Monday, January 14, 2013

Anti-introductionism. Treatise No 8.

Summary.

The subject of this treatise is to discuss Zeno’s paradoxes with runners on the basis of immediate considerations.

Some philosophers understand the concept of limit of a sum-function as being identical with the concept of a sum of infinitely many numbers, as far as such a sum exists. It proves, however, that the solution of these paradoxes is found in (1) the way the story of the race between Achilles and the tortoise is told, which can be rendered recursively without a stop. Moreover, the right understanding of the concept of infinity proves to dissolve an alleged paradox concerning (2) how it is possible to have passed infinitely many points (in a finite time). This corresponds to the difference between respectively 1) being in the present and 2) considering a past-construction.

A later treatise deals with the discussion in Wesley C. Salmon’s anthology Zeno’s Paradoxes ([Salmon 70]).

1. Achilles and the tortoise.

The paradoxes with runners of Zeno of Elea can obviously be solved by mathematical formalism, e.g. that of the race between Achilles and the tortoise. However, the question is whether they deal with the mathematical world or with the physical world, i.e. the phenomenal, in which not all theoretical concepts have a counterpart. The fact that the theories of natural science can be used to predict the phenomena is a different matter, as this does not demand an analogy between the mathematical and the physical world, but just their usability or being empirically adequate, such as Bas van Fraassen argues in The Scientific Image ([Fraassen 80], p. 12, 18).

1.1 A description of the paradox.

In the popularized version of one of Zeno’s paradoxes, Achilles and the tortoise, Achilles has to catch up with a tortoise that has a lead. It must be observed that the paradox consists of two parts: 1) our common sense view of the race, which is based on memory impressions of finished processes, and 2) Zeno’s account of it.

According to the implicit reasoning in (2) Zeno’s account of the run, Achilles will never catch up the tortoise. Nevertheless, we will assert (1) that we know that Achilles will catch up with the tortoise. This is a paradox concerning our conception of time. Of course, Zeno has a point here.

Re 1: Zeno’s reasoning can be recounted in this way: Let us assume that Achilles runs G times as fast as the tortoise, and that the leap is F units of length. According to principles that are in accordance to our experience, it can be figured out that that Achilles has cached up with the tortoise when he has run the distance F G/(G - 1).

Re 2: When Achilles has run F units of length, the tortoise has run F/G. When Achilles has cached up with this lead, the tortoise has run F/G². When Achilles has run F/G², the tortoise has run F/G³. Etc. After each of these parts of the run, the tortoise still has a lead (that certainly gets smaller and smaller, but never zero).

This means two things: 1) Each time one of these stages has been finished, Achilles has yet to traverse a stage. I.e. that Achilles is always in the same situation. 2) In a situation where Achilles has caught up with the tortoise, he must have run through infinitely many stages. This is another aspect of the paradox above. The first one can be comprised in:

1.1.1 A recursive description of the race.

After each of the described parts of the race, the same situation is present, except that the tortoise has a lead that is 1/G times what it was at the start of the run.

We can call the length of the stretch to the starting point of the tortoise d, and relation between Achilles’ velocity and that of the tortoise g. Then, the race between Achilles and the tortoise can be described by an account, B(d).

B(d): “Achilles catches up with the tortoise that has a leap d”.

This account has the following recursive form where the expression R(s) means, “Achilles runs the distance d”:

B(d) -> R(d) + B(d/g).

If the initial leap was F and the relation between the velocities g = G, the whole account can be expressed as

B(F).

If this account is regarded as a pure mathematical description, the situation after each step is quite the same as at the start of the race, for there are no absolute lengths on the line in geometry. Thus, according to this mathematic description, no changes are present that imply that the race will stop.

Thus, from the description above we get:

B(F) -> R(F) + B(F/G).

B(F/G) -> R(F) + R(F/G) + B(F/G²).

B(F/G²) -> R(F) + R(F/G) + R(F/G²) + B(F/G³).

B(F/G³) -> R(F) + R(F/G) + R(F/G²) + R(F/G³) + B(F/G⁴).

This recursive description can be compared to a recursive description that contains a not-recursive case that will even be satisfied and thus finishes the description.

Let “Run(N)” mean: The runner runs the remaining N/M parts of the stretch, and let R(M) mean: ”The runner runs 1/M of the whole track”. Then, the run can then be described by these recursive definitions:

Run(0).

Run(N) -> R(M) + Run(N-1).

Then the run can be described in this way:

Run(M).

Example. M=3:

Run(3) -> R(M) + Run(3-1).

Run(2) -> R(M) + Run(2-1).

Run(1) -> R(M) + Run(1-1).

Run(0).

1.2 Mathematical proposals for solution.

This subsection looks at two mathematical proposals for solution based on mathematical formalism for so-called summation of infinite many values. It proves that none of these attempts at solving the paradox succeeds. The first attempt, which consists in a simple computation, is circular, while the other cannot make good that which takes place in the description of the race between Achilles and the tortoise will lead to a termination.

1.2.1 Summation of infinite many values.

We can attempt to let the paradox deal with a summation S_∞ of all the steps until Achilles has caught up with the tortoise according to the common sense view[1]:

S_∞ = F ∑^∞_i=1 G^-i+1

From this, we get:

S_∞ = F +F ∑^∞_i=2 G^-i+1

S_∞ G = F G + F ∑^∞_i=2 G^-i+2

S_∞ G = F G + F ∑^∞_i=1 G^-i+1

By this, we get the following computation of the summation:

S_∞ G = F G + S_∞

S_∞ = F G/(G – 1)

However, this calculus with a thought summation of infinitely many numbers presupposes that the summation can be carried out, i.e. that the paradox is solved. Thus, understood as a solution of the paradox, this attempt is circular. The circularity is committed in the line in which the summation is substituted by S_∞, as this substitution presupposes that the summations understood as a summation of infinitely many numbers can be carried out, and that it has semantic meaning.

1.2.2 Mathematical limit.

In mathematics, the summation symbol including its parameters denotes the limit of S_nfor n going towards ∞, i.e. for n increasing without limit. Thus, it does not denote a summation of infinitely many numbers in any literal way.

More specifically, a function f(x) is said to go towards the limit b for x going towards ∞, if

"εÎR+: $hÎN: "x: x > h => 0 < |f(x) - b| ≤ ε.

This definition can be applied to

S_n = F ∑ⁿ_i=0 G^-i.

This means that the following must be proved:

"εÎR+: $hÎN: "n: n > h => 0 < |S_n - S_∞| ≤ ε, where S_n and S_∞ can be substituted by the expressions in the above subsection, after which the correctness can be confirmed.

