An Example of Begging the Question

It is often helpful to have included in an apologetic arsenal a basic understanding of fallacies. One popularly used fallacy is called “Begging the Question”. It may be summed up in simple terms as merely assuming the same thing one is attempting to prove. Do not misunderstand, there is nothing wrong with an assumption or attempting to prove an assumption, but there is something wrong with setting forth a mere assumption as though it constitutes an argument; as though the assumption of the very thing someone is attempting to prove is itself the proof! An interesting illustration of this fallacy may be found on Urban Philosophy in a post by Mitch LeBlanc.1 Mitch asks us to consider two propositions, (11) and (12). Only (11) is needed for the purpose of this post.

(11) It is not the case that it is not that P and not P (law of non-contradiction denied, meaning it would be possible for your apple to be both orange and not orange simultaneously)

Mitch then writes about how there are problems with affirming (11).

In attempting to affirm (11), one arrives at an obvious logical incoherence. How could an apple be both orange and not orange simultaneously? In this sense, it is logically incoherent to affirm (11).

There are undoubtedly many who would accept this part of the argument and move on, however it is important to follow even this step closely to see whether or not Mitch has actually proven something or if he has just assumed that which he has set out to prove in which case he commits the fallacy of Begging the Question. Recall his proposition (11).

                        (11) It is not the case that it is not that P and not P

Proposition (11) expresses a denial of the law of non-contradiction. If proposition (11) is true then an apple might very well be both orange and not orange at the same time and in the same respect. Mitch then makes the assertion, “In attempting to affirm (11), one arrives at an obvious logical incoherence”.2 Mitch claims that there is a logical incoherence in affirming (11). Does he support this claim?

If Mitch does in fact support his assertion that affirming (11) results in logical incoherence, it is difficult to find where he does so. In his very next line Mitch writes, “How could an apple be both orange and not orange simultaneously?” One might wonder why the answer to the question is not obvious to Mitch. An apple might be both orange and not orange at the same time and in the same respect (“simultaneously”) if one affirms (11). Why Mitch misses this is puzzling, as the exemplary consequence of (11) he provides when stating (11) is that “it would be possible for your apple to be both orange and not orange simultaneously”. From here, he concludes, “In this sense, it is logically incoherent to affirm (11)”. In what sense? Mitch has not shown us what he states about the logical incoherence of the affirmation of (11), he has merely assumed it and hence commits the fallacy known as Begging the Question.


1 Click to read the original post.
2 It is worth mentioning that in philosophical discourse the use of words such as “obvious” are usually quite inappropriate, for sometimes what one individual finds “obvious” another rejects as “absurd”. The serious use of a word like “obvious” in an argument is likely to be mere rhetoric, even question begging rhetoric. While Mitch and even I may believe something to be “obvious”, there are those who would disagree with our assessments so that nothing is really added to the argument by the use of the word.


24 Comments

Nocterro

“It is worth mentioning that in philosophical discourse the use of words such as “obvious” are usually quite inappropriate,”

I would like to point out that Mark Alan Walker, in his paper “The Anthropic Argument Against the Existence of God”, uses the words “obvious” and “obviously” a combined 10 times.

Mitchell LeBlanc

The LNC is a necessary truth, hence the denial of it is logically absurd.

One must simply ask the question, “Is there any possible world where an apple is both orange and not orange simultaneously?” It does not seem that there is, and we cannot thereby falsify the LNC.

“An apple might be both orange and not orange at the same time and in the same respect (“simultaneously”) if one affirms (11).”

If you deny the LNC, not only would it be true that:

(1) An apple can be both orange and not orange at the same time and in the same respect

But any proposition would be implied from the denial. Necessarily false propositions imply any proposition. As such, the denial of the LNC would imply every proposition conceivable, clearly this renders our logical system trivial. This alone is justification enough for not denying the LNC.

I do not see that I have begged the question:

(4) If there is no possible world in which the LNC fails, it is absurd to deny the LNC

(5) There is no possible world in which the LNC fails, since possible worlds are determined by the LNC

(6) Therefore, it is absurd to deny the LNC

You might respond that if one denies the LNC, then (5) is false and my argument is defeated. You might respond by saying if the LNC is denied, then there IS a possible world where the LNC fails. The problem here, of course, is that ‘possible/impossible’ become meaningless terms if the LNC fails, so if there is the LNC fails, there are no possible worlds.

