Logic as Theory, Not Dogma

There are many interesting remarks that arise when people are discussing areas of disagreement, perhaps especially in areas of philosophical disagreement. These include:

  • “That’s illogical!”
  • “It’s logically impossible for that to happen!”
  • “That violates the Laws of Logic™!”
  • Etc. etc.

There are a number of interesting questions that can be asked here: “What is logic? What is the relationship (if there is one) between logic and reality? What are these ‘Laws of Logic’ and why are they special?” However, let’s stick with the question of what logic itself is. This can be phrased a number of ways:

  • The study of valid argument forms
  • The study of the correct principles of reasoning or inference
  • The study of the logical consequence relationship
  • The study of what follows from some set of truths, and why it follows

And so on. One fundamental reason we want to have the correct answers about how to reason is that we want to be able to discern how to determine what else is true, given some set of known truths. And if a party makes an invalid inference, we want to be able to point out that there is a gap between what’s asserted & what is concluded.

But there’s an interesting quality to the discourse about logic. When speaking about whether or not some piece of reasoning is valid, the remarks I mentioned at the beginning seem to conceptualize logic as some concrete, unchanging thing. It seems to view logic and logical rules as something handed down, rather than as a topic that has changed over time. And this is flatly untrue.

Without getting into the discussion about Non-Classical Logics, logic has changed over time. For about 2,300(-ish) years, Aristotelian Logic was the dominant logic in Western Philosophy. However, around the end of the 19th century, logicians began to realize that Aristotelian logic was unable to account for the inferences that were being made in mathematics at the time. In order to make logical sense of the reasoning mathematicians were engaging in, the systems of logic we now call “Classical Logic” were born. Logicians like Frege intended for this new logic to form the foundation of mathematics (a program known as “Logicism”). This project, however, ended in failure thanks to the work of other logicians like Kurt Gödel and Bertrand Russell.

But there is something important to note here: Logic changed. And it didn’t change by the pure light of natural reason or some intuition about a priori truths. Rather, logicians had data which they needed to account for – the reasoning mathematicians were engaging in at the time. The new logic had a different logical consequence relation than the old one.  Some argument forms which were valid in Aristotelian Logic were no longer valid, & some previously invalid argument forms were now valid. Take the following syllogism:

  • All Bs are Cs
  • All Bs are As
  • Therefore some As are Cs

Aristotelian logic considers this a valid argument, but it is invalid when translated into Classical Logic. What I aim to get at is fairly simple. The picture of logic as this inscrutable, unquestionable entity is blatantly ahistorical. Logical systems are theories about what follows from what, and why they follow. Just as other fields construct theories to account for the relevant data, so too are logics created to ascertain what the norms of correct reasoning are. Unsurprisingly, there are many debates about the respective virtues of logical systems and the problems they purport to solve.

But what exactly should qualify as correct reasoning is a complex topic. Is there only one correct system of reasoning, one true logic (logical monism)? Or perhaps different logics are apt to different domains, so that there is no one true logic (logical pluralism)? How do we decide between logical systems in the first place? And in doing so, must we privilege a particular logic?

Irrespective of your view on these & other related philosophical problems, you must be able to account for the historical facts about how logic has developed. Otherwise you seem to be giving a baseless “just so” story, and this makes it difficult to take your view as anything other than dogma.

If you’re interested in why exactly Classical Logic superseded Aristotelian Logic, I’ve uploaded an edited part of a talk Graham Priest once gave. It outlines the history & reasons behind the shift from Aristotelian Logic to Classical Logic. I hope this is helpful!

Link: https://www.youtube.com/watch?v=f3gMR0qVjRc

http://plato.stanford.edu/entries/logic-ontology/#Log

Priest, Graham. Doubt Truth to Be a Liar. Oxford: Clarendon, 2006. Print.

An Introduction to the Is-Ought Problem

Of all the dialectical bludgeons, the alleged inferential gap between “ought” and “is” is ubiquitous. The thesis is used to rebut numerous normative claims, but few in popular circles are aware of its pedigree, and because of that, they’re prone to misunderstanding its significance and meaning. Usually, those who employ the is-ought problem in its orthodox guise don’t realize that it’s a double edged sword. If the thesis is true, its undermining effects do not discriminate.

