Wiki. Source.

Kennethamy:

Well, here is an example: in English we use the terms, “believe” and “know” very differently, from which we can infer that there is a difference between “believing” and “knowing”. For instance, we say, “Joe believes that La Paz is the capital of Ecuador, but he is wrong”. We never say, “Joe knows that La Paz is the capital of Ecuador, but he is wrong”. However, we have to be cautious. There are often extraneous circumstances which govern what we say so that if we attend only to what we say, will mislead us. A good example is that we do not say “It is raining, but I do not believe it is raining”. But that cannot show that it cannot be true that it is raining but I not believe it is raining. (Moore’s Paradox). Here is an interesting example of a sentence that may be true, but which, for extraneous factors not having to do with its semantics (meaning) it would make no sense to say.

Emil:

What is funny about “It is raining, but I do not believe it is raining” is that it is equivalent with “It is raining and Moore does not believe that it rains” (since “I” refers to Moore). However the latter one is not viewed as paradoxical. The difference seems to be that it is an implicit assumption in most communication contexts that the utterer (here Moore) believes what he claims. With that assumption in mind, we get the contradiction: It is raining, Moore does not believe that it is raining and (from the assumption and the utterance) Moore believes that it is raining. Thus, Moore believes and does not believe that it is raining. Voila!

Kennethamy:

(since “I” refers to Moore).

Why do you think that? Do you think that when Descartes wrote, “I think, therefore I exist” he was referring to Descartes? He was referring to no one in particular. The first person personal pronoun there is a very impersonal personal pronoun, just as when I say something like, “If you believe that the claim that a miracle has occurred is justifiable, then you are wrong”need not be addressed to anyone in particular. The “you” there just means the impersonal, “one”. (As in the French, “on” and the German, “Man”). But your explanation of the paradox is right. A person who makes a claim is assumed either to believe or know what he claims. (In fact, Moore pointed that out in a different context). But that fact about conversation is not about the semantics of what the person says, it is about the pragmatics of what he said. It does not seem to me that the person who says, “It is raining and I don’t believe it” is contradicting himself (and you did not say he was). But, as you said, from the premises that the person who says it is raining but that he does not believe it, together with the premise that he does believe it is raining, a contradiction can be derived. But that, to repeat, is no reason to think that the person is contradicting himself.

Emil:

Why do you think that?

I never heard of impersonal “I”‘s before. The pronoun “I” refers to the speaker, you defined it yourself in another thread.

Do you think that when Descartes wrote, “I think, therefore I exist” he was referring to Descartes?

Yes.

He was referring to no one in particular.

I disagree. I think he was referring to himself. But alas, the justification works equally well no matter who uses the argument. That does not imply that the “I” is impersonal.

The first person personal pronoun there is a very impersonal personal pronoun, just as when I say something like, “If you believe that the claim that a miracle has occurred is justifiable, then you are wrong”need not be addressed to anyone in particular. The “you” there just means the impersonal, “one”. (As in the French, “on” and the German, “Man”).

Or the danish “man”, (The german one isn’t capitalized, since “man” isn’t a noun but “Mann” is (means man). To avoid confusion with impersonal and personal pronouns in english, I try to always use “one” but it slips from time to time. You know, the bewitchment of our language.

But, as you said, from the premises that the person who says it is raining but that he does not believe it, together with the premise that he does believe it is raining, a contradiction can be derived. But that, to repeat, is no reason to think that the person is contradicting himself.

Right. Here is a more formal argument for the ‘contradiction’.

1. Moore utters “It is raining but I don’t believe it.”

2. For any person and any utterance, if the utterance is uttered in a truthful context, then the person believes all the propositions expressed by his utterance.

3. “It is raining but I don’t believe it.” was uttered in a truthful context.

Thus, 4. Moore believes all the propositions expressed by this utterance. (2, 3)

5. The propositions expressed by “It is raining but I don’t believe it.” are {that it is raining, that Moore doesn’t believe that it is raining}.

Thus, 6. Moore believes that it is raining. (4, 5)

Thus, 7. Moore believes that Moore doesn’t believe that it is raining. (4, 5)

This isn’t actually a contradiction, but it is somewhat paradoxical in a looser sense.