Mitchell LeBlanc

“…so if the LNC fails…”*

C.L. Bolt

Nocterro,

Counting the number of times Walker uses the word “obvious” or “obviously” has absolutely no bearing upon my comment that the use of the word in philosophical discourse is usually inappropriate. You have not provided any context with the uses, you falsely imply that Walker is incapable of using unhelpful words, and you ignore the subjective nature of the word.

Mitch,

I am surprised at your response. One might just as easily state that the existence of God is a necessary truth; hence the denial of it is logically absurd, yet in the original context you wish to deny this move to the theist. There are many propositions which are contradicted by the affirmation “God does not exist”, and many consequentialist arguments one might advance in favor of not affirming the proposition, howbeit fallacious ones. Again, you wish to deny these moves to the theist. This aside, what you still have not shown is that the affirmation of (11) is logically incoherent or absurd. Repeating what you have already written is insufficient to accomplish this task, and adding more arguments, as you have, only evidences that you did beg the question.

Nocterro

http://www.nmsu.edu/~philos/documents/anthropic-argument-dec-2008.doc

There’s his paper. Could you point out any inappropriate use of the word “obvious”?

Can you point to any inappropriate use of the word “obvious” in ANY paper?

Mitchell LeBlanc

“One might just as easily state that the existence of God is a necessary truth; hence the denial of it is logically absurd”

Yes, and many (such as yourself) do. Such a claim would require some investigation. What are the reasons to accept that God is a necessary truth? (this is rhetorical, I know your reasons). We’d explore this in the same way that we explore the necessary truth-ness of the LNC.

As I’ve said above, the LNC is a necessary truth because there is no possible world in which the LNC fails. That is, there is no conceivable arrangement of things where the LNC fails. If you claim to be able to conceive of one, you are simply deluded (or perhaps worse). Are you honestly claiming that you can conceive of an apple which is both orange and not orange simultaneously?

Affirmation of “God does not exist” might contradict many propositions, sure. But an affirmation of “The LNC is false” implies ANY proposition. We can derive anything from necessary falsehoods. There’s simply no way to distinguish true propositions from false propositions.

So let’s recap:

The affirmation of (11) is logically incoherent because logical coherence itself depends on the falsehood of (11). That is to say, should (11) be true, any subsequent logical system becomes trivial, proving every proposition.

If you think that you can maintain a logical system that denies the LNC (or some equivalent function) and remains non-trivial, I’d be very interested to see it.

Assume for the time being that the proposition “God exists” is necessarily true. If the proposition is necessarily true, a denial of it is incoherent. What needs to be shown, of course, is that the proposition “God exists” is true in every possible world. This has been shown with the LNC, and this is why any denial of it is incoherent.

I doubt that you actually think the affirmation of (11) is coherent, so if I may ask, what are your reasons for thinking this and how do they avoid being ‘question-begging’?

C.L. Bolt

Yes, I know where the paper is Nocterro. The burden is not on me to provide myself with the argument that you have not made.

C.L. Bolt

“We’d explore this in the same way that we explore the necessary truth-ness of the LNC.”

So, by advancing further arguments, since that is what you have done with the LNC.

“As I’ve said above, the LNC is a necessary truth because there is no possible world in which the LNC fails.”

This is not an argument Mitch, this is an assertion. A necessary truth is a truth that does not fail in any possible world. You have merely asserted that the Law of Non-Contradiction is necessary, defined what you mean by this assertion, and set the assertion forth as an argument. Thus, once again, you beg the question.

“That is, there is no conceivable arrangement of things where the LNC fails.”

See above.

“If you claim to be able to conceive of one, you are simply deluded (or perhaps worse).”

This also begs the question. I wonder if we can prove other propositions through claiming that those denying the propositions are deluded?

“Affirmation of ‘God does not exist’ might contradict many propositions, sure.”