Historical Background:

The is-ought problem can be traced back to A Treatise on Human Nature. There are several interpretations of Hume’s words, and some others will be investigated in future posts, but for now the dominant 20th century interpretation will be explored. The passage in which the is-ought problem makes its appearance goes as follow,

“In every system of morality, which I have hitherto met with, I have always remarked, that the author proceeds for some time in the ordinary ways of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when all of a sudden I am surprised to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, ’tis necessary that it should be observed and explained; and at the same time that a reason should be given, for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it. But as authors do not commonly use this precaution, I shall presume to recommend it to the readers; and am persuaded, that this small attention would subvert all the vulgar systems of morality, and let us see, that the distinction of vice and virtue is not founded merely on the relations of objects, nor is perceived by reason” (Hume 302).

The orthodox interpretation is that Hume believes that no evaluative judgment may be the conclusion of a valid deductive argument that only has non-evaluative premises. For any set of descriptive or factual premises, no evaluative conclusion can follow without additional evaluative premises or some inferential rule that is essentially evaluative in content. Another way of putting the thesis is that there is no rule of deductive inference that licenses the move from factual or descriptive premises to evaluative conclusions.

The dominant interpretation of the 20th century aligns Hume’s is-ought thesis with non-cognitivism. Since evaluative claims are distinct in kind (“ought”) from factual/descriptive claims (“is”), it seems natural to embrace some form of non-cognitivism. Statements of fact are truth evaluable, whereas other kinds of utterances don’t seem to be. Examples of such utterances are expressions of fright, such as screaming, and expressions of pain, such as saying “ouch” and groaning. These utterances express non-cognitive attitudes through such phrases or noises. The attitudes are distinct from propositional attitudes due to the fact that the latter are truth-conducive (your beliefs may be true or false).

The orthodox interpreters tend to point to Hume’s motivation arguments to establish the non-cognitivist reading. Given Hume’s non-cognitivism being established by such arguments, the standard reading of the is-ought problem makes more sense; it would just be an entailment of Hume’s anti-rationalism about morality.

A brief statement of the more well known argument is that reason alone cannot motivate action (given the soundness of Hume’s first anti-rationalist argument), but morality can, so morality cannot be grounded in reason alone (Cohon 2010). If the dominant 20th century interpretation of Hume is correct, then this argument aimed to establish some form of non-cognitivism, which, in essence, would carve an ontological gap between fact and value. So, on the non-cognitivist reading, there are facts, which are those things that our beliefs aim to represent in some way, and there are values, which are products of our faculty of moral sentiment.

It should be noted, however, that the non-cognitivist reading of Hume is something that is no longer taken for granted, given recent Hume scholarship (Radcliffe 2006).

In essence, this would carve an ontological gap between fact and value. So, on the non-cognitivist reading, there are facts, which are those things that our beliefs aim to represent in some way, and there are values, which are products of our faculty of moral sentiment.

The problem for people who employ this interpretation of the is-ought problem as an argument against evaluative positions they disagree with is that it is embedded in an interpretive framework that includes a non-cognitivist element as an overarching theme. For the most part, the people in popular circles that I’ve encountered using this argumentative strategy tend to have cognitivist sympathies, and with such sympathies come evaluative claims that are believed to be truth evaluable. Insofar as their opponents’ arguments are supposed to fall prey to this problem, so will theirs.

Logical Maneuvers:

There are various ways to respond to the orthodox version of the is-ought problem. The first way involves what could be deemed logical tricks. The first trick, originally from Arthur Prior, goes as follows:

P1. It’s raining outside.

Therefore,

C. Either it’s raining outside or you ought not to steal.

This is a valid deductive argument that employs disjunction introduction. Now, if you claim that this isn’t really getting an ought from an is because the conclusion isn’t really an statement with evaluative content, then this example will evade your concern,

P1*. It isn’t raining outside.

P2*. Either it isn’t raining outside or you ought not to steal.

Therefore,

C*. You ought not to steal.