If we include the utterance (re-worded) as a premise. A contradiction follows:

8. It is raining and Moore doesn’t believe that it is raining.

Thus, 9. Moore doesn’t believe that it is raining. (8)

Thus, 10. Moore doesn’t believe that it is raining and Moore believes that it is raining. (6, 9)

Give it a read. It is divided into 4 parts:

My Take on the Liar Paradox (Part I of IV)
My Take on the Liar Paradox (Part II of IV)
My Take on the Liar Paradox (Part III of IV)
My Take on the Liar Paradox (Part IV of IV)
All four articles combine to a total of about 8,000 words, so it will not take long for a dedicated reader to read through it.

I was kindly sent a PDF version of this essay (same as this one). The text is all there, I think, but the textformat is annoying to read. So, I made my own version. The essay itself is about 14100 words long. It is part of the book with the very similar name Conjuctures and Refutations, see Wiki about the book.

Karl Popper – SCIENCE CONJECTURES AND REFUTATIONS

This will not involve many science facts as the discussion is wholly philosophical in nature. This is an epistemological, not scientific essay, it just happens to use some facts of science.

I want to show the value of thinking of things as inconsistent sets of propositions (or whatever truth carrier you like, but I like propositions) or at least implausible sets of propositions (when at least one inference is inductive (or non-deductive, if you like that term better)).

Consider this set of propositions:

1. Newton’s physics is correct.
2. Things are in a such and such way at time t1.
3. That Newton’s physics is correct and things are in a such and such way at time t1, implies that things will happen in such and such way at time t2.
4. A study found that such and such did not happen at time t2.
5. The study is correct.
6. That the study is correct implies that such and such did not happen at time t2.

This set is plainly inconsistent; it cannot be true. At least one proposition in this set is false. Suppose we are around the time when Einstein introduced his relativity theories. At that time physicists had pretty good reason to believe (1) (among others: good explanatory power, lots of empiric confirmation), and I’m sure some people called physicists who did not stop believing in Newton’s physics even when some studies found results that are contrary to the predictions of Newton’s physics given some antecedent state of affairs dogmatic. I’m fairly sure such a claim of dogmatism is often thrown around in similar cases.

My point is that it is unwise to claim someone is being dogmatic quickly. For there are many things other than some widely accepted theory that could be wrong (in this case (1)). We could be wrong about the antecedent states of affairs (in this case (2)), or wrong about what the theory predicts (in this case (3)) given that state of affairs; perhaps the scientist that make the prediction from the theory made a calculation error. Something similar applies the the study that ‘challenges’ the accepted theory (in this case (5)). So there are many things that could be wrong without the accepted theory being false. It is wise to consider that before calling people that are being epistemically conservative for dogmatic.

The method of putting the relevant propositions in an inconsistent set forces us to be made aware of some perhaps not normally discussed propositions without which the set would be consistent (or not-implausible). Usually in a moderately complex case such as the one with Newton’s physics, a set of propositions that form as inconsistent set (or implausible) will contain 5-10 propositions. In more complex cases, the sets can be much longer (such as very complex cases involving the impossibility of an infinite past which involves temporal and modal logic). In general, the more propositions we can find that together forms an inconsistent set (or implausible), the better overview, and the easier to is to make a justified decision about which proposition(s) to stop believing in in the case that one actually believes all of them. If we are to avoid inconsistent beliefs (=inconsistent objects of beliefs), then we should think of the many potentially epistemically justified ways there are to deal with a such inconsistent set.

In the above case, rejecting (4) would probably not be a wise decision, neither would it be to reject (6). If there is only one study and it is not exceptionally well done, then rejecting (5) is probably not a bad decision to begin with. If more studies (by competent scientists) confirm the first study, then sooner or later we should begin wondering if not our beliefs would have better coherence were we to reject the theory (1). But before we do that we should consider other alternatives such as (2) and (3). It would not be good if we rejected some theory and later found it that we had no grounds to do that because we were wrong about what the antecedent state of affair was (2).