However, this mathematical formalism does not solve the problem, since as just mentioned it does not deal with any sum, but with something else, for the definition above just means this:

A limit of a sum of n numbers for n going towards infinity is not a sum of infinitely many numbers in some literal sense, but is a value to which this sum of n numbers can get arbitrarily close without coming farther away for any higher n.

Our talk about infinitely many elements in a certain set does not mean that the set contains a number of elements we can call “infinite” just as when we talk about there being 1017 elements in a set, but that the set of these elements has no end, i.e. that we can continue pointing out new elements in the set. Here we have an ordered set of infinitely many intervals on a piece of the line, which means that we can continue pointing out new, still smaller intervals, even succeeding ones in the ordered set. The proof above is not in contradiction to Zeno’s paradox, but rather copies it.

Finally, it must be observed that the above definition only means that S_n comes relatively close to S_∞, but not absolutely closer, as there are no absolute distances in geometry. It is even so that the division of the line from S_n+1 to S_∞ has the same shape as the division from S_n to S_∞. So much the more the runner’s situation is not changed.

1.3 An unfinished account.

The following attempt at a solution is inspired by the fact that if Achilles velocity is v, the sum of the first n intervals of time is S_n/v. Number n of these time intervals has the duration F/(G^n-1 v). This lead to that solution of the paradox about Achilles and the tortoise that after each of its steps the above account of it has only concerned a certain space of time and not the whole run.[2] Thus, it only deals with what takes place within a sum of time intervals each of which has become still smaller until some moment before and arbitrarily close to the point where we would expect that Achilles would catch up with the tortoise:

It is thus not the race that never finishes but the very account of the race that is put in such a way that it never finishes, and therefore it self-evidently does not deal with the whole fiction about the race. What is the case is therefore that Achilles does not catch up with the tortoise within the space of time that the account deal is supposed to deal with. The reason to this is that the account has the above-described recursive form.

We can imagine that that we have just attended the race between Achilles and the tortoise and seen Achilles catch up with the tortoise. Nevertheless, we can subsequently start describing the race in the following way that can never end:

The tortoise started with a lead of the length F. Achilles ran G times as fast as the tortoise. At first, Achilles reached the place from which the tortoise started. At that time, the tortoise had moved a stretch of the length F/G. Thereafter Achilles reached the place where the tortoise was after the first stage, etc.

As mentioned, this account can never end for the reason that it is told in such a way that the sum of these intervals of time at no point exceeds the duration of the race.

However, it is also told in way that makes clear that Achilles’ situation is in principle is unchanged for each stage.

Does this mean that the paradox is solved? It can be put forward that the account just points out a number of points one after one on the time axis to which this fiction about past can be attached. This takes place according to a definite algorithm defined by the account. It is not paradoxical that, just as we cannot finish many other algorithms, we cannot finish this algorithm either. In fact, we can both put forward and combine many algorithms to division of a piece of line or a track into intervals, even with more than one point of accumulation. These can of course be passed. It can also be put forward that they just make up an intellectual construction that as such has nothing with the race to do. However, this way of looking at the paradox is to ignore Zeno’s message.

1.4 Scientific limitations.

After this going through, scientific considerations concerning the paradox are strictly speaking irrelevant. However, this shall not prevent us from looking at a scientific based proposal for a solution of the problem the account obviously implies, viz. that Achilles only gets arbitrarily close to the tortoise, but never catches up with it. The proposal is based on the idea that the mathematical distances can be insignificant according to scientific theories. Thus, it could be asserted that when, for the one or the other reason, the difference in position cannot be measured, Achilles and the tortoise have reached the same position on the racing track. According to this, the race would simply be finished when the distance between the two competitors and less than a certain magnitude. On its own premises, however, this does not explain the fact that Achilles not only catches up with the tortoise, but also runs past the tortoise, i.e. also with a length of half a point.

Below it is explained that this proposal for a solution does not fall in with Zeno’s premises, but just rejects the paradox. This will also be discussed in a later treatise.

Zeno’s account cannot fully deal with the physical world, for it is a question, which two physical points on the tortoise and Achilles have to be compared during the race, especially as they are moving. If we also involve Achilles’ steps and movements, when we talk about minimal distances, the discussion becomes boundlessly complex. Thus, we must regard the race as dealing with two points A and B that are moving along a line. Mixing physical contingencies into the paradox is not to look at its fundamental character. On the other hand, the mathematical definitions have to be correctly understood and their terms not to be literally understood.

1.5. Zeno’s dichotomy paradox.

In The Presocratic Philosophers, it is advanced about “Zeno’s arguments about motion ...”:

“The first asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal…” ([Kirk 1983] p. 270)

Because of its short form, this argument it can be interpreted in two ways. (Cf. [Kirk 1983] p. 270.)

1.5.1 The right recursive dichotomy-paradox.

One of the interpretations reminds of the paradox about Achilles and the tortoise, and is right recursive like this paradox:

To reach his goal a runner must first run halfway to the goal, then the half of the rest, etc.

Let us presuppose that the goal is the point 1 on the x-axis, and define the statement R(s).

R(s): “The runner runs a distance of the length s”.

We can then define a recursive account C(d) about how the runner runs from the point d to the point 1:

C(d) -> R((1-d)/2) + C((1+d)/2).

The whole account can thus expressed by:

C(0).

The first four stages have the following form:

1: C(0) -> R(1/2) + C(1/2).

2: C(1/2) -> R(1/4) + C(3/4).

3: C(3/4) -> R(1/8) + C(7/8).

4: C(7/8) -> R(1/16) + C(15/16).

This gives the following composite result:

1-4: C(0) -> R(1/2) + R(1/4) + R(1/8) + R(1/16) + C(15/16).

The account is analogous to that about Achilles and the tortoise. Thus, after each stage, the situation in this account is the same as before the stage. For the remaining account still deals with the fact that the runner is running a stretch that can described in the same way as before the stage except that its length is here halved for each stage. Thus, we are again dealing with an account that due to its form never finishes. Moreover, it must be observed that just as it was the case with the paradox about Achilles and the tortoise, after each stage no real change has occurred, as there are no absolute distances in the mathematical universe.

We can imagine that that we have just attended the runner run a distance of 1 length unit. Nevertheless, we can start describing the run in the following retrospective way that never reaches an end:

The runner started from point 0. At first, he reached the middle of the distance. Then he reached the middle of the remaining distance, etc.

As just mentioned, this account will never end for the reason that it is told in such a way that the sum of these intervals of time at no point exceeds the duration of the run and especially that the runner’s situation remains unchanged in principle.

1.5.2 The left recursive dichotomy paradox.

The other interpretation of the paradox is left recursive and can be rendered in this way:

To reach a point P halfway before his goal, a runner must first run to a point halfway before the point P, etc.

