, Steve Hays, John Byl, David Byron, James Anderson, and Greg Welty (among others). I’m also grateful for Mr. Courtney’s patience during our exchange and willingness to debate someone with no experience in formal debate.

Transcendental argument for God from mathematics
Hermann Weyl famously defined mathematics as “the science of the infinite.” Set Theory combined with Predicate Calculus provides the foundations of mathematics. The ultimate goal is to describe the structure of the mathematical universe, emphasizing systems of internal consistency and proof. Certain equations imply other equations, membership in one set implies membership in others, addition implies subtraction, etc. In a system with internal relationships, such as the number 4’s relation to 2, all of the relations must be consistent in order for any of them to be consistent. 2+2=4 because 1+1=2 and 4-2=2, etc. So, in a system of infinite internal relations, the infinite must be actual rather than potential.

Mathematical objects also appear to be inherently mental objects. What else could they be? 2+2 doesn’t transform into 4. 2,000,000 doesn’t have any more mass than 2. The existence of a number is independent of the existence of a particular instantiation of its properties, i.e. if I erase the symbol “9” from a chalkboard or smash two apples into sauce I haven’t affected the number 9 at all. But if numbers are mental objects which are members of an actual infinite set, this requires the existence of an infinite mind where they inhere—the mind of an eternal, omniscient God. 2+2=4 only if God exists.

Anderson and Welty’s argument for God from logic
“The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts.
So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person. A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily. Thus, if there are laws of logic, there must also be a necessarily existent, personal, spiritual being. The laws of logic imply the existence of God.” (James Anderson, Greg Welty. “The Lord of Non-Contradiction,” Philosophia Christi 13.2)

Argument against ultimate non-personality
According to the law of excluded middle, reality is ultimately either personal or non-personal. (A minimalist definition of “personal” would be a “rational, self-conscious entity.”) If reality is ultimately personal, then the existence of human persons is almost self-evidently explicable: persons come from other persons (via creation or reproduction). However, if one maintains reality is ultimately non-personal, as atheists do, then problems arise in explaining how personality emerges from non-personality, how rationality is produced by non-rationality. Note that there is not even a standard accepted theory of abiogenesis (despite many experiments conducted by highly rational persons), which is a much less difficult question than the origin of personality, given ultimate non-personality.

Argument against atheism as self-refuting
Mr. Courtney is about to make his opening statement. I predict there will be truth claims within that opening statement. Regardless of one’s theory of truth (correspondence vs. coherence vs. pragmatic, etc.), that theory will depend upon the existence of a mind, in which propositions correspond with external reality or cohere with other true propositions or are most expedient, etc. However, if we combine atheism with standard scientific theories on the evolution of life, there was a time when no minds existed—but would it be true to say of that time that no minds existed then? Answering “no” is plainly self-contradictory. If the answer is “yes,” then how can something that was not true at that time become true now with reference to then? Either answer is self-refuting. Only if we grant a divine mind, where this truth may inhere, can one even predicate that there was a time when no human minds existed.

I look forward to reading Mr. Courtney’s opening statement.


1. Definition: sin – any thing contradicting the moral nature of God.

2. Is it logically possible for God to sin?
No, per the definition above.

3. Is Jesus God?
Yes, per the New Testament.

4. Was it logically possible for Jesus to sin?
No, per the conjunction of 2 and 3.


Fristianity Refuted

Here’s a really rough thumbnail sketch of a non-question begging argument refuting Fristianity (written from my phone).

In Christianity, the categorical three term syllogism (“Barbara”) is grounded in the intratrinitarian relationships within the Godhead:

1.) All that belongs to the Son (B) belongs to the Father (A).
2.) All that belongs to the Spirit (C) belongs to the Son (B).
3.) Therefore, all that belongs to the Spirit (C) belongs to the Father (A).

1.) All Bs are As.
2.) All Cs are Bs.
3.) Therefore, all Cs are As.

The Fristian quadrinity, even with a mysterious role for the fourth person, by the nature of the unity in the quadrinity would produce a four term syllogism, which is formally fallacious. The Fristian god cannot provide the necessary preconditions for logic.


(Argument inspired by Vern Poythress.)

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 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.

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