This way of solving problems (which usually involve an inconsistency of we add together the relevant propositions to a set), is applicable to every topic that I have thought of. It is especially useful to very complex situations where it is hard to get an overview and it seems hard to settle on a specific solution (that is, hard to find out which proposition is the epistemically most justified to deny).

Introduction

Abstract

In this essay I attempt to clarify what it means to say that an argument begs the question. One may think that it is a fairly straightforward matter but my analysis reveals that it isn’t so.

Shorthands

“BTQ” means begging the question, or begs the question whichever is grammatically correct on the context.

The phrase “begs the question” in english

The phrase “begs the question” has at least two meanings in english. The first and perhaps most common meaning is that of raising an important question. As it is written on FallacyFiles.org:

The phrase “begs the question” has come to be used to mean “raises the question” or “suggests the question”, as in “that begs the question” followed by the question supposedly begged. The following headlines are examples:

• • • • Warm Weather Begs the Question:
        To Water or Not to Water Yard Plants

      • Latest Internet Fracas Begs the Question:
        Who’s Driving the Internet Bus?

      • Hot Holiday Begs Big Question:
        Can the Party Continue?

This is a confusing usage which is apparently based upon a literal misreading of the phrase “begs the question”. It should be avoided, and must be distinguished from its use to refer to the fallacy.”¹

The second meaning of “beg the question” is in the informal logical fallacy of begging the question. It is this meaning that this essay attempts to clarify.

Proposed definitions

So what does it mean to say that an argument BTQ? There are surprisingly many different answers from good sources. Below I quote many of the different definitions given, some by authorities and some not.

FallacyFiles.org

In an article entitled “Begging the Question” FallacyFiles.org writes:

“The phrase “begging the question”, or “petitio principii” in Latin, refers to the “question” in a formal debate—that is, the issue being debated. In such a debate, one side may ask the other side to concede certain points in order to speed up the proceedings. To “beg” the question is to ask that the very point at issue be conceded, which is of course illegitimate. “²

And:

“Any form of argument in which the conclusion occurs as one of the premisses, or a chain of arguments in which the final conclusion is a premiss of one of the earlier arguments in the chain. More generally, an argument begs the question when it assumes any controversial point not conceded by the other side.”³

Notice how vague the one mentioned in the first paragraph is. To the defense of FallacyFiles.org, we may note that that paragraph is entitled “Etymology”, and is perhaps not meant to actually explain clearly what it means to BTQ but only to explain how the etymology relates to the meaning of the term.

The second paragraph is entitled “Exposition” and is clearly meant to explain the meaning of the term. However the paragraph features two independent definitions, a strict (which is a disjunction) and a general (or rather, broad) one.

butterfliesandwheels.com

In the article entitled “Bad Moves: Begging the question” butterfliesandwheels.com writes:

“Begging the question – assuming what needs to be argued for [...]”⁴

skepdic.com aka. The Skeptic’s Dictionary

In an article entitled “begging the question” it is written on skepdic.com:

“Begging the question is what one does in an argument when one assumes what one claims to be proving.”⁵

And a bit later:

“If one’s premises entail one’s conclusion, and one’s premises are questionable, one is said to beg the question.”⁶

Notice that these two definitions are not at all identical. Examples will show this later.

Wikipedia.org

In an article entitled “Begging the question” it is written on Wikipedia.org:

“The fallacy of petitio principii, or “begging the question”, is committed “when a proposition which requires proof is assumed without proof.”[3] More specifically, petitio principii refers to arguing for a conclusion that has already been assumed in the premise. The fallacy may be committed in various ways.