Let us presuppose that the goal is the point 1 at the x-axis, and define the statement R(s):

R(s): “The runner runs a distance of the length s”.

We can then define a recursive account C(d) about how the runner runs from the point 0 to the point d:

D(d) -> D(d/2) + R(d/2).

By means of this, the whole account can be expressed by:

D(1).

The first four stages have the following form:

1: D(1) -> D(1/2) + R(1/2).

2: D(1/2) -> D(1/4) + R(1/4).

3: D(1/4) -> D(1/8) + R(1/8).

4: D(1/8) -> D(1/16) + R(1/16).

This gives the following composite result:

1-4: D(1) -> D(1/16) + R(1/16) + R(1/8)+ R(1/4)+ R(1/2).

By this, it has been illustrated that the account D about the whole race has to be finished before the account of runs of the single stages can begin. This has already been established by the left recursivity. Therefore, the account D will never explicitly mention or concern the start of the run in any of its stages. This version is retrospective, and regarded in this way, it is analogous to the first version.

We can again imagine that that we have just attended the runner run a distance of 1 length unit. Nevertheless, we can start describing the run in the following way that never will end:

The runner started from point 0. Before he reached the middle of the distance, he had to run half way to this point. Before he reached the latter point, he had to run half way to this point, etc.

1.7 Aristotle’s arguments.

Aristotle asserts that length and time can be called “infinite” as regards both divisibility and their extremities, and concludes from this:

“So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility: for in this sense the time itself is also infinite: and so we find that the time occupied by the passage over the infinite is not a finite but an infinite time, and the contact with the infinites is made by means of moments not finite but infinite in number. (After Gaye)” ([Kirk 70], p. 270)

Aristotle naturally has a point in saying that a piece of line can be both 1) infinitely long and 2) infinitely divisible, i.e. also if its length is finite, such as Zeno demonstrates. Moreover, it is clear that about a runner’s passage of a line piece we can say the same about the division of the time the run lasts as about the division of the line piece traversed. For the passage of the line piece and the passage of time goes together. This means, however, that with his above pointing out Aristotle does not solve the paradox, but only shows two sides of it.

Thus, we can again look at the situation in which a runner has reached his goal. This is a paradox, as it is impossible to him according to Zeno’s account. For in order to arrive at it, the runner first must run half-way, and to arrive at that point he must run half-way of this distance, etc. However, if the runner’s velocity was h, he reached the halfway after the time (1/2)/h, he reached 1/4 of the distance at the time (1/4)/h, etc.

Obviously, there is no end to the related problems we can think over in connection with the three discussed paradoxes. According to The Presocratic Philosophers, from Aristotle’s’ discussion the following left-recursive reasoning can be deduced:

“(1) To reach his goal a runner must touch infinitely many points ordered in the sequence 1/2, 1/4, 1/8, ...

(2) It is impossible to touch infinitely many points in a finite time.

(3) the runner cannot reach his goal.” ([Kirk 70], p. 270)

According to Aristotle’s argumentation above n, it is possible to pass infinitely many points in a finite time, wherefore (2) is false. As this argument, however, deals with a space of time regarded as a whole, it does not deal with the runner’s situation, which is in the now. Therefore, the demonstration that (2) s false does not solve the paradox, but only illustrates one aspect of it.

Aristotle puts forward that this argument presupposes that the single intervals only exist potentially. However, Aristotle wants to discuss this condition:

”... when someone asks the question whether it is possible to traverse infinite things - either in time or in distance - we must reply that in a way it is but in a way it is not. For if they exist actually it is not possible, but if potentially, it is; for someone in continuous movement has traversed infinite things incidentally,...” ([Kirk 70], p. 271)

It is true that this applies to e.g. the retrospective description. The question is what it would mean that the intervals should exist actually, i.e. as intervals. The answer is that this is the case for the single interval when it is pointed out, which it is in the now. It is exactly intervals pointed out we have to do with in the recursive interpretation of Zeno’s description. It is true that according to this recursive account the run has no beginning, just as it has no ending according to the right recursive account.

It must be observed, that it cannot be the case that the intervals exist all of them actually as something different from existing potentially; for we cannot point them all out at one time.

1.7 Summarizing considerations.

As it is simpler to comment on the right recursive account C above, a concluding remark shall deal with this account. We can imagine that we are in a situation in which a runner has reached the goal, and we can then ask how the runner has been able to pass infinitely many distances of the lengths (½)ⁿ. The fact that there are infinitely many distances of this kind before the point 1 just means that for each such distance we can point at, we can point at one distance more. The fact that the runner has run infinity many of this kind of distances before the point 1, therefore just means that for each distance of this kind the runner has run, we can point at yet a distance the runner has run further along the running track. To each n corresponds the interval from 1-(½)^n-1 to 1-(½)ⁿ. In this way, the runner passes infinitely many points within a finite time: there is no end of the set of points he touches in a finite time.

It can be noted that Zeno’s account of the run deal with the present time, i.e. the runner’s situation, while the retrospective explanations deal with past fictions. We cannot explain the flight of time. We can only explain how it is to be in the present time and look at a past-construction, as here, and at a future-construction.

As already touched on we can certainly imagine and that a person objects: “A little while ago you were talking to me. That was both real and present at that time. Now it is past time. This proves that time is passing.”[3] However, this only proves the fact that we have memory impressions, and that the person in question is placing them in a past-construction. Naturally, an unsolved philosophic problem cannot be solved by insufficient explanations. It must rather remain unsolved for the moment, only illuminated.

Literature.

[Fraassen 80] Bas C. van Fraassen: The Scientific Image
Oxford University Press (Oxford 1980)

[Kirk 83] G.S. Kirk, J.E. Raven), M. Schofield: The Presocratic Philosophers, 2. ed.,
(Cambridge 1983)

[Salmon 70] Wesley C. Salmon, ed.: Zeno’s Paradoxes
Bobbs-Merrill (Indianapolis & New York, 1970)

[1] I have seen this argumentation somewhere, but have not been able to find it again.

[2] Here I owe to refer to Aristotle who discusses this subject in ([Kirk 70], p. 270).The subject id treated in the subsection “Summarizing considerations”.

[3] Cf. the subsection, “The present and past time and the future of the past” in Treatise No 1.

Anti-introductionism. Treatise no 7.

Summary.

This treatise starts with reproductions of three contributions from my blog ([Arguments]). This has the following reasons:

Treatise No 6 ended with an investigation of whether there is an objective justification of ethics. This investigation appeared to be indirect, as it was based on the necessity of an interest in finding a solution, and as the interest in debating a question does not immediately seem to have anything to do with the answer to it.

