FAITH AND REASON

"Omne verum, a quocumque dicatur, a Spiritu Sancto est"

Every truth, whosoever shall say it, comes from the Holy Ghost.

(Saint Thomas Aquinas)


¿Is it possible to prove a negative statement?

The following is an article by Richard Carrier, from "Internet Infidels", in which he argues that it is possible to prove negative statements in general, and the non - existence of God, in particular. Below I have included my own analysis of Carrier's article.


Proving a Negative (1999)

Richard Carrier

I know the myth of "you can't prove a negative" circulates throughout the nontheist community, and it is good to dispell myths whenever we can. As it happens, there really isn't such a thing as a "purely" negative statement, because every negative entails a positive, and vice versa. Thus, "there are no crows in this box" entails "this box contains something other than crows" (in the sense that even "no things" is something, e.g. a vacuum). "Something" is here a set restricted only by excluding crows, such that for every set S there is a set Not-S, and vice versa, so every negative entails a positive and vice versa. And to test the negative proposition one merely has to look in the box: since crows being in the box (p) entails that we would see crows when we look in the box (q), if we find q false, we know that p is false. Thus, we have proved a negative. Of course, we could be mistaken about what we saw, or about what a crow is, or things could have changed after we looked, but within the limits of our knowing anything at all, and given a full understanding of what a proposition means and thus entails, we can easily prove a negative in such a case. This is not "proof" in the same sense as a mathematical proof, which establishes that something is inherent in the meaning of something else (and that therefore the conclusion is necessarily true), but it is proof in the scientific sense and in the sense used in law courts and in everyday life. So the example holds because when p entails q, it means that q is included in the very meaning of p. Whenever you assert p, you are also asserting q (and perhaps also r and s and t). In other words, q is nothing more than an element of p. Thus, all else being as we expect, "there are big green Martians in my bathtub" means if you look in your bathtub you will see big green Martians, so not seeing them means the negative of "there are big green Martians in my bathtub."

Negative statements often make claims that are hard to prove because they make predictions about things we are in practice unable to observe in a finite time. For instance, "there are no big green Martians" means "there are no big green Martians in this or any universe," and unlike your bathtub, it is not possible to look in every corner of every universe, thus we cannot completely test this proposition--we can just look around within the limits of our ability and our desire to expend time and resources on looking, and prove that, where we have looked so far, and within the limits of our knowing anything at all, there are no big green Martians. In such a case we have proved a negative, just not the negative of the sweeping proposition in question.

The Method of the Best Bet

Logicians note that it is easier to prove that there are such beings than to prove there aren't simply because we only need to find one of them to accomplish our proof, and thus will not have to look everywhere--unless we are so unlucky that where the one Martian is just happens to be the last place we look. But in the final analysis, it is not being "negative" that makes a proposition difficult to prove, but the breadth of the assertion. For instance, "there is gravity on every planet in every universe" could be disproven by searching just one planet and finding no gravity, but if we kept finding gravity we could never decisively prove it true, any more than if we kept failing to find Martians in the universe would we be able to decisively prove that "there are no Martians in the universe." Thus, what people call the "you can't prove a negative" axiom is actually nothing more than the eternal problem of induction: since we can't test a proposition in every place and at every time, we can never be absolutely certain that the proposition remains true in all times and places. We can only infer it.

In computers this sort of proof (of the positive or negative variety) results in an infinite loop (or quasi-infinite loop), and clever programmers can give software the tools to recognize such routines before executing them. Then, instead of executing them, they have them execute a simpler subroutine that equates to a "best guess." Not surprisingly, we all do the same thing: since we have neither the ability nor the desire to devote a dangerous proportion of our time and resources to testing every proposition of this kind, we adopt a simpler rule: given insufficient evidence, then no belief. This is the same thing as "given sufficient evidence, then belief," since insufficient evidence is the same thing as sufficient evidence for denial.

This amounts to a "best guess" solution, where we recognize that a statement may be true, but have insufficient grounds to believe it. Or, in the case of propositions for which we have abundant but incomplete proof, we recognize that it may be false, but have insufficient grounds to disbelieve it. This is the basic principle behind all hypothetical thought, from the theories of science, to the "sun will come up tomorrow" variety of common sense. Given the set of all propositions of the first kind (where there is a lack of evidence despite some reasonable measure of checking), nearly all of them are false, so it is a safe bet to assume they are all false until proven otherwise. Conversely, given the set of all propositions of the second kind (where there is continuous evidence after some reasonable measure of checking), nearly all of them are true, so it is a safe bet to assume they are true until proven otherwise.