If you claim that the conclusion of the first argument lacks evaluative content, then the second argument only employs non-evaluative premises (since P2* is assumed to be non-evaluative for the sake of argument) and gets you to the evaluative conclusion C*.

The second trick goes like this,

P1$. It is raining outside and it is not raining outside.

Therefore,

C$. You ought not to steal.

This is also a valid deductive argument that employs the principle that from a contradiction, anything follows. Start with (i) P and not-P, simplify to (ii) P, (iii) not-P. Apply disjunctive addition to (ii) and you can deduce (iv) P or Q. Disjunction elimination on (iii) and (iv) gets the conclusion Q (Joyce 153).

Another logical trick involves an appeal to authority, but it raises issues about what constitutes evaluative content. If you’re interested in that, you can read chapter seven of Armstrong’s book, Moral Skepticisms.

There are other, more complicated, attempts at bridging the inferential gap between is and ought, such as Toomas Karmo’s proof. Unfortunately, there is no space to give a sufficient explanation of his argument.

Robust Bridges:

A different sort of attempt at bridging the alleged gap involves more than just logical trickery. One problem people may raise about the previous solutions is that they don’t involve deductions from non-evaluative premises that produce genuine moral knowledge or justification. Mere disjunction introduction and explosion aren’t sufficient because one could replace the evaluative disjunct with any other evaluative disjunct without affecting the argument. So, a more robust inference from is to ought needs to be explored.

It could be useful to step back and rethink the framework in which we’re trying to understand the is-ought problem. If we think of the regress problem in the context of moral justification, then there are only a few non-skeptical solutions: (i) foundationalism, (ii) coherentism, (iii) infinitism, and (iv) inference from non-evaluative knowledge. Granting for the sake of argument that i-iii all fail to secure moral justification, we need to evaluative our fourth option. So, we can think of the is-ought gap as epistemic rather than ontic.

So, the problem becomes finding a way to make an inference from a body of non-evaluative knowledge to an evaluative conclusion such that the inference transfers justification or warrant from the body of knowledge to the evaluative conclusion.

There are quite a few attempts in the literature to provide such an inferential link, so the selection of views here is going to be, to some extent, arbitrary.

Searle’s Metalinguistic Argument:

The first attempt, a metalinguistic strategy, is found in the work of John Searle:

P1. Jones utters the words, “I hereby promise to pay you, Smith, five dollars.”

P2. Jones promised to pay smith five dollars.

P3. Jones placed himself under an obligation to pay Smith five dollars.

P4. Jones is under an obligation to pay Smith five dollars.

Therefore,

C. Jones ought to pay smith five dollars (Searle 1964).

Searle’s argument aims to bridge Hume’s chasm by employing what he calls, “institutional facts,” and other things being equal, it is an institutional fact that the utterance of, “I hereby promise to . . .” is a performative by virtue of which the utterer undertakes an obligation (Searle 1964). So, it seems as though the gap between is and ought is bridged by institutional facts. It also seems as though the moral regress problem is solved by the fourth option alluded to in the last section. We could infer evaluative conclusions with robust content from non-evaluative premises.

The main issue is that the argument fails to rule out moral skepticism and the error theory, so it fails as a means of obtaining moral knowledge and justification. To see how Searle’s argument fails, notice the distinction between purporting to undertake an obligation and actually undertaking an obligation. An illuminating analogy comes from Michael Huemer,

“. . . suppose you call me collect, and I agree to accept the charges, but due to a mistake, the phone company never actually charges me. My having “accepted” these charges does not entail that I ever actually receive the charges. In a similar sense, a person might conceivably “accept” an obligation without ever actually having the obligation” (Huemer 75).

Somebody may undertake an obligation in the weaker sense of just purporting to if there are no actual obligations or if nobody is ever actually obligated to do anything. In other words, if the error theory is true, then Jones only purports to undertake an obligation. The problem arises, then, because the argument fails to rule out that possibility; and any argument employed to vindicate moral knowledge that fails to rule out the possibility that we lack moral knowledge is a dialectical failure.

