“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.


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.

1. For all things, that it is a truth carrier logically implies that it is a sentence.

2. There exists a thing such that it is a truth carrier and that it is logically necessarily the case.

Thus, 3. There exists a thing such that it is a sentence and that it is logically necessarily the case. [from 1, 2]

4. For all things, that it is a sentence logically implies that (that it is logically necessarily the case logically implies for all possible worlds, that sentence is the case in that possible world).

Thus, 5. For all possible worlds, there exists a sentence such that it is the case in that possible world. [from 3, 4]

6. For all possible worlds and for all things, that a thing is a sentence logically implies (that that a thing is the case in that possible world logically implies that that thing exists in that possible world).
Thus, 7. For all possible worlds, there exists a thing in that possible world such that it is a sentence. [from 5, 6]

8. There exists a possible world, such that it is not the case that there exists a thing such that that thing is a sentence.

Proof of inconsistency

Readers who do not doubt that the above set is inconsistent may skip this section, as it is a technical proof of the inconsistent of the above.

The numbered formulas here are formalization of the above sentences.

Interpretation keys

Domain x ≡ things

Domain w ≡ possible worlds

Tx ≡ is a truth carrier

Sx ≡ is a sentence


1. (∀x)(Tx⇒Sx)

2. (∃x)(Tx∧□x)

⊢ 3. (∃x)(Sx∧□x) [from 1, 2, Simp., MP, Conj.]

4. (∀x)(Sx⇒(□x⇒(∀w)(xw)))

⊢ 5. (∀w)(∃x)(xw) [from 3, 4, Simp., Simp., MP,)

6. (∀w)(∀x)(Sx⇒(xw⇒(∃xw)))

⊢ 7. (∀w)(∃xw)(Sx) [from 5, 6, MP]

8. (∃w)¬(∃xw)(Sx)

(7) and (8) are inconsistent. I don’t know if I got the names of the inferences right, I need to read up on that at some point. It should be intuitively clear to anyone that studied predicate logic that the set is inconsistent.

The formalization could have been simplified if I had introduced more domains that were connected to a predicate, such as a domain of sentences. Then I could have avoided the implications inside another implication and could simply have written “for all sentences”.


I also think that the above set is minimally inconsistent, by which I mean that if one removed a single sentence, it would no longer be inconsistent. The interesting thing about such minimal inconsistent sets is that the set of all except truth carrier logically implies the negation of the last truth carrier. From such a set the last truth carrier can be constructed a valid argument. Thus, a good deal of arguments can be constructed from the above list.

Suppose a person finds himself believing all the above truth carriers. Which should he stop believing? One might take it as an argument against monistic sentence theory (1), or an argument against a fundamental part of possible worlds semantics, (4), or the additional premise about existence of sentences in the relevant possible world, (6), or as evidence that there are no possible worlds where there isn’t a sentence, negation of (8), or that there are no necessarily the case truth carriers (2). It is very hard to make the decision.

Generally, a rational agent ought to reject the truth carrier that is the least plausible to him. But even that is a tough job. Which one is the least plausible? I think it is (1) given other arguments against monist sentence theory given by Swartz and Bradley. I am not very sure about this and it may be (6) instead which I find the second least plausible. On the other hand, I find (2) the most plausible and (8) the second most plausible. (4) is somewhat plausible I think, even though I have doubts about possible world semantics.

One may construct an ordered set after which truth carrier one has the most reason to reject. To me that would be {1, 6, 4, 8, 2}.1 Though one should bear in mind that these may not be independent. For instance, a web of belief with a belief in (1) would probably result in a more justified web of belief if one also rejected (2), (4) and (6).

1If two truth carriers are tried for plausibility, one may instead have them in an unordered set together inside the other. {1, 2, {3, 4}, 5, 6}

Link to article on SEP.

Consider the following quote:

“The term “pornography” is used in all of these different ways in everyday discourse and debate, as well as in philosophical discussions: sometimes it is used to mean merely material which is sexually explicit; sometimes it is used to mean material which is sexually explicit and objectionable in some particular way; and so on. It seems to me that we do not need to choose between these different definitions, for all of them capture something of the term’s everyday use. What matters crucially is that we know which definition is being used in a particular case. For the fact that “pornography” has different senses can have two very unfortunate consequences if these differences are not clearly noted and kept in mind: it can make it seem that there is disagreement when there is not; and it can obscure the real nature of the disagreement when there is.