Unprovable Statements

Consider the negative case. When it comes time to decide what to believe, if we did not assume such "unprovables" were false, we would either have to choose which unprovables to believe by some totally arbitrary means, which amounts to a ridiculous "belief by whim" method, or else we have to assume that all such statements are true. Of course, we only have to believe true those unprovables that do not contradict other proven statements or that do not contradict each other, but even in the latter case we have no grounds for choosing which of two contradictory unprovables we will believe, and this is the same "belief by whim" dilemma. But even with these provisions, this policy would result in a great number of absurd beliefs (like "there are big green Martians in the universe"). Thus, when finally deciding what to believe, it is clear that the best policy is to assume that all unprovables are false, until such time as they are proved. In other words, it is reasonable to disbelieve a proposition when there is no evidence. Even if it is less certainly false than propositions which are actually contradicted by evidence (although even that does not amount to a complete certainty), it is still reasonable to regard them as false so long as we've done some checking, and don't ignore new evidence that we come across.

A similar line of reasoning establishes the opposite in all positive cases. If we did not assume all such unprovables were true, we would either have to choose which unprovables to disbelieve by some totally arbitrary means, which again amounts to a ridiculous "belief by whim" method, or else we have to assume that all such statements are false. Of course, it would be plainly absurd to believe that all the statements for which we have some evidence are false. Although "absolute skeptics" actually claim to assume this, they put in place of truth a concept of assent which amounts to the same solution as I have discussed above: betting on the truth of a statement that we have many reasons to believe but can never be certain of. Thus, when finally deciding what to believe, it is clear that the best policy is to assume that all unprovables for which we have good evidence are true, until such time as they are disproved. In other words, it is reasonable to believe a proposition when there is good evidence. Even if it is less certainly true than propositions which are actually irrefutable, such as mathematical truths or "I am thinking, therefore I am," it is still reasonable to regard them as true so long as we've done some checking, and don't ignore new evidence that we come across. In all cases, we can perhaps move the bar up and down--changing the amount of "checking" that counts as reasonable and sufficient before resolving to believe--but this affects all our beliefs, as the bar cannot be set differently for different things without again engaging in "belief by whim" methods, and we will all find that there is such a thing as having the bar too low or too high, as one can find through the same reasoning as I have engaged in here.

The Unbelievability of Christian Theism

Christian Theism in its most basic sense entails observations that would necessarily be made by everyone everywhere and at all times, and thus it is as easily disproven as the alien in the bathtub. For instance, God is theoretically omnipresent, and granted us the ability to know him (to feel his loving presence, etc.), yet I have absolutely no sensation of any God or anything that would be entailed by a God, even though the theory states that he is within me and around me wherever I go. Likewise, God is theoretically the epitome of compassion, and also all-knowing and all-powerful and beyond all injury, yet I know that what demonstrates someone as compassionate is the alleviation of all suffering known to them and safely within their power to alleviate. All suffering in the world must be known and safely within the power of God to alleviate, yet it is still there, and since the Christian theory entails the opposite observation, Christianity is false. Likewise, God theoretically designed the universe for a moral purpose, but the universe lacks moral features--animals thrive by survival of the fittest, not survival of the kindest, and the laws of physics are no respecter of persons, they treat the good man and the bad man equally. Moreover, the universe behaves like a mindless machine, and exhibits no intelligent action of its own accord, and there are no messages or features of a linguistic nature anywhere in its extra-human composition or behavior, such as we would expect if a thinking person had designed it and wanted to communicate with us.

Christians attempt to preserve their theory by moving it into the set of unprovables that lack all evidence. They do this arbitrarily, and for no other reason than to save the theory, by creating impassable barriers to observation, just as requiring us to look in every corner of every universe creates an impassable barrier for one who is asked to decisively disprove the statement "there are big green Martians." For instance, the advanced theory holds that God alleviates suffering in heaven, which we conveniently cannot observe, and he has reasons for waiting and allowing suffering to persist on Earth, reasons which are also suitably unobservable to us, because God chooses not to explain them, just as he chooses, again for an unstated reason that is entirely inscrutable, to remain utterly invisible to all my senses, external and internal, despite being always around and inside me and otherwise capable of speaking to me plainly.

The problem is not, as some theists think, that we can find no explanations to "rationalize" a god in this world of hurt. I can imagine numerous gods who would be morally justified and even admirable, and others who would be neither evil nor good, and still others who are evil, but none of these would be the Christian god. The fact is that Christianity is the proposal of a theory, and like all theories, it entails predictions--but these predictions are not being born out. So Christians invent excuses to save the theory--excuses which have absolutely no basis in any evidence or inference, except the sole fact that they rescue the theory. This is Ptolemy's hypercycles all over again: the motions of the planets and sun refused to fit the theory that they all revolve around the Earth, so Ptolemy invented numerous complex patterns of motion that had no particular reason to happen other than the fact that they rescue the theory of geocentricity. It is simply far wiser to conclude that instead of this monstrously complex and bizarre architecture of groundless saving suppositions, it makes far more sense, and uses far fewer suppositions, to simply admit that the universe doesn't revolve around the Earth after all. As for all the other theories--all the other possible gods--there is no more evidence for them than for this incredibly complex deity with a dozen strange and mysterious reasons that only too conveniently explain why we never observe him or his actions in any clear way.