If one introduces additional premises to the effect that the argument rules out error theory and moral skepticism, then those premises will have evaluative content, which means that they must be justified, which then reintroduces the moral regress problem. The evaluative premises would also need to be justified by virtue of inference from some body of evaluative knowledge, given our rejection of the other non-skeptical solutions.

A second problem with Searle’s argument is the inference from P1 to P2. Such an inference presupposes a large body of background knowledge about the norms of the social context in which Jones is embedded (Huemer 75). On one reading, the constitutive facts of that knowledge would all be non-evaluative, but on another reading, they would not be.

There are two ways to understand the move from P1 to P2: the evaluative (internal) sense, and a non-evaluative (external) sense (Mackie 66-72). The external sense merely takes the move to be a descriptive account of a rule governing  Jone’s speech act under a linguistic institution. It would be as if an alien was evaluating the argument from outside the linguistic institution of promising. Such an alien would require an additional premise that says, if person utters, “I promise to X” within a particular linguistic institution, then that person has made a promise within that linguistic institution (James 154). But that rule would teach the alien a fact about the rules of a particular institution, such as a rule for moving chess pieces across a board. It becomes a description of what Jones ought to do within that particular institution, not what Jones ought to do, full stop (James 154-155).

Viewed from the inside, Jones is surely obligated to pay his debt, but from the outside, it’s merely a statement of fact about particular linguistic conventions. The problem is, though, that when viewed from inside the institution of promising, the argument requires an additional inferential rule to secure the conclusion.

In other words, there is a dilemma for Searle’s argument. If we view it from the outside, then the conclusion is merely a brute fact, and we haven’t really gotten an ought from an is. If we view it from inside the institution, then the argument requires an additional premise in the form of an inference rule that says if one utters, “I promise to do X,” then one ought to conclude that that person promised to do X (James 157). But that is a rule which tells us what we ought to do, and as such is subject to the same requirement of justification as any other normative statement, thus restarting the regress. Evaluating the argument from within the institution, then, requires accepting particular normative statements (James 157). So, on the internal reading, Searle’s argument fails to solve the moral regress problem, and the external reading doesn’t even interact with it.

So, we’ve gone over Searle’s argument and found that it doesn’t provide a means to end the regress problem; but that doesn’t render the entire strategy bankrupt, as there are more promising metalinguistic arguments, such as Jesse Prinz’s. Also, it should be noted that Searle did not intend for the argument to be employed as a solution to the moral regress problem. Searle saw his argument as an example of how one might bridge the deductive is-ought gap by way of institutional facts and the notion of speech acts (Searle 1964). I merely used it as a means of illustrating one way the metalinguistic strategy for ending the regress problem for moral justification may be developed.

Geach’s Attempt:

The next argument is from Peter Geach,

P1. If Evan were to promise to adopt some practice he would adopt it.

P2. If Evan were to utter sentence W, he would be promising to adopt the practice of doing something wrong twice a day.

P3. Nobody should adopt the practice of doing something wrong twice a day.

Therefore,

C1. If Evan were to utter W, he would adopt the practice of doing something wrong twice a day.

Therefore,

C2. Evan should not utter W (Geach 1977; Huemer 2005).

The first thing to note about this argument is that premise three has evaluative content. Geach claims that the third premise is analytically true (Geach 1977). So, if the argument was successful, it would bridge the is-ought gap by virtue of an analytic truth that would be known by grasping the content of the proposition being expressed; in other words, understanding the content would just be acquaintance with its truth conditions.

The problem is that this would be to smuggle in a moral epistemology insofar as there is some account of grasping the content of the analytic moral proposition that doesn’t rely on the fourth solution to the moral regress problem. If it relied on the fourth account of the structure of moral justification, then it would merely push the problem back a step.

If premise three requires an account of content-grasping for its justification that makes use of moral foundationalism, infinitism, or coherentism, then it merely assumes that there is no gap by virtue of adopting a solution in which it cannot be formulated.  In other words, the epistemic gap only makes sense given the fourth solution to the regress problem, so adopting another solution changes the subject.

Another problem is that the argument is invalid. The inference from P3 to C1 is valid just if,

P1*. S ought not to do A.

P2. If S did B, S would do A.