It was asserted, however, that perhaps the answer was not quite far-fetched, and this can be clarified here. For in the meanwhile, the writing of a summary of this important investigation (for my blog) has uncovered a greater coherence between interest and solution. Therefore, this coherence is cleared up. This takes place in the first section, “An ethical basis”.

Treatise No 5 ended with the section “Semantic critique of religious sequences of signs”. In the meantime, I have been more explicitly acquainted with the concept of ignosticism, which may seem to comprise this criticism of religious expressions. There is a decisive difference, however. This is made clear in the section “Ignosticism and semantic meaning”.

This contribution referred to another contribution, which therefore is first reproduced. This is done in the section “Presuppositions in religion and the realism debate”, which among other things presents the two most basal presuppositions that can be thought of. These are made in all statements. They are illustrated with examples of erroneous presuppositions.

Like the first three, the fourth subject belongs to practical philosophy. The discussion of it is occasioned by some often-heard excuses of and accusations against religions in connection to persons’ religiously related objectionable behaviour: The religions are respectively called innocent or guilty. As religious texts involve the extra problem that they are semantically meaningless, it can be clarifying first to look at the isms since these have a semantic content that can be discussed. Besides being semantically meaningful, the isms can contain well-founded ideas. Contrary to this, there can be no religiously justified ideas. It is concluded that people themselves chose to act, whether this happens on the background of an ism or a religion. This subject is treated in the section “Religion, isms and responsibility”.

1. An ethical basis.

It is decisively important to find out whether there is an objective basis of ethics and politics, i.e. one or more objectively substantiated statements about how it is most right to act.

The question has already been answered in Treatise No 6, which also advances some examples of the consequences for politics of the answer. Some points are made clear in this section: It is a part of one’s ethical deliberations to clarify the very question whether these have a basis. The individual person too must clarify different circumstances in order to evaluate his acts.

The discussion referred to the point of view Alfred Ayer states in Language, Truth and Logic ([Ayer 74], pp. 136-150), that the only thing we can argue for concerning moral is the facts that sustain our moral conclusions given a particular moral attitude, whereas we cannot argue for the very moral attitude concerned. ([Ayer 74], p. 146-7) As far as I can see, Ayer does not substantiate his own view, oddly enough.

Alternatively, as the next best answer to this question, we can imagine that a basis follows from a particular assumption that it would be unreasonable not to accept. However, luckily we do not have to leave it at that.

As regards the necessary basis, we can make the following considerations.

1.1 The principle of argumentation.

With due reference to Aristotle’s principle of contradiction, we can talk of a “principle of argumentation”. The principle is rather evident and sounds:

It is necessary to be able to argue for what one asserts if it is to be a standpoint.

In other words, one cannot both assert that a statement P is true, and that P has not been justified. Of course, people can choose not to discuss their standpoints. Those who have this attitude can just insistently assert, “I chose to think whatever that suits me to think”; but in that case, we only are dealing with an arbitrary, unfounded sentence. However, it is not a philosophical problem if people are satisfied with that, but it is a serious sociological problem.

It can certainly be argued against this standpoint, as far as it can be called a standpoint at all, and not just an attitude, that it implies that any standpoint can be just as good bad as any other, and that it leads to a situation in which arbitrary standpoints are facing each other, unable to be decided by argumentation. However, it is of no use to say this to the person who advances it, as he does not accept argumentation. We can only convince the holder of this view by getting him argue for his standpoint. For then, the standpoint is not just a choice, but a standpoint the holder thinks is right, and for which he wants to argue.

This argument is an imitation of Aristotle’s argumentation for the principle of contradiction: that we cannot argue against the person who denies it, as it presupposes what is to be proved. We can only convince him by getting him follow the principle. Cf. [Aristotle 1968] 1006a.

1.2 The derivation of a basis of ethics.

Instead, if a person wants to discuss the question whether there is a basis of an ethic and politics at all, he must admit that there is such a basis, and even which basis it proves to be. I.e. not only can we conclude that the basis exists; we can also point it out. This has the following reason:

If 1) we want to discuss and search for an answer to this question whether there is a basis of an ethic and politics, then 2) we must concentrate on it and seek to clarify all the circumstances that can illuminate the matter. 3) This demands favourable life conditions for those who will endeavour to make the necessary investigations and considerations. With this, we have succeeded in finding the basis of an ethics and a politics: the consideration that everybody has good life conditions and a demand for it. This basis is objectively true, because we could allow ourselves to presuppose the condition (1). This basis has concrete implications concerning how the society ought to be in order to fulfil this demand, and concerning how we ought to act. It must be pointed out that this demand originates in (2) the necessity of clarification and knowledge.

Of course, each person’s individual situation and surroundings ought to be involved in his evaluation of his acts. Thus, the individual must concentrate on a number of different circumstances. For ethical questions must be decided on the basis of an understanding of the case itself and of what this involves. Moreover, this means that any kind of command ethics must be rejected.

As touched on, it can be objected to the above argument that it is very far-fetched to argue that there are objective arguments concerning how we ought to act and to arrange society arguments, and that these arguments are based on the conditions for the very discussion of whether there is an objective ethical basis.

To this, it can be answered that all kinds of investigations and clarifications certainly demand good conditions of life. This applies for instance to the investigation of the existential question of whether life has meaning (in the sense of purpose), and whether this concept has a semantic meaning at all. This applies to philosophy, linguistics, and all kinds of education, both to receive it and to give it. However, the question is whether this argument is sufficient to point out a basis of ethics. It would of course be fine if it were so, so it is not to belittle this argument that the following must be considered. However, we must be quite sure. For this reason, the two answers must be compared:

If we presuppose that am existential question is to be answered, this certainly involves that the question must be investigated and that this demands good life conditions. However, there exists no necessary demand for an answer of the question. Thus, the moral basis does not follow with necessity, but only as a side issue of this precondition.

However, if we presuppose that we have to answer the very question whether there is a basis of ethics, then it is self-evidently a necessary demand that the question of the basis of an ethics must be answered, just because it is put forward. Therefore, the above found moral basis follows of necessity.

This answer is neither farfetched nor technical as it is exactly a part of one’s ethical considerations to consider whether the ethic is based on a necessary basis, and thus whether one’s acts and chosen politics are based on a necessary basis.

How broad this basis is, i.e. which types of acts it has clear implications, however, is not immediately clear.

It must be observed that we cannot sell out of this basis, understood such that reducing persons’ favourable life conditions can be justified with the argument that they will benefit from this later in some future fiction. We live here and now and thus need good life conditions here and now. All what we do must always be related not only to the consideration of all persons good life conditions, but also to the reason to this consideration, which consists in each individual’s possibility for enlarging his horizon..