When the fallacy of begging the question is committed in a single step, it is sometimes called a hysteron proteron,[4] as in the statement “Opium induces sleep because it has a soporific quality”.[5] Such fallacies may not be immediately obvious in English because the English language has so many synonyms; one way to beg the question is to make a statement first in concrete terms, then in abstract ones, or vice-versa.[5] Another is to “bring forth a proposition expressed in words of Saxon origin, and give as a reason for it the very same proposition stated in words of Norman origin”,[6] as in this example: “To allow every man an unbounded freedom of speech must always be, on the whole advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.”[7]

When the fallacy of begging the question is committed in more than one step, it is sometimes referred to as circulus in probando or reasoning in a circle[4] but incorrectly if we look at the definition Aristotle gave us in Prior Analytics.[1]

“Begging the question” can also refer to making an argument in which the premise “is different from the conclusion … but is controversial or questionable for the same reasons that typically might lead someone to question the conclusion.”[8]”⁷

And:

“In informal situations, the term begging the question is often used in place of circular argument. In the formal context however, begging the question holds a different meaning.[1] In its shortest form, circular reasoning is the basing of two conclusions by means of which there is demonstrated a reversed premise of the first argument. Begging the question does not require any such reversal.

Begging the question is similar to the Fallacy of many questions: a fallacy of technique that results from presenting evidence in support of a conclusion that is less likely to be accepted than merely asserting the conclusion. A specific form of this is reducing an assertion to an instance of a more general assertion which is no more known to be true than the more specific assertion:

* All intentional acts of killing human beings are morally wrong.

* The death penalty is an intentional act of killing a human being.

* Therefore the death penalty is wrong.

If the first premise is accepted as an axiom within some moral system or code, this reasoning is a cogent argument against the death penalty. If not, it is in fact a weaker argument than a mere assertion that the death penalty is wrong, since the first premise is stronger than the conclusion.”⁸

New York Times

In an article entitled “ON LANGUAGE; Take My Question Please!” it is written in New York Times:

“”This sentence fragment uses ‘begs the question,’ ” he writes, ”in the sense of a question that begs to be asked, usually because it is obvious to all. However, I am plagued by my logic course of some years ago, which taught me that begging the question is nothing of the kind. Rather, begging the question is a logically invalid form of argument that uses the point to be proven as part of the argument for its proof.”

Amen. Readers have been protesting this misuse of a term about a concept set down by Aristotle, a student of Plato Cacheris, in his book on logic written about 350 B.C. (Here comes mail on B.C.E.) His Greek term en archei aiteisthai was translated by the Romans as petitio principii, and rendered into English in 1581 as begging the question. In whatever language, it described the fallacy known as ”the assumption at the outset.”

In his 1988 book, ”Thinking Logically,” Prof. James Freeman explains: ”An argument begs the question when the conclusion, in the same or different words, or a statement presupposing the conclusion, is introduced as a premise. The case for the conclusion ultimately depends on accepting the conclusion itself.””⁹

Notice how it says that it is an invalid form of argument. But surely any argument that commits the strict fallacy of BTQ, that is, the conclusion is identical to a premise, is a valid argument. Why? Valid arguments are precisely those arguments where the premises logically imply the conclusion. Since any proposition implies itself [P⇒P], then any argument that BTQ in the strict sense is valid.

nizkor.org

In an article entitled “Fallacy: Begging the Question” it is written on nizkor.org:

“Begging the Question is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true. This sort of “reasoning” typically has the following form.

1. Premises in which the truth of the conclusion is claimed or the truth of the conclusion is assumed (either directly or indirectly).

2. Claim C (the conclusion) is true.

This sort of “reasoning” is fallacious because simply assuming that the conclusion is true (directly or indirectly) in the premises does not constitute evidence for that conclusion. Obviously, simply assuming a claim is true does not serve as evidence for that claim. This is especially clear in particularly blatant cases: “X is true. The evidence for this claim is that X is true.”

Some cases of question begging are fairly blatant, while others can be extremely subtle.”¹⁰

The Cambridge Dictionary of Philosophy

In an article entitled “Circular Reasoning” Robert Audi writes:

“circular reasoning, reasoning that, when traced backward from its conclusion, returns to that starting point, as one returns to a starting point when tracing a circle. The discussion of this topic by Richard Whatley (1787–1863) in his Logic (1826) sets a high standard of clarity and penetration. Logic textbooks often quote the following example from Whatley:

To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State; for it is highly conducive to the interests of the Community, that each individual should enjoy a liberty perfectly unlimited, of expressing his sentiments.