Well I am glad you agree. The same is true with respect to the affirmation of (11), and by providing such propositions you have attempted to argue against (11), though you did not do so originally. Thus it has been established that the theist is within his or her rights to advance other propositions to show the problems with affirming the proposition “God does not exist” and that you did beg the question in your original argument.

Since you asked, I would proceed to argue for the Law of Non-Contradiction by the impossibility of the contrary.

Mitchell LeBlanc

Type your comment here…

Mitchell LeBlanc

“This is not an argument Mitch, this is an assertion. A necessary truth is a truth that does not fail in any possible world. You have merely asserted that the Law of Non-Contradiction is necessary, defined what you mean by this assertion, and set the assertion forth as an argument. Thus, once again, you beg the question.”

Did you not see where I stated: “The affirmation of (11) is logically incoherent because logical coherence itself depends on the falsehood of (11). That is to say, should (11) be true, any subsequent logical system becomes trivial, proving every proposition.”

It does not beg the question to say that you cannot conceive of a state of affairs in which P and not P, it’s derived. This is why it’s silliness to state that you can conceive of P and not P, it’s impossible to do so.

The affirmation of (11) does not contradict “many” propositions, it implies ALL propositions, thereby contradicting ALL propositions. This is not the same thing.

Please offer the justification for the necessity of the LNC using the impossibility of the contrary. It will be interesting to see a justification for the LNC which is not, itself, contingent on the LNC.

C.L. Bolt

Yes, I did see where you stated, “The affirmation of (11) is logically incoherent because logical coherence itself depends on the falsehood of (11). That is to say, should (11) be true, any subsequent logical system becomes trivial, proving every proposition.” but this is irrelevant to where I stated “This is not an argument Mitch, this is an assertion.” and what followed the statement.

“It does not beg the question to say that you cannot conceive of a state of affairs in which P and not P, it’s derived.”

You have not shown this. Derived from what?

“This is why it’s silliness to state that you can conceive of P and not P, it’s impossible to do so.”

Well it is easy to write that it is “silliness” and “impossible”, but once again where have you shown this?

“The affirmation of (11) does not contradict ‘many’ propositions, it implies ALL propositions, thereby contradicting ALL propositions. This is not the same thing.”

Yes Mitch, I know the proof for showing that anything follows from a contradiction. I also know that if it is true that all propositions are contradicted by the affirmation of (11) then it is also true that many propositions are contradicted by (11), so what you have written here is actually contradictory since you deny that (11) contradicts many propositions and affirm that (11) contradicts all propositions.

What you continue to either miss or ignore is that none of this was given in your original argument. You have brought to light by virtue of the defense that you have given here that there are a number of assumptions in your original argument that you take for granted and do not even state in the argument. Again, this is because it is question begging.

“Please offer the justification for the necessity of the LNC using the impossibility of the contrary. It will be interesting to see a justification for the LNC which is not, itself, contingent on the LNC.”

I think you just did.

Mitchell LeBlanc

“You have not shown this. Derived from what?”

The fact that you cannot conceive of a state of affairs in which P and not P is derived from the fact that P and not P is an impossible state of affairs. The fact that it is an impossible state of affairs is derived from the fact that logical coherence depends on the falsity of P and not P.

“Well it is easy to write that it is “silliness” and “impossible”, but once again where have you shown this?”

By virtue of the fact that the LNC must be presupposed in all thinking. Are you saying that this fact hasn’t been shown?

“Yes Mitch, I know the proof for showing that anything follows from a contradiction. I also know that if it is true that all propositions are contradicted by the affirmation of (11) then it is also true that many propositions are contradicted by (11), so what you have written here is actually contradictory since you deny that (11) contradicts many propositions and affirm that (11) contradicts all propositions.”

Surely our discussion is not going to descend into this type of discussion. I distinguished “many” from “all” because I feel it is an important distinction. It is more accurate to state that “all” propositions are contradicted by (11), since “many” implies a large number, where “all” implies the whole.

You are right in that I did not branch the article onto a discussion about the justification of classical logical laws. I still think you are confused in calling my statement question-begging. Just as existing is a necessary precondition of rational thought, so is a law with the function of the LNC.