2. Presuppositions in religion and the realism debate.

The well-known, teasing question, “Do you still beat your wife?” presupposes the truth of at least two assumptions (i.e. implies their truth for different semantic reasons): that the respondent has a wife, and that he has beaten her. If this is not the case, the respondent can answer neither in the affirmative nor in the negative without admitting what is presupposed. Instead, he may answer e.g., “In fact, I have never beaten my wife”.

This popular example comes under H. P. Grice’s considerations about communication in the article “Logic and conversation”. Grice’s main result is that the successful communication comprises exactly what is necessary in order to communicate the message aimed at. It must be observed that yet an essential example of presupposition can be added:

1) Any statement presupposes one particular, overriding condition, viz. that the statement has semantic meaning, especially that the individual words have word meaning.

The reason is that nobody would just express the mere sounds, i.e. semantic meaningless sign sequences. This must be the most important presupposition of all kinds of presuppositions. Moreover, the following applies:

2) Any sentence presupposes that the interlocutor can accept the contained concepts.

The reason is here that this is the condition of a clear understanding of the utterance. This must be the next most important presupposition of all. Moreover, the following applies.

Any sentence presupposes that contained concepts are thought-through, and that they are not up for discussion.

However, this is just another aspect of point 2, and it can just as well be an overestimated view as a presupposition. Corresponding presuppositions of course apply to questions, mutatis mutandis.

It must also be observed that when a sentence can be declared semantically meaningless, it qualifies neither to be disproved nor proved, neither empirically nor rationally. For it has no semantic content.

Among the examples of sign sequences that may have semantic meaning but which some do not want to accept for specific reasons, can be the Danish term “starthjælp”[1] or metaphorical use of the term “arbiter of taste”. Their reason may be that the former is used as a kind of new speech about reduced social benefits and the latter about persons who have studied a field.

It must be observed that to explain what something, i.e. some X or other, is, it is insufficient just to say “X is something that has these and these qualities” or “X is that which is so and so”, unless the defining relative clause refers to the concept that should be the starting point of the definition. However, this would make the sentence unnecessarily clumsy. (It would e.g. be clumsy to say, “A table is something that is a piece of furniture that...”) Instead, we must use the schema “X is a Y that has these and these qualities”. We could e.g. say “A table is a piece of furniture that...” or “A table is a physical object that...” In other words, we can only define something by means of already clarified concepts.

2.1 Religion.

An important example of this error is the question “Do you believe in God?” which presupposes that it consists of words, especially that the sign sequences “believe” and “God” are words.[2] The section “Semantic critique of religious sequences of signs” in Treatise No 5 makes good that this is not the case at all, but that these sign sequences only borrow an appearance of semantic meaning from usages in which they in fact have semantic meaning and thus are words. This, we can answer this question neither in the affirmative nor in the negative without presupposing that the two mentioned sign sequences “believe” and “God” have semantic meaning. Likewise, the concepts theist, agnostic and atheist presuppose too much, if we for instance define a theist as a person that asserts, “I believe in God”. Thus, we cannot either answer the question “Are you an atheist?” without accepting the religious persons’ putative concepts. Instead, we can only say that those who call themselves atheists have not understood the religious persons’ error, and explain this the way it has been done in the treatise referred to above.

From the arguments above in can be concluded that when A. J. Ayer in Language, Truth and Logic advances a stringent rational proof against the existence of a putative God, this is superfluous. ([Ayer 74], pp. 151-158) For there is neither something to prove nor disprove.

Certainly, also Ayer concludes that the theists are not sufficiently critical. However, his reasons are that they accept statements such as ‘There is no transcendent god’, which are “nonsensical”, because they are metaphysical and for that reason are not propositions. ([Ayer 74], p. 153) However, it must be observed that when Ayer says that “the term ’God’” is a metaphysical term ([Ayer 74], p. 152), he erroneously attributes some semantic meaning to the sign sequence “God”, or at least he presupposes that this sign sequence has a semantic meaning, for otherwise it cannot be a term.

The difference between the anti-introductionistic criticism and Ayer’s criticism is that according to the former religious sentences are semantically senseless while according to the latter they are just metaphysical, which according to Ayer does not mean that they are semantically meaningless (cf. [Ayer 74], p. 55-56). As mentioned, however, the semantically meaninglessness of the religious sentences is due to their lack of word meaning.

2.2 The realism debate.

In his treatise Reality Lost and Found, Søren Harnow Klausen commits an unfortunate, unfounded presupposition by advancing this statement:

“Since antirealism is the denial of realism, the definition of this term becomes absolutely crucial”. ([Klausen 04] p. 13)

The reason is that the premiss about anti-realism presupposes that the anti-realist can accept the concepts that enter into this definition, which does not have to be the case at all. It is just as wrong to assert that anti-realism is the opposite of realism as it is to assert that atheism is the opposite of theism – for similar reasons. Thus, there are far more that have to be thought-through than what Søren Harnow Klausen presupposes.

This also applies to what follows. S. H. Klausen presents this definition of realism:

“Realism about the external world is the view that the world exists and has its fundamental properties independently of the way it is experienced, conceived, spoken or written about or coped with by conscious beings.” ([Klausen 04] p. 13-14)

However, S. H. Klausen does not thematize what it means to say that the world exists. Instead, S. H. Klausen copies what he wants to negate into his definition of anti-realism, which is exactly what one cannot do if one wants to do full justice to the realism debate:

“Anti-realism is any denial of – or refusal to subscribe to - the view that the world exits...” with the same additions as referred above. ([Klausen 04] p. 14)

However, the anti-realist does not at all need to deny that the world exists, or that the attributes of the world depend of how it is experienced. For of course an anti-realist will not deny the statement, “the world exists” but just have a different interpretation of the statement than the realist has, as far as the latter has an interpretation. Thus, the anti-realist may think that it is absurd to ask whether “the world exists”, and that the realism debate is about the semantic meaning of this statement, including what it means that things exist and have the qualities they have.

It is thus expressive of a simplified idea of the substance of the realism debate if the expression “the denial” is supposed to denote the directly contrary viewpoint. For then it presupposes that the anti-realist can accept the realist’s view of the problem as being about existence versus not-existence. If, however, the expression is just to denote some alternative view among other, it becomes too loose and not a definition of anti-realism.

For safety’s sake, S. H. Klausen makes clear his simplified with of the problem with this statement:

“Realism is of course the belief in the existence of reality”. ([Klausen 04] p. 14, my underlining.)

However, as already made clear, the realism debate does not deal with existence versus not-existence, but with the semantic meaning of our existence statements; and it does not at all deal with any form of belief or supposition, but with arguments. This naturally turns the attention to the fact that S. H. Klausen’s lacking accept of this is already suggested by the title of S. H. Klausen’s book, Reality Lost and Found. This title suggests that reality does not exist according to the one part of the realism debate, but exist according to the other part, Klausen himself, who has realized “the existence of reality”.