Here is one topical example of how this might happen. Some feminists object to pornography on the grounds that it harms women. Other feminists claim that pornography may not always be harmful to women, and may even sometimes be beneficial. It seems that there is genuine disagreement here. But is there? Not necessarily. For the two sides might mean different things by “pornography”. Suppose that feminists who object to pornography are defining “pornography” as sexually explicit material that subordinates women. So pornography, for them, is that subset of sexually explicit material that in fact harms women. This definition makes it an analytic truth that pornography, wherever it exists, is bad from a feminist point of view. Feminists who defend pornography, however, may be using “pornography” to mean simply sexually explicit material (regardless of whether it is harmful to women). There may thus be no genuine disagreement here. For both sides might agree that sexually explicit material that harms women is objectionable. They might also agree that there is nothing objectionable about sexually explicit material that does not harm women (or anyone else). If protagonists in the debate are using “pornography” in different senses in this way, they may simply be talking past each other.”

It seems to me that it is important to keep this to mind when using a word that has different meanings in a debate. It is entirely gereralizeable to other issues that are not pornographic.

pdf version


On the prohibition of animated child pornography

Emil Kirkegaard, member of Piratpartiet and essayist, emilkirkegaard.dk

Translated by Jens Arhøj, translator and proofreader of Mr. Kirkegaard

I will, in this essay, discuss the prohibition of animated child pornography and address a number of points. My sources are all the web sources I could find. All of these, are mentioned under “References”. Since the quotes are taken from newspapers, unlucky- and misquotes may be found, and the relevant policitians and their respective parties will have the benefit of the doubt.

Animated child pornography is not child pornography

Some may believe the following to be true: “All F G’s are G’s”, but this is incorrect. Certain designations exist, which will make this one false. For instance, think of “All imaginary cats are cats”, which is wrong. Imaginary cats do not at all exist, and are, therefore, not cats. It is the same with “All fictional persons are persons”, which is also wrong. It is an unlucky quality about the language, that it is possible to create misleading sentences like these.

When one reads the following in Information: “A completely legal form of child pornography” which continues “Denmark is the only country in Scandinavia, where some child pornography is legal”, one will find it grossly misleading, since animated child pornography is not child pornography. Child pornography is:

”The question of what constitutes child pornography is extraordinarily complex. Standards

that are applied in each society or country are highly subjective and are contingent upon

differing moral, cultural, sexual, social, and religious beliefs that do not readily translate into

law. Even if we confine ourselves to a legal definition of child pornography, the concept is

elusive. Legal definitions of both “child” and “child pornography” differ globally and may

differ even among legal jurisdictions within the same country.

The legal definition of a “child” varies among nations. The UNCRC defines a child as a

person under 18 years of age. This definition, however, is far from being universally

adopted. For example, in all Australian States and Territories, child pornography legislation

defines “child” as a person under 16 years of age. In Canada (Penal Code Sec. 163), a minor,

for purposes of child pornography, is a person under 18 years of age. In various jurisdictions

of the United States (U.S.), minors as young as 15 may legally consent to sexual activity

with an adult. However, that same adult could not create, distribute, or possess a visual

record of that activity because federal child pornography statutes (18 U.S.C. 2252, 2256)

define a minor as any person under that age of 18 years. Despite national differences, some international bodies have been able to arrive at common definitions of child pornography, most of which focus on visual, rather than written material. The Council of Europe defines child pornography as “any audiovisual materials which uses children in a sexual context.” Council of Europe, Recommendation R(91)11 and Report of the European Committee on Crime Problems(1993). International Criminal Police Organisation (“INTERPOL”) delegates define child

pornography as “the visual depiction of the sexual exploitation of a child, focussing on the

child’s sexual behaviour or genitals.” Interpol Recommendations on Offences Against

Minors, INTERPOL 61st General Assembly (1995).” [8]

In these definitions, there is meant (real) children, not animated children. Animated characters have no legal age, as they, funnily enough, don’t exist, and has not been born at any point. Given the above definition, animated child pornography is not child pornography, since there are no children in animated child pornography.

One would almost think that the politicians were trying to blur the clear difference between child pornography and animated ditto, when they make statements such as this from Karen Haekkerup:

»I am completely resistant towards that. I have heard freedom of speech being used for many strange things, but to legalise child pornography through freedom of speech is just grotesque.«

The statements bears a different sound when adding the necessary distinction:

»I am completely resistant towards that. I have heard freedom of speech being used for many strange things, but to legalise animated child pornography through freedom of speech is just grotesque.«

Denmark is the only country in Scandinavia that…

It is mentioned several times that Denmark is the only country in Scandinavia that does not have a law against animated child pornography. Let us look at a couple of examples:

“Denmark is the only country in Scandinavia, where some child pornography is legal.