This passage illustrates how circular reasoning is less obvious in a language, such as English, that, in Whatley’s words, is “abounding in synonymous expressions, which have no resemblance in sound, and no connection in etymology.” The premise and conclusion do not consist of just the same words in the same order, nor can logical or grammatical principles transform one into the other. Rather, they have the same propositional content: they say the same thing in different words. That is why appealing to one of them to provide reason for believing the other amounts to giving something as a reason for itself. Circular reasoning is often said to beg the question. ‘Begging the question’ and petitio principii are translations of a phrase in Aristotle connected with a game of formal disputation played in antiquity but not in recent times. The meanings of ‘question’ and ‘begging’ do not in any clear way determine the meaning of ‘question begging’. There is no simple argument form that all and only circular arguments have. It is not logic, in Whatley’s example above, that determines the identity of content between the premise and the conclusion. Some theorists propose rather more complicated formal or syntactic accounts of circularity. Others believe that any account of circular reasoning must refer to the beliefs of those who reason. Whether or not the following argument about articles in this dictionary is circular depends on why the first premise should be accepted:

(1) The article on inference contains no split infinitives.

(2) The other articles contain no split infinitives.

Therefore, (3) No article contains split infinitives.

Consider two cases. Case I: Although (2) supports (1) inductively, both (1) and (2) have solid outside support independent of any prior acceptance of (3). This reasoning is not circular. Case II: Someone who advances the argument accepts (1) or (2) or both, only because he believes (3). Such reasoning is circular, even though neither premise expresses just the same proposition as the conclusion. The question remains controversial whether, in explaining circularity, we should refer to the beliefs of individual reasoners or only to the surrounding circumstances. One purpose of reasoning is to increase the degree of reasonable confidence that one has in the truth of a conclusion. Presuming the truth of a conclusion in support of a premise thwarts this purpose, because the initial degree of reasonable confidence in the premise cannot then exceed the initial degree of reasonable confidence in the conclusion.”¹¹

What can we gather from this?

There is consensus about a strict definition of BTQ which is identical to circular logic. This is defined as: An argument is circular iff one of the premises is identical to the conclusion.

There is no consensus about a broad definition of BTQ. At best this is some intuitive notion. Further analysis could try to find a meaning appropriate for this broad sense. That task I will take up in a forthcoming essay.

Notes

In an earlier essay I mentioned that that meaninglessness is contagious with respect to sentences. One can pretty easily formulate the principle in normal english – if a sentence is meaningless, then so is any more complex sentence of which it is a part of. To get a proper, formal formulation of this we may simply think of the rules in logic systems used to form well-formed formulas (=wff’s) and then formulate some similar principles for the meaninglessness of sentences. Here’s what I have in mind:

Negation. For all sentences, iff it is not the case that a sentence is meaningful, then it is not the case that the negation of that sentence is meaningful.

(∀S)(¬M(S)↔¬M(¬S)

Conjunction part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the conjunction of that sentence with another sentence is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S∧Z)¹

Disjunction part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the disjunction of that sentence with another sentence is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S∨Z)

Implication/conditional part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the implication of the first sentence to the second is meaningful, and it is not the case that the implication of the second sentence to the first is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S→Z)∧¬M(Z→S))

Bi-implication/bi-conditional part. For all sentences, if it is not the case that a sentence is meaningful, then for all sentences, it is not the case that the bi-implication of the first sentence to the second is meaningful, and it is not the case that the bi-implication of the second sentence to the first is meaningful.

(∀S)(¬M(S)→(∀Z)¬M(S↔Z)∧¬M(Z↔S))

This should cover propositional logic. It is left to the reader can invent the relevant principles for modal logics and predicate logic.

Notes

By sentence theory I just mean a theory of truth carriers that implies that some sentences are true or some are false. Not necessarily a monist sentence theory (=theory that implies that sentences are the only kind of truth carriers) or a theory of sentences as primary truth carriers (=theory that implies that sentences are the primary truth carriers). For more about these terms, see my earlier writings on the subject.

Anyway, I read the newest post on my favorite logic blog (Blog&~Blog). It dealt with the sentences which I have given incredibly clever names (in footnotes):

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is true.