S. H. Klausen defines reality and the world in this remarkable way:

‘And reality is simply “the world” as defined above”: that which exists independently of its being experienced...’ with the most of the additions above. ([Klausen 04] p. 14)

What is remarkable in this quotation is its use of the following concept:

“that which exists independently of its being experienced...”.

This definition reminds incredibly much of past definitions of some entity X called “God”, e.g. “that which is the greatest”. Both definitions presuppose that it has been clarified what kind of “that” we are dealing with.

Firstly, the definition presupposes that it has sense to discuss the subject in this way, which as mentioned is exactly what the realism is about and which some anti-realists want to argue against. Secondly, the definition presupposes that the opponent can accept it. However, as it has already been concluded, definitions demand clarified concepts.

Søren Harnow Klausen’s erroneous approach has also been touched on in the section “The semantic approach the realism debate” in Treatise No 4.

3. Ignosticism and semantic meaning.

The article “Presuppositions in religion and the realism debate” inter alia pointed out the error of defining atheism as the opposite of theism. Certainly, this broader definition of atheism can be suggested: “Being an atheist is the same as not being a theist”. (Cf. the homepage [Skepticism], my translation.) According to this homepage, atheism is the absence of belief in gods. However, this definition demands some goodwill, as not all who do not want to call themselves atheists can accept it. They have good reasons not to do this, as it is possible to argue that religious sentences are semantically senseless, as e.g. the sign sequences “god” and “belief” lack word meaning when used in religious contexts, and as the definition of theism is based on these sign sequences. Cf. the section “Semantic critique of religious sequences of signs” in Treatise No 5, in which it is explained why religious sentences lack word meaning and therefore are semantically senseless. Persons that have understood this can be called neither theists nor atheists. For as mentioned, it is possible neither to deny nor to affirm a semantically senseless sentence, but only to assert and make good that it is in fact semantically senseless. Some may call this view agnosticism, but as mentioned, this term does not have semantic meaning either.

Finally, it must be observed that the statement that a particular sentence is semantically senseless is stronger than the statements that the sentence is true or that that it is false; the reason is that it does not even qualify itself to be evaluated as true or false.

3.1 Ignosticism.

The view ignosticism or igtheism is apparently in agreement with these considerations; however, but it is too unclear as it also suggests a certain acceptance of the religious sign sequences.

According to www.wiktionary.org, the etymology of the word “ignosticism” is:

“ig- (from ignorant) + gnostic + -ism. Coined by Rabbi Sherwin Wine.” ([Etymology])

Here I will only consider the definition of ignosticism as it is worded in the British version of Wikipedia, and some of the resuming remarks in the article.

Wikipedia states two definitions of ignosticism. According to the first, ignosticism is:

“The view that a coherent definition of God must be presented before the question of the existence of God can be meaningfully discussed.” ([Ignosticism])

As far as it goes, this corresponds to what has been put forward in the above-mentioned section “Semantic critique of religious sequences of signs”, but only after a necessary correction. For in order not to be semantically erroneous by presupposing too much, it ought to be worded in this way:

“The view that a coherent definition of the term “God” must be presented before the statement “God exists” can be meaningfully discussed.” ([Ignosticism], my underlinings of the corrections.)

In the just referred section from Treatise no 5, however, it has also been argued that in fact such a semantic meaning cannot be established, as a number of possibilities of this were gone through and criticized.

The referred lexicon article also states:

‘A simplified maxim on the subject states “An atheist would say, ‘I don't believe God exists’;’ an agnostic would say, ‘I don't know whether or not God exists’; and an ignostic would say, ‘I don't know what you mean when you say, “God exists”’.”’ ([Ignosticism])

To this, it must be remarked that it is misleading to rank the latter view with atheism and agnosticism. These two views on religions can certainly be ranked each other and to agnosticism, as all three presuppose that the above-mentioned sentences, which their adherents would put forward, have a semantic meaning and do not just borrow an appearance of semantic meaning from real words. However, in its best wording, ignosticism is just a result of the quite elementary truth that all sentences must have a clarified meaning in order to be discussed.

Above all, however, the quotation simply turns the case upside down. The persons that can argue for the semantic senselessness of the religions are not ignorant. First, they can exactly ague for their view. Second, it is not them but the religious persons that must be able to explain their own putative concepts, before they can attribute a semantic meaning to them. As long as the religious persons cannot do this, they are ignorant concerning what diffuse ideas they have themselves. In the above-mentioned section “Semantic critique of religious sequences of signs”, this has been gone through and justified in a number of respects, and with increasing goodwill. We are here dealing with the same kind of misuse of the word “ignorant”, as when a person is called ignorant if he does not know where his neighbour keeps his toolbox.

According to the second definition of the lexicon article, ignosticism is synonymous to theological noncognitivism.

3.2 Theological noncognitivism.

This ism is defined in this way:

’Theological noncognitivism is the argument that religious language, and specifically words like God, are not cognitively meaningful. It is sometimes considered to be synonymous with ignosticism. ([Theological noncognitivism])

However, the former statement is too week, as the concept of cognitive meaningfulness only demands that what is discussed has to be decidable, either analytically or empirically. However, as religious sentences are not semantically meaningful, they do not even qualify to be objects of an analytical or empirical examination.

However, the lexicon article also asserts the following, which bears a greater likeness to ignosticism:

“As with ignosticism, the consistent theological noncognitivist awaits a coherent definition of the word God (or of any other metaphysical utterance purported to be discussable) before being able to engage in arguments for or against God's existence.” ([Theological noncognitivism], my use of bold types.)

It is true that we cannot express ourselves about sentences that use unclarified concepts and therefore is not statements. However, it is misleading to call the knowledge of this fact being waiting. We are just dealing with the elementary demand that any sentence must have a clarified meaning for it to be a statement we can take a position on.

Moreover, the quoted passage is semantically senseless itself, as it contains the unclarified sign sequence “God’s existence”, and it does not help to change this to “a putative God’s existence”. The wording intriguingly suggests that it is granted that this sign sequence can be attributed a meaning we just wait for. The quotation contains the same error as the sentence “Before it can be decided whether Kryxir exists it must be decided what ‘Kryxir’ denotes”. This sentence suggests that, it is granted that “Kryxir” denotes something we have just not clarified yet. Certainly, we can refer to sign sequences whose meaning we do not know, but we do not use them as words. Instead, we can say, 'Some people assert that there is something they call “Kryxir”. Before we can address this, they must explain what they talk about’.