In some countries, they have witnessed the consequence of this, and among other, both Norway and Sweden have chosen to make animated child pornography illegal.


In Sweden, where animated child pornography is illegal, websites are a well known phenomenon.


He is worried that animations will be part of the law, as has been done in Norway and Sweden.


»It inspires people to abuse children sexually. I certainly think that we should look at how it has been done in those countries, that we usually compare ourselves with,« says Peter Skaarup.”


“The ‘fictional’ kind of child pornography is – as opposed to the other Scandinavian countries – allowed in Denmark, but this is completely unreasonable, thinks Socialdemokratiet, who have absolute support from SF and Dansk Folkeparti.”[3]

“Yes, we know that Denmark is the only country in Scandinavia that does not prohibit this. Of course, that is not an argument for Denmark to get it per se, but my immediate thought is, that it is absurd that we don’t..”[6]

Etc.. Apparently, a great deal of importance surrounds the notion of what has been done in other Scandinavian countries. But why this great emphasis? Why would the following, which Karina Lorentzen Denhardt believes, “»it seems absurd, if Denmark should be the only country to allow animated child pornography«.” be absurd if Denmark was the only country(in Scandinavia? The world?) without a law against animated child pornography?

Could it not be possible that these other countries having such a law, is a mistake? I see no reason to believe that it is a good idea to introduce a law like that, just because Norway and Sweden has introduced a similar law.

If the politicians do not think, that the other Scandinavian countries having a law against this, is a good idea, how come they keep mentioning it(according to the last quote)? On the other hand, Peter Skaarup was close to something better, when he stated “I certainly think that we should take a look at how it has been done in those other countries, that we usually compare ourselves with”. It could be the case, that these laws do not help at all in the other countries, and therefore, in the best case scenario, is a waste of time and money to introduce.

Reasoning for introduction – Puritanism or rational politics?

What is the real reasoning or motivation for imposing this law, and similar laws? Is it enough that the majority of the population finds something to be in bad taste? If that is the case, then we should start by banning a number of other kinds of pornography which the majority finds unsavoury, and possibly several books, films and the likes, too. I see no reason to believe, that just because the majority finds something to be in bad taste, this is a requirement to ban it. But it could look like certain politicians are trying to use a “bad taste”-argument to get the law through the system.


»Then, my personal opinion is that child pornography is a phenomenon so atrocious, that we absolutely have to intervene further,« says Lars Hedegaard of Trykkefrihedsselskabet(Company of Freedom of Press).[5]

If one reads closer in the articles I have been able to find, one will not find a single definite inquiry, but, at the most, a few vague or blurred expressions regarding unnamed “scientists” or unidentified “research”. However, one expert in the field is mentioned. Let us begin with a few examples of the former:

“Scientists indicate that animated child pornography can the exact same effect on potential violators, as real child pornography. Research in violation behaviour shows, that the use of child pornography can be used as a slippery slope towards paedophiles committing real assaults.”[1]

Which scientists? What research? This is like giving the reason “the wise people say…” for one’s beliefs, but a reason such as this one is useless. Which wise people say what?

“Practitioners indicate that the animations can lead to use of real photos, and, at some point, abuse of children.”[2]

Which practitioners? Notice the plural form. Only one practitioner is even mentioned in the article. To use appeal of authority, one should establish the consensus among relevant experts, but this seems not to have been done. Just one or more experts have been found who agreed with the opposing side, and these have then been interviewed. This will not work as reasoning for introducing laws of any kind. I am not familiar with the consensus, if there even is one regarding whether child pornography is harmful i.e. causes people to violate children (and to which degree?). One should, at least, have a few scientific inquiries which strongly indicate this, before removing peoples’ freedom. I do not know of any such inquiries, and no concrete tests are mentioned in all articles I could find about the subject. Not even in what one would expect to be a valid text, which is the proposal to the government. [1]

All you find is, more or less, speculative theories about what animated child pornography can cause. Consider:

“Scientists do point towards that animated child pornography can have the exact same effect on potential violators, as the ‘real’ child pornography can.