NMNT.¹ (∀S)(¬M(S)→T(S))

For all sentences, if it is not the case that it is meaningful, then it is not the case that it is false.

NMNF.² (∀S)(¬M(S)→F(S))

With the obvious interpretation keys.

This seems like plausible sentences to many when faced with sentences such as the Chomsky:

C. Colorless green ideas sleep furiously.

Which Ben, btw, got wrong as he forgot the first word.

Let’s also agree that:

1. It is not the case that C is meaningful.

¬M(C)

However, this along with some other sentences is inconsistent (=implies a contradiction). First sentence bivalence:

SB.³ For all sentences, it is either true or it is false.

(∀S)(T(S)∨F(S))

The contradiction is easy to derive here:

2. ¬T(C) [from 1, NMNT, MP]

3. ¬F(C) [from 1, NMNF, MP]

4. T(C) [from 3, SB, DS]

5. T(C) ∧¬T(C) [from 2, 4, conj.]

Contradiction! So this doesn’t work. Here I told Ben (author of the blog) that I would drop SB.⁴ However that apparently doesn’t work either.

Say hi to the T-schema, or the semantic theory of truth:

TS1. For all sentences, iff it is true, then it is the case.

(∀S)(T(S)↔S)

TS2. For all sentences, iff it is false, then it is not the case.

(∀S)(F(S)↔¬S)

Now these are obvious to most people. Not something is that plausible to deny unless the alternatives are really bad. However from these one can get their contra-positional versions:

TS1-CP. For all sentences, iff it is not the case, then it is not the case that it is true.

(∀S)(¬S↔¬T(S))

TS2-CP. For all sentences, iff it is not the case that it is not the case, then it is not the case that it is false.

(∀S)(¬¬S↔¬F(S))

And from these, we can derive their converses (and we can do that because these are bi-conditionals that can be conversed without problems). Do the same for TS1 and TS2:

TS1-CP-C. For all sentences, iff it is not the case that it is true, then it is not the case.

(∀S)(¬T(S)↔¬S)

TS2-CP-C. For all sentences, iff it is not the case that it is false, then it is not the case that it is not the case

(∀S)(¬F(S)↔¬¬S)

TS1-C. For all sentences, iff it is the case, then it is true.

(∀S)(S↔T(S))

TS2-C. For all sentences, iff it is not the case, then it is false.

(∀S)(¬S↔F(S))

And these actually need to be simplified too before I can use them, but I’m too lazy to do that, so I’ll just add a simp. step. No big deal.

Now:

6. ¬C [from 2, TS1-CP-C, simp., MP]

7. F(C) [from 6, TS2-C, simp., MP]

8. F(C)∧¬F(C) [from 3, 7, conj.]

Contradiction. And I didn’t need to use double negation to get it though one could do that too with TS2-CP-C, and of course I didn’t use SB either. It seems to me that this is terrible and the best way out of the contradiction is to deny NMNT and NMNF, and believe instead that sentences like C cannot even meaningfully be said to be true or false, nor can they meaningfully be said to be not true or not false. Any complex sentence with a meaningless part is itself meaningless.⁵

There is a tendency for people to conflate denial of properties with the denial of the meaningful application of these properties to things. This seems to be the case here too. So instead of saying things like:

Meaningless sentences are not true.

Cars are not true.

We should say things like:

Meaningless sentences cannot meaningfully be said to be true.

Cars cannot meaningfully be said to be not true.

Maybe some people sometimes, confusingly, use the first versions as a shorthand for the second. If they do and really mean what the second ones mean, then they should use them.

In a web of beliefs approach one could set up an inconsistent set of sentences and see which one is the least plausible. I figure that my readers can do that in their heads without I needing to write it out in this case. Maybe the readers will agree with me that NMNT and NMNF are the least plausible ones in the set.

Notes

I noticed a small dissimilarity between the two words. As I have pointed out numerous times in the past, the phrase “I don’t believe that p” is ambiguous between belief in not-p and lack of belief in p. However the similar phrase for knowledge, “I don’t know that p” is not similarly ambiguous. It is however ambiguous in another way; between lack of belief in p and in not-p, and lack of knowledge that p.