Both those who assert “Kryxir exists” and those that assert, “God exists” may simply be expected to have an explanation ready, i.e. to know what they say themselves. The ability of pointing out the fact that the religious persons are not able to do this is naturally just a knowledge that does not need a name. However, it deserves to be discussed for the sake of peace.

4. Religion, isms and responsibility.

This section looks at the following two problems:

R1: Occasionally, criticism of a person’s religiously conditioned behaviour is countered with the argument R1.1: that this criticism does not concern the religion of the person in question, but solely the person in question himself. R1.2: This suggests that in some way religions exist in themselves or are independent entities that cannot be touched by such a criticism.

R2: Conversely, sometimes a person’s bad behaviour is explained with the allegation that the person in question is an adherent of an especially criticisable religion.

Therefore, it is relevant to examine these two views, including whether by any means way it makes any sense to talk about an entity that can be called “a religion in itself”.

Strictly speaking, this rather practical subject is slightly outside the field of these philosophical treatises, however, parts of the discussion refer to subjects already treated.

Concerning the examination of in what a religion in itself should consist, religions involve the special problem that the religious sentences are semantically meaningless sign sequences. (Cf. the section “Semantic critique of religious sequences of signs” in Treatise No 5.) However, isms do not necessarily contain semantically meaningless sign sequences. By way of example, socialist ideas can be described in a semantically meaningful way. For this reason, it may be useful to clarify the corresponding problems concerning isms first.

4.1 Isms and responsibility.

The question of existence of isms in themselves falls within the question of concepts in themselves. This question can immediately be compared to what has been advanced concerning detecting a world in itself in the subsection “A fundamental critique of the approach” in the subsection “The problem of the external world” in Treatise No 5. Here, the statement “an external world exists” was compared to the statement “There is water on the moon”, which we can immediately understand, as we know what it means that there is water on the moon. For we know what we have to search for to find the water, and when we have found it. Moreover, we know something about how we have to search for it. Thus, we know the verification conditions or assertability conditions of the statement, i.e. its meaning.

If the statement “There are isms in themselves” are to be justified, this justification must similarly involve answers to the following questions: What does it mean that there is an ism in itself? What do we have to search for to find an ism in itself? When have we found or detected an ism in itself? What shall we do to find an ism in itself? Of course, this involves neither finding anything physical nor finding a description, but what it otherwise should involve is exceedingly unclear. Those who think that there are isms in themselves must be able to explain this.

By analogy with the conclusion in the referred subsection, we can moreover infer that we can express the same thing independently of, or without referring to, that indeterminable extra that may lie in the idea of “an ism in itself”. Therefore, this idea cannot be about anything. The same applies to not-expressed ideas.

The reason is that if a person draws up a theory or ism about how society is to be organized and why, this is the only thing that is present to us:

We must be able to explain and justify any idea we present, whether it has appeared to us in a flash, or is something we have read. The idea only exists as an idea by virtue of the presented explanations and justifications. Without these, it at most consists in arbitrary statements.

So much the less does it have any sense to assert that it has always existed. Overall, it is an uninteresting assertion that this or any other ism has always consisted in something in itself, i.e. as something else besides the now expressed ism.

However, these results only say something about what an ism cannot be. We still need to clarify what an ism is in fact. Therefore, we have to examine what kind of entity an ism can at most be said to be. The result proves to be a semantically meaningful concept of isms, which involves the concept of justification.

The question is whether e.g. socialism consists in a text, specific ideas, behaviour, or possibly something else. If socialism consists in a text, however, the text in question is only interesting if it can be understood as interpreted sentences, for otherwise we are only dealing with signs. Thus, we must regard socialism as consisting of ideas sought to be expressed, or which can be deduced from a text. If we by socialism understand an activity based on socialist ideas the adherents seek to follow or propagate, the word “socialism” is just a short-form of the expression “the socialist activity”. This does naturally not touch what is essential to this discussion, as it deals with ideas as such.

In all cases, as a political ideology the socialist ideas must consist in a number of statements about how the world ought to be. We can compare these expressed socialist ideas with how the world actually is and examine how far it is from the ideals in question. With this, the description of them has a clear semantic meaning. Therefore, socialism consists in these expressed ideas, just as any other political ism consists in expressed ideas that can be compared to how the world is.

Hereafter we can look at the responsibility for acts carried out with reference to an ism. The question is whether the responsibility can be attributed to the ism. We must of course distinguish between the ethical quality of the ism and the personal responsibility. Moreover, the chain of cause and effect has to be involved.

Irrespective of which specific ism we are dealing with, there might be a person that calls himself an adherent of it, and who acts badly in the name of the ism in question. If this ism does not recommend acts of the committed kind, the act does of course not fall back on the ism in question. In other cases, it may inter in a chain of cause and effect.

If a person on the background of the recommendations of an ism chooses to carry out a certain act, this decision is based on his accept of the ideas of the ism. This accept may be due to there being argued for them in the text in such a way that they can convince him, because he can be influenced by exactly these accidental causes or by the fact that the ideas and arguments are valid, and that he can understand this. Other elements of the chain or complex of cause of effects may be that the person in question already has some similar ideas in a vague version, or that the content of the text or rather his understanding of it makes him feel important.

Though an ism can thus be part of a chain of cause and effect, the person that acts because of the ism chooses his act himself:

The person who adheres to an ism chooses this himself. If he acts because of an ism, he himself has the responsibility for this, for he does not have to accept the ideas of any ism, and he does not have to act because of any ism. It is not a question of necessity but of a choice.

Therefore, we cannot attribute the very cause of persons’ acts to an ism.

Whether the individual person adheres to an ism because of its content, such as this meaningfully can be described, or for other reasons, such as pressure, or just because he let himself be influenced by his surroundings, the following demand must be made:

Under all circumstances, it is reasonable to expect or demand that that the person who accepts an ism can justify his acceptance.

Thus, the acting person also has the responsibility for an act he relates to an ism, whereas it is a category error to attribute it to the very ism. For other persons will perhaps just immediately realize that the text is wrong, shake their head at it and argue against it. Moreover, it can be advanced that we can certainly argue against an ism, but since we cannot blame it for anything the very ism and its content are only part of the chain of cause of effect that leads to the act.

We can now look at a variant of the problem that opened this section, as we let it be about isms instead of religion. It may sound like this:

I1: Occasionally, criticism of the behaviour that a person relates to an ism is countered with the allegation I1.1: that this criticism does not concern the ism in question, but solely the person in question. I1.2: By this, it is suggested that in some way isms exist in themselves or are independent entities that cannot be touched by such a criticism.

I2: Conversely, sometimes a person’s bad behaviour is explained with the allegation that the person in question is an adherent of an especially objectionable ism.