The justification was given in my paper, call it the “absurdity” of the contrary if you will. You even cite the questions I’ve asked, how “could” it be the case that P and not P. I am not merely stating that “based on our logical system (which affirms the LNC) how could P and not P”. I’m asking a much more thorough question, that is, is there any conceivable non-trivial logical system which denies the LNC

I am confused as to your last statement, I asked you to provide your justification for the LNC but you stated that I’ve just done so. What do you mean?

Furthermore, the “impossibility of the contrary” doesn’t seem different than my points about absurdity. Surely it is no different from my explanation to say that the LNC holds because the contrary is impossible. You’re even using the modal term “impossibility” which is already affirming the LNC. If my justification truly is question-begging, then unfortunately so is yours.

C.L. Bolt

“Surely our discussion is not going to descend into this type of discussion.”

Surely it is not going to “descend” into what “type of discussion”? The type of discussion where I point out contradictions in what you have written? Even if this is to be thought of as bringing the conversation ‘down’ to some sort of ‘lower level’, how would I be the one at fault?

“It is more accurate to state that ‘all’ propositions are contradicted by (11), since ‘many’ implies a large number, where ‘all’ implies the whole.”

Perhaps, but this is not what you wrote. You wrote, “The affirmation of (11) *does not contradict ‘many’ propositions*”, which is both false and contradicted in the very same sentence you wrote. I should hope that you will not become upset with me for an apparent failure on your part to either express yourself clearly and or without contradiction.

“I still think you are confused in calling my statement question-begging.”

You are apparently still missing my point, perhaps due to a failure on my part to express myself clearly. You continue to appeal to propositions outside of (11) which contradict it and advance arguments made up of other propositions other than (11) that were not present in your original post. There is nothing immediately objectionable about your approach, but you did not use it in your original claim that the affirmation of (11) is logically incoherent. If you had, then you would not have been able to complete your argument with respect to the existence of God. Let me be abundantly clear; all you did was to state that it is logically incoherent to affirm (11), but you needed to show that this is the case. Since you did not, you begged the question.

Now then, God exists necessarily and it is incoherent to affirm the proposition “God does not exist”. It is in fact inconceivable that God does not exist. That this is the case is self-evident and obvious, etc.

Mitchell LeBlanc

“Surely it is not going to “descend” into what “type of discussion”? The type of discussion where I point out contradictions in what you have written? Even if this is to be thought of as bringing the conversation ‘down’ to some sort of ‘lower level’, how would I be the one at fault?”

No, the type of discussion where we quarrel over which quantifier better accurately grasps the state of affairs.

“Perhaps, but this is not what you wrote. You wrote, “The affirmation of (11) *does not contradict ‘many’ propositions*””

I put ‘many’ in single quotation marks to point out that I am criticizing the use of the word, clearly, italics would have been better. I’m not upset at all Chris, I just thought the sentence was a lot clearer than it apparently was.

I didn’t feel the need to justify as much I have in these comments because I do not actually know anyone who denies the LNC. Further, if we take the LNC as an informal axiom it does not seem such justification is even required. Perhaps you disagree.

I am curious though, you said that if I did such a demonstration in my post I’d be unable to complete my argument. Why is this?

As for your last bit, I don’t know if you have noticed but I’ve been tending to shy away from any discussions on the existence of God for the last little while. I’m currently working on a paper which is to be submitted to a few Canadian philosophy journals. The focus of the paper is indeed Bahnsen’s TAG, and as such I’ve thought it good measure to wait until the peer review before advancing my main argument. I’d also like to withhold online publication until I get either a yay or nay from the journals.

With that said, please understand if I withdraw prematurely.

Whereas the reasons for the incoherence of denying the LNC are best explained in exemplifying the further incoherence of any subsequent system, with regards to God, the establishment of God’s necessary existence comes through (I believe) one of two arguments. Either the Ontological Argument, or the Transcendental Argument.

The two propositions do not seem equatable, whereas it is immediately obvious that a denial of the LNC leads to absurdity, it is not as immediately obvious (at least to me) that a denial of God’s existence does.