Therefore,

C*. S ought not to do B.

is a valid form of inference (Huemer 77). An example that illustrates the invalidity of the above inference form is provided by Huemer,

“John is a judge about to pass sentence on Mary, a convicted marijuana dealer. Mary’s crime is minor at worst; John, however, has an intense, irrational hatred for all drug users, as a result of which he is determined to sentence Mary to either life imprisonment or death. He could sentence Mary to only a brief prison term, but he would not in fact do so. Now consider the following inference:

P1$. John ought not to sentence Mary to life imprisonment.

P2$. If John were to refrain from sentencing Mary to death, then he would sentence Mary to life imprisonment.

Therefore,

C$. John ought not to refrain from sentencing Mary to death” (Huemer 77).

It seems obvious that P1$ is true given the fact that John could sentence her to a minor term, assuming we put aside the regress problem for the sake of argument. P2$ is stipulated as a fact about John’s psychology. However, the conclusion is clearly false (Huemer 77). So, the argument form is invalid.

A third problem with the argument is that P1 is evaluative (Huemer 77). The premise goes like this,

(∀x) (Evan promises to do x > Evan does x)

The evaluative nature of the premise can be revealed by substituting “act wrongly” for x.

Evan promises to act wrongly > Evan acts wrongly

Once more, I’ll draw from Huemer to illustrate this point,

“. . . once we fix the natural facts about how Evan would behave upon making such a promise, whether the whole sentence is true then depends on whether the behavior would be wrong” (Huemer 78).

Let’s say that if Evan promised to act wrongly, he would rob a bank and go for a walk. The facts about what Evan would do are fixed, but the whole sentence is true just if the things he would do if he made such a promise are actually wrong (Huemer 78). So, the truth conditions for P1 are such that P1 is true if and only if some evaluative state of affairs obtains.

It seems as though Geach’s argument fails to provide a means of overcoming the regress problem due to the problems explored above.

The Naturalist’s Alternative:

The next attempt at providing a means of making the fourth solution to the regress problem work is more indirect. So far, we’ve only looked at attempts that aimed at establishing evaluative knowledge through deduction from non-evaluative premises. But what if being unable to establish an ought by deducing it from non-evaluative premises isn’t that interesting? For instance,

P1. My glass contains the liquid H2O.

P2. I am about to drink the liquid in my glass.

Therefore,

C. I am about to drink water.

This argument is invalid by Tarskian standards because a translation of the argument into predicate calculus would allow for models where P1 and P2 are true but C is false (Joyce 154).

However, we don’t deny that we can have knowledge of the molecular structure of the liquid in my glass, despite the invalidity of such arguments. Perhaps something analogous holds for the nature of normativity. To further illustrate the point, the worldview that physics gives us clearly allows for biological facts without the need for us to be able to deduce such facts from propositions about fundamental particles, fields, and the laws of nature (Joyce 154). So, a moral naturalist who is of the non-reductivist or synthetic reductivist stripe has room to maneuver insofar as she can show that the is-ought gap is as uninteresting as the H2O-water gap and the physics-biology gap.

One avenue for the moral naturalist is inference to the best explanation. For example, perhaps the best explanation for Hitler’s behaviors during WW2 and prior is that Hitler had a morally depraved character. The fact that Hitler was morally depraved or vicious (along with non-evaluative background knowledge) best explains his actions, or so this form of reasoning goes. So, the explanation of Hitler’s actions makes them more probable than without the explanation, or with an alternative explanation.

Another way to think about it is in terms of a hypothesis making certain observations more expected than they otherwise would be. Some thinkers such as Nick Sturgeon adopt this strategy. The merits of abduction applied to evaluative knowledge cannot be assessed here, since the post would become too lengthy and disjointed. Suffice it to say, however, that the Sturgeon strategy involves conceptions of explanation that are controversial.

Conclusion:

There are several other attempts to bridge the is-ought gap that were not explored here. I will assess them over the course of several future posts. Also, the Sturgeon explanatory strategy will be explored in the future, as will alternative ways to interpret Hume’s is-ought thesis, and my own solution to the moral regress problem. So far, the prospects for the fourth solution to the regress problem seem dim. However, there may be options for those who wish to endorse the fourth solution that are more satisfactory than the ones explored here.