When the paedophiles discover that others have the same fantasies about children, then it is especially that solidarity, that can push possible violators toward real assaults.”[2]

“»People who watch animated child pornography, stay in a violation behaviour, and are not confronted with, that it is illegal to do those things in the real world. That is why it can lead these people towards regular child pornography and real violations«, says Karen Haekkerup, spokeswoman of Socialdemokratiet.” [3]

“»They will not be able to separate fantasy from reality, and will, like that, be sucked into the universe in question, and become so occupied with it, that they will want to try it for real«.” [4]

“»It will not just stay in their imagination, and that is why we need to close that hole in the legislation.«” [5]

“Research into violation behaviour indicated that the use of child pornography can work as a slippery slope towards the paedophiles committing serious assaults. Psychologist and scientist at the Sexological clinic of Rigshospitalet, Thomas Hammerbrink, believes that the animations can be a chain in that process. He is quoted for saying: “The paedophile will reach a point, where it will not just be enough in itself to watch child pornography. It will accelerate, and some buckle, and end up violating children. I can not see why the animations should not have precisely the same effect on potential violators.”” [6]

Consistent with all of the above quotes, there is a theory that scientific evidence is not at all the motivational factor for the politicians to introduce/support such laws, but more their own puritanism, their resistance against what they think to be disgusting or distasteful.

According to the theory, these unnamed scientists(unless they all refer to Thomas Hammerbrink) are all post rationalisations, something which people are good at creating.

From my point of view, there is not enough evidence, neither for believing that there is a connection between animated child pornography and actual abuse of children, nor for believing such a post rationalisation theory. Time will tell.

Slippery slope arguments(SSA)

Many adversaries of the proposal express slippery slope arguments. SSA’s work by pointing out, that if one does x, then that choice opens up for y, z, t, s etc. and that y, z, t and s are bad. Consider these examples:

“»If we want to ban animations of this type, then we are creeping closer to what could look like official censorship,« says substituting political spokeswoman, Tina Nedergaard.” [5]

“Lawyer Bjoern Elmquist does not believe that a tightening of the law is the way to go. He is lawyer and chairman of Retspolitisk Forening(Political Law Society), which is an organisation of lawyers who fight for maintaining the citizens’ rights security. He is worried about including animations in the law, like it has been done in Norway and Sweden, because he believes that it will have consequences for freedom of speech and the security of rights.

»What about violent films? Or video games? Would it be fair, that in one scenario, it is completely without punishment to shoot 30 people in a videogame, but seeing someone take the pants of a drawn child, is to be punished?« says Bjoern Elmquist.

»It is invalid that such a difference in the law is to exist. That would mean having to makes laws for everything.«

Same concern can be found with Thomas Thorhauge, chairman of Danish Cartoon Counsel, who is a newspaper illustrator and cartoonist himself.

»I am a father myself, and can fully appreciate that some people feel offended from animations like these. But then, where will the line go of what one can draw, and what one cannot?« he asks. Thomas Thorhauge is troubled by the thought of intensifying the law. He is especially worried about the art being caught in between, if the law is tightened.” [2]

The underlying point is, that if you prohibit animated child pornography just because it can(in some undefined sense) ‘inspire’ paedophiles to abuse children, the you should also, per analogical reasoning, prohibit violent games, books and in a wider sense, fiction where a person you can identify yourself with, commits illegalities, because it can inspire people to commit illegalities.

There does not seem to be any boundary for what can eventually be prohibited, if arguments like those above are good enough for banning something. It seems that this is the first step towards total governmental control of culture, depending on what can be said to ‘inspire’ illegalities.


“Justice spokesman Tom Behnke is hesitant to support the prohibition.

»When we are talking child pornography, it is something that we take very seriously. The sins must be punished hard and consistently. Men when we are talking animated child pornography, it is a different situation. After all, it is fictional, and no children have suffered or been hurt in the creation of the material – unlike real child pornography«, he says.


Tom Behnke, in the meantime, asks for composure, and notes that this is about the children – not the thoughts.

»It is a victimless situation, and that is why I am somewhat skeptical towards this proposal. Because what is it, exactly, that you punish for? The next thing will be looking into peoples’ heads and punishing them for their thoughts«, says the conservative spokesman.


But the scientific proof already exists, says psychologist with Red Barnet(Save the Children Denmark), Kuno Soerensen. There is, in fact, a risk that the sexual actions that the children are exposed to on sketches and in films, can inspire some to try it in reality.

»Research shows that a vulnerable group can be affected by this«, he states.


Similar mechanisms are seen with people who play violent games, read anorexia manuals or deepen themselves in racist and nazi texts on the internet, tells Kuno Soerensen.