I will wager that your establishment of “God exists necessarily” arises from the TAG, so it is prudent to discern whether or not the TAG is a sound argument. You, of course, know my position on this matter.

P.S: Feel free to delete my above “empty” comment, I accidentally clicked Submit before I wrote anything =(

C.L. Bolt

“No, the type of discussion where we quarrel over which quantifier better accurately grasps the state of affairs.”

You raised the issue over the quantifier, not me. I think you are probably right, but not about the contradiction.

“I put ‘many’ in single quotation marks to point out that I am criticizing the use of the word, clearly, italics would have been better.”

Perhaps, but the trouble is with stating “does not contradict ‘many'” regardless of the quotations, italics, etc.

“I didn’t feel the need to justify as much I have in these comments because I do not actually know anyone who denies the LNC.”

Do you believe there are people who do, or at any rate claim to?

“Further, if we take the LNC as an informal axiom it does not seem such justification is even required.”

Your assertion regarding (11) would still need to be supported even if through appeal to the axiom which is external to (11).

“I am curious though, you said that if I did such a demonstration in my post I’d be unable to complete my argument. Why is this?”

You write that it is logically incoherent to affirm (11) but not (12), initially attempting to keep the discussion in terms of the propositions themselves rather than other propositions they may contradict. If we may appeal to propositions other than (11) in showing that it is logically incoherent to affirm it then we may do the same with (12).

“…the establishment of God’s necessary existence comes through (I believe) one of two arguments. Either the Ontological Argument, or the Transcendental Argument.”

See, we are getting somewhere. 😉 🙂

Best to you on the journal submission. I look forward to reading it once published if possible.

Mitchell LeBlanc

“Perhaps, but the trouble is with stating “does not contradict ‘many’” regardless of the quotations, italics, etc.”

I think this is one of those times where it’d be much more obvious if I had said it, rather than typed it.

Do you believe there are people who do, or at any rate claim to?

I honestly don’t. I suppose it’s somewhat similar to your position, simply replace “God” with “LNC.”

“Your assertion regarding (11) would still need to be supported even if through appeal to the axiom which is external to (11)”

I was referring to the axiom in my writing, though perhaps indirectly. This is what I intended to convey when I used the rhetorical questions you cited. Again, I did this because I did not think that anyone actually denied the LNC.

“You write that it is logically incoherent to affirm (11) but not (12), initially attempting to keep the discussion in terms of the propositions themselves rather than other propositions they may contradict. If we may appeal to propositions other than (11) in showing that it is logically incoherent to affirm it then we may do the same with (12).”

Ah, the argument has been reformulated in parts 2 and 3 of that series. We could certainly state that a denial of (12) is a denial of a necessary truth, but the necessary truth-hood is what I was attempting to discuss. I do think the later formulations are, if anything, more clear in their presentation. In stating that there is no incoherence in denying (12) I was trying to show that if there is an incoherence it’s not the same as the incoherence in (11). I do, now, find this first formulation somewhat inadequate.

Interestingly enough I think (12) is closer to being a question begging premise than (11), this became evident after I looked at a formalized version of the TAG. If the formalization of the TAG is attempting to show that God exists, then (12) seems to be non-question begging. But if the TAG is attempting to show that God exists *necessarily*, (12) does seem to beg the question.

I didn’t realize this until I saw a modal formalization of the TAG.

Thanks for the kind wishes. Whether or not it gets approved for publishing, I will be sure to post the paper after I receive a decision. I’m looking forward to some interaction. Currently, it’s being reviewed by a theist Philosopher, Klaas Kraay at Ryerson University. He was raised a presbyterian, but all I know of his religious affiliation now is that he is theistic.

At any rate, I’ll be sure to get it to you somehow. Cheers!

An Example of a Red Herring | Choosing Hats

[…] the last post at Choosing Hats an example of the fallacy of Begging the Question was presented with the […]

ZaoThanatoo

Which bubble would you have shaded on the SATs?

True or False:

“This sentence is not true.”

Mitchell LeBlanc

I’d say true.

“This sentence [this sentence is not true] is not true” = It is not the case that this sentence is not true.