Works Cited:

Cohon, Rachel, “Hume’s Moral Philosophy”, The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2010/entries/hume-moral/>.

Geach, P. T. “Again the Logic of ‘Ought’.” Philosophy: 473. Print.

Huemer, Michael. Ethical Intuitionism. Basingstoke England: Palgrave Macmillan, 2005. Print.

Hume, David, and Mary J. Norton. A Treatise of Human Nature: A Critical Edition. Oxford: Clarendon, 2007. Print.

James, Scott M. An Introduction to Evolutionary Ethics. Chichester, West Sussex, U.K.: Wiley-Blackwell, 2011. Print.

Joyce, Richard. The Evolution of Morality. Cambridge, Mass.: MIT, 2006. Print.

Mackie, J. L. Ethics: Inventing Right and Wrong. Harmondsworth: Penguin, 1977. Print.

Radcliffe, Elizabeth S. “Moral Internalism and Moral Cognitivism in Hume’s Metaethics.” Synthese (2006): 353-70. Print.

Searle, John R. “How to Derive “Ought” From “Is”” The Philosophical Review: 43. Print.

Beg Your Pardon, What is Begging the Question?

We’ve all met them. Usually they are fresh off of a critical thinking, or informal logic course. They are the fallacy mongers. Taught to identify informal fallacies in headlines and textbooks, they begin to “see” fallacies at every turn. And suffering them in any conversion is nearly intolerable. For those unfamiliar, I am talking about people who behave like this. Now, I am not saying that it isn’t important to be able to know and be able to identify informal fallacies. It is. But it can also become a hammer that turns all arguments into nails. This is especially dangerous because informal fallacies tend to be vaguely defined, and often resemble perfectly good methods of reasoning. Pro-tip: When you encounter such people, inform them that it is not sufficient to merely burp up fallacies at you. Ask them to explain to you what the fallacy means, and specifically how your argument matches the description of the argument. If they misrepresent your argument, resist the urge to shout “strawman” or any other fallacy term at them, as this only aggravates the situation.

As of late, however, I’ve noticed that one fallacy-accusation has become ubiquitous in debates, reviews, conferences, and blogs. I think of it as the last refuge of the philosophical scoundrel since, if all else fails, you can be sure that they will tell you that you’ve committed this particular fallacy. Surprisingly, it is not uncommon to see professional philosophers smugly appeal to it, brush the dust off of their shoulders, and walk off as if they’ve done you a huge favor. Which fallacy is this? It is none other than Begging the Question. So here, I want to discuss the fallacy: what it is, and what it is not.

Begging the question is an informal form of reasoning in which the question under discussion (typically the conclusion of the argument being discusses) is assumed in one premise or another. I say one premise or another because, in a sense, every conclusion is contained in the premises of a valid argument. A valid argument just takes two or more premises together and shows that another proposition is logically entailed by taking those premises together. This can confuse some people, because they will see a series of premises, note that, jointly, they logically entail the conclusion, see that all the premises are uncontroversial except for one, and then cry that the one premise is question begging. This may not be the case if that one premise can be a) justified by considerations that are independent from the conclusion, and b) the premise is not an obfuscated restatement of the conclusion.

So when has an argument committed the fallacy of begging the question?