The discussion above leads to the following conclusions concerning this variant:

Re I1.1: It is in fact the individual adherent of an ism who is responsible for his behaviour, even if this is related to the ism, for the single person chooses himself whether he will follow the ism in question.

Re I1.2: Isms do not exist in themselves. However, there are isms that can be explained and justified, which also means that they are ethical acceptable, for otherwise they would not be (correctly) justified.

Re I2: There are of course also isms that can be criticized for calling for objectionable acts. Thus, there exist both well-founded and unjustified isms. The former are ethically defensible, while some of the latter may contain erroneous and unethical ideas. However, the individual person has the responsibility for following these calls, for he does not have to follow the bad recommendations of the ism.

4.2 Religions and responsibility.

Hereafter we can return to the discussion of religion and responsibility that introduced this section:

As mentioned in the section “Semantic critique of religious sequences of signs” in Treatise No 5, it has been made good that religious texts in their basis consist of semantic meaningless sequences that just loan an appearance of semantic meaning from sign sequences that in fact have semantic meaning and thus are words. What happens is that the religions reuse some words without using the meaning that the words in questions have in their original, not-religious use, but just use them in a vague way, as if they had a meaning that in some way or other is relates to the original meaning or to some of the original meanings. This applies to sign sequences as “belief” and “salvation”. In the subsection “Word meaning versus lacking reference” in Treatise No 6, it has be clarified how this is possible.

Certainly, a religious text can contain sentences that by themselves are semantically meaningful, e.g. orders to perform certain acts; i.e. that they are real statements that express ideas. However, none of these sentences can be justified on the basis of the semantic meaningless statements that enter into other parts of the religion. In fact, nothing can be asserted that does not have to be justified by reference to the case itself. Thus, ethical statements can only be justified by reference to the case itself:

If any ethical statements should true, this truth cannot be due to any religion. For it is not possible to put forward any reasonable religious statement that cannot be justified by reference to the case itself, as that which does not concern the case cannot be used as a premise. The semantic meaningless sentences of the religions especially cannot concern the case because of their lacking semantic meaning. They cannot be used as premises of any statement at all.

The religious orders to perform certain acts just make up attached ethical statements, e.g. of the form “You ought to perform / omit the act A”. As already justified, the semantic senseless sentences of the religion cannot be used as a premise to ethical statements. Besides, attempting this would just lead to semantic meaningless statements of the form: “The God X asserts that we have to perform / omit the act A”. The attached ethical statements cannot themselves contain justifications, for in that case they would have to refer to the case itself, and therefore cannot have anything to do with religion.

Nevertheless, it must be observed that the individual religious person himself puts something uncertain and diffuse into the semantic meaningless sentences of the religion, which according to him for some reason can be related to the in fact meaningful concepts in which the religious ideas originate.

We can now look at the problems concerning responsibility and religion that introduced this section:

Re R1.1: It is in fact the individual adherent of a religion who himself is responsible for his behaviour, even if the person in question is motivated by his religion, for the single person chooses himself whether he will follow the religion in question. Thus, for logical reasons, the critique of such acts does not concern the religion.

Re R1.2: It has appeared that there are no religions in themselves. Religions do not even have a religious content that can be explained and justifies. Overall, it must be concluded that there is no religion based on which it can be argued what are the good acts and what is the good life. The reason to this is that religions do not contain valid religious arguments for or against any acts, but only semantically meaningless sentences and attached ethical statements.

Re R2: Besides its semantically meaningless sentences, a religion can also contain orders to perform certain acts. For the corresponding reasons as above, of course it is also true that it cannot contain valid arguments for these.

Generally, it must be observed that if an ethic allegation can be defended or criticized, this cannot be due to any religion, for religions do not contain usable religious premises. A religion may contain true ethic allegations, but these must be justified by reference to the case itself. Thus, a person that acts on demands does not act on the basis of the case itself.

4.3 Conclusion.

It can be concluded that isms can be discussed, criticized and possibly accepted, as they have a semantic content. Therefore, in some cases there can be good grounds for acting in compliance with of an ism, i.e. not because of the ism, but because of an understanding of the case itself. Contrary to this, the following applies to religions:

Religious sentences only have an appearance of semantic meaning and are thus unfounded. Therefore, religion contains no good reasons to particular acts, and therefore there is no reason to regard religion as superior to anything in any way.

Concerning the comparison of religions that enters in the discussed problem, it can be concluded that there are no reasons for any religion being more preferable to any other religion. Some persons may nevertheless maintain that the religion X may contain worse demands and statements than the religion Y. This is possible; however, it has just been made good that religious statements about the world are completely unjustified. Therefore, these demands and statements are accidental additions. It is incumbent on the individual to be so critical that he can consider this.

It must further be observed that it is an accident that there are the religions that exist. It is an accident that the religions are the way they are. It is an accident that the religions are geographically spread as they are spread. It is accidentally that the adherents of the different religions behave as they do. These circumstances are accidental simply because they might conceivably have been different.[3] It is impossible to justify a complete determinism that can contradict this.

To this, some will object that one of these accidental states could be better the other states. However, such a comparison presupposes that it can be justified, which must be done on the basis on the case itself, i.e. rationally. Otherwise, it has no sense to characterise religions in this way. However, the religious person will hardly accept that his religion should be rationally based.

Litterature:

[Arguments] http://ovemk2.blogspot.dk.

[Aristoteles 68] Aristoteles: The Metaphysics,
English translation by High Tredennick,
Harvard Univ. Press, William Heinemann Ltd. (Great Britain 1968).

[Ayer 74] A. J. Ayer: Language, Truth and Logic, Penguin Books Ltd (Harmondsworth, 1974).

[Etymologi]: http://en.wiktionary.org/wiki/ignosticism.

[Grice 94] H. P. Grice: “Logic and Conversation”, i Basic Topics in the Philosophy of Language, Robert M. Harnish (ed.), (Harvester Wheatsheaf 1994).

[Ignosticism]: http://en.wikipedia.org/wiki/Ignosticism.

[Klausen 04] Søren Harnow Klausen: Reality Lost and Found, University Press of Southern Denmark, (Denmark 2004).

[Salmon 70] Wesley C. Salmon, ed.: Zeno’s Paradoxes
Bobbs-Merrill (Indianapolis & New York, 1970).

[Skepticism]: http://www.skepticisme.dk/2008/12/hvis-man-ikke-er-teist-s-er-man-ateist.html.

[Theological noncognitivism]: http://en.wikipedia.org/wiki/Theological_noncognitivism.

[1] Until 2012, in spite of its name (“start help”), this term denoted a low social benefit.

[2] As this precondition is not fulfilled, this sign sequence is only called a question in order to not to make the text too prolix.

[3] This originates from the article, “The contingency of religions” in my blog [Arguments].