»They will not be able to separate fantasy and reality, and will, because of that, be sucked into the universe in question, and become so obsessed with it, that they will want to try it for real«.” [4]

One would almost think that Kuno Soerensen was trying to make my point about the slippery slope. He, himself, mentions the very things that could be banned as well, with similar reasoning.

Let us say, hypothetically, that animated child pornography causes assaults

Does it then follow that we should prohibit it? No. It would still be a question of weighing the consequences.

First of all, would such a law help? It has been mentioned that one could shut down or block such websites, men such blocks are incredibly easy to pass, and if a person wanted to pass them, he would easily be able to. It is not possible to block content on the internet without a considerable amount of surveillance (e.g. in China), or a total restructuring of the entire internet. This becomes even clearer when considering that people can do things to pass this surveillance and control. Alternative DNS servers, proxy servers and VPN connections make it impossible to monitor and control people on the internet, with the internet as it is at the moment.

People with more knowledge than me, can, without a doubt, mention more small ways to pass most blocking systems.

Has it been researched whether the animated child pornography has been harder to access in Norway and Sweden? This seems highly relevant, and the answer is quite possibly “no” because of the things I mentioned above.

Second of all, regardless of whether the law will work(i.e. reduce assaults on children), it must be considered if it is reasonable to introduce it compared to the things that will accompany it. If the law only works to a lesser degree, but entails great costs because of the increased monitoring and control, then it should be considered if there is a more effective way to spend the money, such as improving the treatment of paedophiles, who rarely only molest children once, but instead, a number of times. This is a question of price/effect in a metaphorical sense.

Consider the following quote from the American Supreme Court:

“The Government submits further that virtual child pornography whets the appetites of

paedophiles and encourages them to engage in illegal conduct. This rationale cannot sustain

the provision in question. The mere tendency of speech to encourage unlawful acts is not a

sufficient reason for banning it. The government cannot constitutionally premise legislation

on the desirability of controlling a person’s private thoughts. First Amendment freedoms are

most in danger when the government seeks to control thought or to justify its laws for that

impermissible end. The right to think is the beginning of freedom, and speech must be

protected from the government because speech is the beginning of thought.

To preserve these freedoms, and to protect speech for its own sake, the Court’s First

Amendment cases draw vital distinctions between words and deeds, between ideas and


The normal method of deterring unlawful conduct is to impose an appropriate punishment

on the person who engages in it. The government may not prohibit speech because it

increases the chance an unlawful act will be committed at some indefinite future time.

The government may suppress speech for advocating the use of force or a violation of law

only if such advocacy is directed to inciting or producing imminent lawless action and is

likely to incite or produce such action.

There is here no attempt, incitement, solicitation, or conspiracy. The Government has shown

no more than a remote connection between speech that might encourage thoughts or

impulses and any resulting child abuse. Without a significantly stronger, more direct

connection, the Government may not prohibit speech on the ground that it may encourage

paedophiles to engage in illegal conduct.”(some parts omitted)[7]

There are wise words among the above, even if some parts are irrelevant to Danish politics, since our constitutions are dissimilar.

Symbolic politics

Lastly, one should consider if a reason for some politicians to be after the animated child pornography, is to send a message to the population that these politicians are not bread-and-butter politicians who do not do anything, but who are actually trying to make a difference. Such symbolic political actions are, in some cases, directly harmful to society. I will not further this point, but take a look at this essay. [9]


1. B 133 Forslag til folketingsbeslutning om forbud mod animeret børneporno. –

www.ft.dk/dokumenter/tingdok.aspx?/samling/20091/beslutningsforslag/B133/som_fremsat.htm (In Danish)

2. En helt legal form for børneporno – www.information.dk/221349 (In Danish)

3. S vil forbyde lovlig børneporno – politiken.dk/politik/article902997.ece (In Danish)

4. Konservative forsvarer animeret børneporno – politiken.dk/politik/article903633.ece (In Danish)

5. Ytringsfrihedsforkæmpere i strid om børneporno – www.information.dk/224815 (In Danish)

6. Skal animeret børneporno forbydes? – www.sf.dk/default.aspx?site=karinalorentzens&func=weblog.entryview&eid=88406 (In Danish)

7. ASHCROFT V. FREE SPEECH COALITION (00-795) 535 U.S. 234 (2002) –


8. Child porn – www.crime-research.org/news/03.08.2004/537/

9. Tragisk symbolpolitik og den heroiske politiker –

blog.politiken.dk/kappel/2009/11/04/tragisk-symbolpolitik-og-den-heroiske-politiker/ (In Danish)