  1. When one premise or another is logically equivalent to the conclusion.
    • Example: 1. It is not the case that if God exists, then God does not exist. Therefore, 2. God exists.
      • Premise one is logically equivalent to the conclusion, even if it seems reasonable. One could literally “prove” the existence of anything by swapping out “God” for another term.
  2. When one premise or another is semantically equivalent to the conclusion.
    • Example: 1. Morphine has dormative virtues. Therefore, 2. Morphine has the power to induce sleep.
      • This example comes from Molière’s Le Malade Imaginaire. There is a semantic equivalence between the premise and the conclusion because “Dormative” just means “sleep inducing” and a “virtue” just means a “power”. So if there is any question as to whether morphine has the power to induce sleep, this sort of argument would be useless as a proof.
  3. When the only justification one can provide for accepting one premise or another is the conclusion of the very argument where the premises appear.
    1. Example: 1. The Bible is the inerrant Word of God. 2. Whatever is inerrant reports no factual errors. 3. The Bible reports that God exists. Therefore, 4. God exists.
      • This is where things get a bit tricky. Technically, I would call this circular reasoning rather than begging the question, but some want to treat circle reasoning as a subset of begging the question. The idea is that A and B imply C. You might defend the truth of A by appealing to D and E, but you say that B is true because of F and C. Well, wait a minute, that means that the only reason you gave to accept B is that C is true. But that is precisely what you are trying to prove! So,an argument is circular if the justification for one premise or another somehow works back to the conclusion. In this example, the reason to think that (1) the Bible is the Word of God will eventually work back to some justification that depends upon the assumption that conclusion, God exists, is true. Since that is the question under dispute, it cannot be used to justify a premise that leads to that conclusion.

Now here are some circumstances where I don’t think one has necessarily begged the question. I say not necessarily because they may have done so in other ways along with meeting the criteria of these circumstances:

  1. When the only people who are willing to accept the truth of the premises are those who are willing to accept the conclusion, or, to put it the other way, those who are willing to accept the truth of the conclusion are only those who are willing to accept the premises of the argument in question.
    • I find that this often leads to the charge of “begging the question” because one has reached the conclusion of the argument he or she is incredulous about the conclusion. So he or she declares that one premise or another must be more dubious than initially thought. Perhaps such a person reasons that everyone else already accepts the conclusion and so have not made the effort to pay the cost of abandoning one of the premises. Such a person would be incorrect to say that the argument begs the question, though, unless a premise can be doubted for the expressed reason that the justification for the premise depends upon conclusion in the ways that I outlined above. The fact that one finds a premise to be dubious, or is more willing to deny a premise than admit a conclusion, is not sufficient to establish that the given premise is question begging in and of itself. In such a case, one should simply deny the premise(s) that he or she finds dubious, and live with the consequences of that commitment.
    • Also, it is not enough to simply note that only people accept the conclusion are those who accept the premises. Suppose, for instance, that there is a certain proposition, p, for which there is only one argument that believers in p find cogent. Let’s also say that no believer in p happens to believe in p without justification (i.e. all believers in p depend on the same set of premises to justify their belief and no one believes p on faith or because p is properly basic). All other arguments for p are universally panned by believers and non-believers alike. That there is only one accepted argument to justify belief in p, and that it happens to be the case that all believers accept p on the basis of the premises contained in that argument is really just a report of the psychology of believers and non-believers with respect to p and arguments in support of p. It is perhaps an accident of history, or something to do with the nature of p that has led to this circumstance. But simply noting the fact that people who accept p also happen to be the same people who accept the those premises that lead to the conclusion p does not sufficiently establish that the argument for p is question begging.
  2. When an argument is made without stating independent justification for the premises.
    • Simply observing that a premise has not been justified independently of the conclusion does not establish that the premise somehow begs the question. At best, one can say that the premises are unjustified or unwarranted. Assuming that the justification or warrant for the premises is somehow found in the conclusion is itself fallacious. One has made an argument from ignorance. The best course of action is to ask one’s interlocutor to give some justification for the premises, if the justifications are not apparent. It may then be the case that the argument is question begging, but only if the premises assume the conclusion in the ways I’ve noted above.
  3. When an argument raises other questions that need to be answered.
    • The idiom “this begs the question” really just means that some statement or fact raises other sets of questions that need to be addressed. That a conclusion of an argument raises other perhaps deeper questions is not a mark against the argument. Something akin to this occurred in Richard Dawkins’ The God Delusion when he used Dennett’s distinct between “skyhook” and “crane” explanations to complain that “God” is merely skyhook explanation given that God raises more questions, in Dawkin’s mind, than answers (like who designed the designer, which is not a question my mind happens to raise). This is not to say that Dawkins actually said that “skyhooks” beg the question, but others made this blunder. For instance, David Thompson writes:

The only thing the evolutionary algorithm is guaranteed to deliver is design: it produces organisms that are “fit” for their environment, i.e., that are well designed. Dennett rejects the idea that we can explain design by appealing to a pre-existing Design (the Platonic option) or a conscious Designer (the theistic option). He describes such explanations as “skyhooks,” –devices hanging from the sky with no visible means of support that still do the heavy lifting in design space. If we are to explain how design comes to be in the first place, we get nowhere by assuming that design already exists. Design and designers are what need to be explained; minds are products of evolution, not (at least initially) producers of it. The Darwinian, algorithmic approach is the only one that is not question-begging (2009, 62).1

What is extraordinary about this passage is that it not only mistakes “raising new questions” with the fallacy of begging the question, it actually commits the fallacy of begging the question in the process of committing this error. An argument that concludes with “A designer initiated and produced the evolutionary algorithm” may raise the question (for some) of who designed the designer, but such a question isn’t question-begging. Rather, it reveals a certain assumption in the questioner, that designers need to be designed! Intelligent Design theorists think that things like minds require explanations that go beyond evolution. But to show that intelligent design is an inadequate explanation for certain design features, Thompson begs the question by assuming that the evolutionary algorithm is the only way to explain minds. He essentially argues that God’s mind cannot explain design because all minds are the products of evolution and no minds initiate evolution. But that is precisely the question at issue in the debate. To put this more pointedly, Thompson reasons that it is not the case that there exists a mind that initiated evolution because there is no mind that initiated evolution. And we can show that his one premise is logically equivalent to his conclusion, where Mx is ‘x is a mind’ and Ix is ‘x initiates evolution’ :

1. (∀x)(Mx ⊃ ~Ix) (assumption for CP)
2. (∀x)(~Mx ∨ ~Ix) (1 Impl)
3. (∀x)~(Mx & Ix) (2 DeM)
4. ~(∃x)(Mx & Ix) (3 QN)
5. (∀x)(Mx ⊃ ~Ix) ⊃ ~(∃x)(Mx & Ix) (1-4 CP)
6. ~(∃x)(Mx & Ix) (assumption for CP)
7. (∀x)~(Mx & Ix) (6 QN)
8. (∀x)(~Mx ∨ ~Ix) (7 DeM)
9. (∀x)(Mx ⊃ ~Ix) (8 Impl)
10. ~(∃x)(Mx & Ix) ⊃ (∀x)(Mx ⊃ ~Ix) (6-9 CP)
11. [(∀x)(Mx ⊃ ~Ix) ⊃ ~(∃x)(Mx & Ix)] & [~(∃x)(Mx & Ix) ⊃ (∀x)(Mx ⊃ ~Ix)] (5,10 Conj)
12. (∀x)(Mx ⊃ ~Ix) ≡ ~(∃x)(Mx & Ix) (11 Equiv)
13. ◻[(∀x)(Mx ⊃ ~Ix) ≡ ~(∃x)(Mx & Ix)] (12 NI)

Since the equivalence is necessary, there is no model where the truth conditions would fail. That is just to say that the premise is logically equivalent to the conclusion. No premises are required to know that “necessarily, no minds initiate evolution if and only if it is not the case that some mind initiates evolution”. Of course, no theist would agree that all minds are the product of evolutionary process, and that no minds can initiated evolution. Theism is the thesis that there is at least one uncaused mind, and that mind could design aspects of evolutionary processes and guide them. The answer to what explains God’s mind is found in the nature of his own necessity. But even if the premises or conclusion of an argument raise questions with no readily apparent answer, the argument is not invalidated.

So, in sum, the fallacy of begging the question can be tricky to spot. When arguments rely on one relatively controversial premise, ask yourself this: a) does my interlocutor provide justification for the premise independently from the conclusion, and b) is this premise merely a logical or semantic restatement of the conclusion. If the identified premise is logically or semantically equivalent to the conclusion, then pay attention to how that premise is justified. If independent justification is provided for the premise, you can help your interlocutor by noting that the real argument is the one that went into independently justifying the premise that you’ve identified as equivalent to the conclusion. That is a far more constructive way to handle a situation where you think an argument has been begged.

Cheers!

1D. Thompson. 2009. Daniel Dennett. New York: Continuum.