I think…

ZaoThanatoo

But if what the sentence states is true, then it must be not true, since that’s what it predicates of itself…

Mitchell LeBlanc

I don’t think my above analysis is subject to that criticism.

ZaoThanatoo

If by “above analysis” you mean the post at 12:52am, where you mistakenly negate the sentence (turning P into ~P for some unknown reason), then, yes, it would be subject to that criticism, since you’ve misinterpreted the question.

However, if by “above analysis” you are referring to your above discussion of the LNC, then I would still contend that it is open to criticism from the dialetheist. You stated, “If you think that you can maintain a logical system that denies the LNC (or some equivalent function) and remains non-trivial, I’d be very interested to see it.” The Liar paradox introduced jovially above in the form of a True/False SAT question is a rather sticky problem which western philosophy has done its best to ignore since Aristotle (at least until quite recently).

So, to summarize, your treatment of the LNC did beg the question, as Mr. Bolt demonstrated. However, it is a question which has been begged for millennia and we often tend to give each other “a pass” on this one for some reason. (Your adoption of TA for the LNC is an interesting move and shows that you are grappling with the difficulties inherent in arguing for entities whose existence we consider necessary. Kudos, on that front.)

I simply introduced the Liar paradox/dialetheism to point out the question begging nature of your position from a whole different angle.

Cheers!

Mitchell LeBlanc

I think you may have misunderstood my above analysis. I was suggesting that the portion of the sentence that refers to “this sentence” must be spelt out entirely, so that the sentence is properly reconstructed as I’ve done so above:

“This sentence [this sentence is not true] is not true”

Without knowing what “this sentence” refers to, and plugging it in, I don’t think we can attempt to answer the problem.

I’m reluctant in using the term “begging the question” when someone attempts to justify these types of things as it is not even clear that they need justification.

If we can discern whether or not the LNC meets the criteria of being an axiom, then perhaps it is clear as to why “justification” becomes so difficult. But, since the LNC is not an axiom of any formal logical system that I know of, it seems (as you observe) that we’d have to argue for it with some type of TA.

At the end of the day, if it is the case that my discussion of the LNC is question begging, it seems to me that any discussion of the LNC would be question begging. If this is too bold of a claim, at least Bolt’s discussion via the ‘impossibility of the contrary (IOC) would be question begging. That is simply because his notion of the IOC presupposes the idea of possibility, which is a modal indicator that must already presuppose the LNC.

Thanks for the thought experiment =)

ZaoThanatoo

I’m not sure where things are getting lost in translation (especially since we’re both typing in English… it’s practically like a second language to me at this point).

“This sentence” refers to, well, this sentence. No “plugging in” seems necessary to understanding its referent. “This sentence is not true” emphatically does not equal “It is not the case that this sentence is not true.” Parenthetically quoting the sentence does not add a second negation. It could possibly be restated as, “It is the case that this sentence is not true” or “it is not the case that this sentence is true,” but your insertion of a second negation (“not the case… not true”) is rather unwarranted. I’m not sure how else to say that more clearly.

If the sentence is true, then it’s false, since that’s what it predicates of itself; but if it’s false, then it must be true, since it is “lying” about its own falsehood. (Hence the name, “the Liar paradox.”) It presents an interesting defeater for the absoluteness of the LNC.

That being put to one side, your statement (“if it is the case that my discussion of the LNC is question begging, it seems to me that any discussion of the LNC would be question begging”) is, I think, a fair and honest assessment of the difficulty in establishing axiomatic presuppositions for necessary entities, especially against someone skeptical of the merit of those presuppositions (or the necessity of the entities).

You see, now that this has been recognized the conversation can advance beyond leveling accusations of question begging at each other’s basic presuppositions and an inquiry can begin into which presuppositions have the most merit. Do (Christian) theistic or non-theistic presuppositions provide the necessary preconditions for intelligibility, ethics, induction, music appreciation, tooth brushing, etc., (pick your apologetic poison)?

Then we can hang up some of these “rusty old hooks” and things can get really interesting…


Leave a Comment

Leave a Reply to Nocterro Cancel reply