This is a common yet relatively unknown fallacy. The typical situation is this: Someone is defending some view or theory. That someone acknowledges the existence of a number of objections to the view/theory that he is defending. He then defeats these objections to his own satisfaction and concludes that there are no good objections. Presuming that the person is rational, this is where he ought to conclude that there are no good objections known to him. He should not conclude that there are none.

Interestingly, I found logician, Graham Priest, that commits this fallacy (oh well, even logicians commit fallacies but hopefully less or less frequently than other people). Graham Priest defends his dialetheism theory in his book In Contradiction. On pages 238-240 he defends a view about the transmission of obligations. He defends that view against some objections and then concludes:

“[...attempting to refute objections...] The principle of the transmission of obligation is, therefore, perfectly acceptable.” (p. 240)

Such a thing does not follow. It is possible and even probable that there are other good objections which render the view not perfectly acceptable.

“Web(s) of belief” ≡ “web”

“Object(s) of belief” ≡ “oob”

The justification of the web of belief

A web is more or less justified. The justification of a web is a function of its members in many ways. Here are some ways that I speculate may increase the justification of a web. I do not pretend to offer much argumentation for my thoughts or much certainty in the conclusions. It seems to me that it is extremely hard to have any strong evidence the beliefs about these matters. That shall not keep me from examining the matter and giving my intuitions.

The number of beliefs in a web

Imagine a web with only two beliefs whose oob logically implied each other. Think of any two logically equivalent propositions. The interconnectedness of that web is extremely high since logical implication is one of the strongest relations two oob can stand in (see below) and all the members are connected to each other by logical implication. But still it seems to me that such a web is not very justified. I suggest that we explain that by the number of beliefs in the web. If a person with the aforementioned web gave an argument to another person, the other person would (and should) respond that it is circular. It seems to me that we cannot avoid circularity in our justification (because of the infinite regress argument and that epistemic foundationalism and epistemic infinitism is false). However circularity is not much of a problem when the web contains many thousand belief as it does of any grown-up human.

The number of relations of certain kinds between the oob

The oob are truth carriers. (Just substitute your favorite truth carrier be it propositions, sentences, beliefs etc.)

We may distinguish between three kinds of relations between the oob: (1) positive relations, these are the relations that increase the justification of a web as a function of their number, and the justification of a web is partial function of the positive relations between oob, (2) negative relations, which is the opposite of positive relations; they decrease the justification of a web, (3) neutral relations, relations that have no effect on the justification of a web. We may note that this distinction is true regardless of the distribution of relations in the three categories.

Then we ask ourselves: Which relations are positive relations? Deductive relations such as (for all x, and for all y) “x logically implies y”, “x materially implies y” come to mind. Inductive relations such as “x is explained by y”, and “x gives good reason to believe y”, “x is best explained by y” seem to me to increase the justification of a web.

Similarly, which are negative relations? Basically the same of the above just with the added change that it is the negation of y. If you believe two things, and the one logically implies the negation of the other, you have an inconsistent web. It is impossible for all the oob to be true at the same time in a such web.

That a web has at least two beliefs whose oob are inconsistent does not imply that the justification of the web is zero. To see this we should simply recall that all grown-ups have inconsistent oob and that not all web of grown-ups have an equal level of justification. Hence, it is not the case that if a web contains beliefs whose oob are inconsistent, then the justification of that web is zero. Since if it was the case, then web of all grown-ups would be equally justified, all having zero justification. However, it is still the case that such inconsistent oob reduce the justification of a web, which I why we ought to change our mind when we discover that we hold beliefs whose oob are inconsistent.

I can’t think of any neutral relation, but they are not very relevant anyway, so lets disregard an example of a such. There may be no such relation for all I know.

Interconnectedness

I mentioned this in passing above but it deserves elaboration. The justification of a web is also a partial function of the interconnectedness of a web. If a web consisted of a thousand beliefs but that these were divided into 10 groups of beliefs each of whose oob did not have any positive relations with the oob of the other groups of belief, then it seems to me that the justification of that web would be very low. This seems best explainable by justification being a partial function of interconnectedness too.