Of course, even these groundless "solutions" to the Christian theory do not really save the theory, because, to maintain it, at some point you must abandon belief in God's omnipotence--since at every turn, God is forced to do something (to remain hidden and to wait before alleviating suffering, etc.) by some unknown feature of reality, and this entails that some feature of reality is more powerful than God. And this feature cannot merely be God's moral nature, since if that were his only limitation, there would then be no barrier to his speaking to me or acting immediately to alleviate suffering or designing the universe to have overtly moral or linguistic features, since any truly moral nature would compel, not prevent, such behavior. Thus, the Christian theory is either incoherent or unprovable, and in the one case it is necessarily false, while in the other it lacks justification, so we have no reason to believe it, any more than we have a reason to believe that there is a big green Martian on some planet in some corner of some universe. This is what it means to "prove a negative."


On proving a negative

(Lic. Néstor Martínez, Uruguay).

In the following lines I shall make reference to the article "Proving a Negative", whose author is Richard Carrier. My standpoint is a theistic one. I grant that it is possible in some cases to prove a negative. I deny that Carrier has proved the non-existence of God.

The article starts with the thesis that negative statements can be proved. One of the first points made is that every negative proposition entails an affirmative one. The author says:

1) "..."there are no crows in this box" entails "this box contains something other than crows" (in the sense that even "no things" is something, e.g. a vacuum). "Something" is here a set restricted only by excluding crows, such that for every set S there is a set Not-S, and vice versa, so every negative entails a positive and vice versa."

It is true that Carrier also says:

"Of course, we could be mistaken about what we saw, or about what a crow is, or things could have changed after we looked, but within the limits of our knowing anything at all, and given a full understanding of what a proposition means and thus entails, we can easily prove a negative in such a case. This is not "proof" in the same sense as a mathematical proof, which establishes that something is inherent in the meaning of something else (and that therefore the conclusion is necessarily true), but it is proof in the scientific sense and in the sense used in law courts and in everyday life."

But then, he says also this:

"So the example holds because when p entails q, it means that q is included in the very meaning of p. Whenever you assert p, you are also asserting q (and perhaps also r and s and t). In other words, q is nothing more than an element of p. Thus, all else being as we expect, "there are big green Martians in my bathtub" means if you look in your bathtub you will see big green Martians, so not seeing them means the negative of "there are big green Martians in my bathtub." "

So we have here a problem: ¿is such a reasoning a necessary conclusion, or not? ¿Is "q" part of the meaning of "p", or not?

The problem seems to be that in the case of the crows or the Martians, we do not have, as in mathematics, a complete certainty of the inclusion of "q" in the meaning of "p", or then, we have it, but we do not know for sure whether in fact "q" is given or not; or both. That is why Carrier uses phrases as: "all else being as we expect", and "within the limits of our knowing anything at all".

Here I think that we must say that:

1) The inclusion or not of a term into the meaning of another is in final analysis a question of intuition, and cannot be dubious, in itself. In the contrary, we could never say that a proposition is not analytical, as we do with certainty in many cases.

2) Also, the actual existence of a certain perceived fact is an intuitive question, about which, into the limits of our normal perceptual capabilities, there can be no doubt.

3) It is true that we can err sometimes about these things, but this does not take away the certainty of intuition. Because in such cases, the error is not an error of intuition, but an error of the subject, about an object that in itself is an object of intuition. For example, if due to a defect in the eye a person does not see the colors of things.

4) A valid conclusion in a deductive argument is always a necessary conclusion. This does not mean that it is always a necessary truth, because a valid conclusion need not be true, and even if it is true, it can be only a probable truth, given that some of the premises is also only a probable truth.

Then, as the proof that Carrier gives is a deductive one, we must test its logical validity in terms of the necessity of the conclusion, even though it is true that we can wonder, in practical cases, whether all the conditions of the certainty of the conclusion are really given. At least this condition must be given always: that the conclusion must be a necessary one.

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The deduction or implication here affirmed seems to be the passage from the universal negative (E) to the particular negative (O), that is, from "No existing thing in this box is a crow" to "Some existing thing in this box is not a crow". In a language more akin to modern simbolic logic, we should say:

"For every X, if X is an existent thing in this box, X is not a crow" (E), and

"There exists an X such that X is an existent thing in this box, and X is not a crow". (O)

We could also say that the propositions are:

"For every X, if X is a crow, X is not in this box" (E)

"There is an X, such that X is not a crow, and X is in this box" (O).

But this, I think, would make our own case too strong. Anyway, what we shall say of the first pairs of sentences can be said, "a fortiori", of the second.

Modern simbolic logic, at least classic predicate calculus, denies that there is a valid implication from (E) to (O). They do this when they criticize the aristotelian doctrine of oppositions. They say that (O) has an existential character, and that (E) does not. And so, we cannot deduce an existential thesis from non - existential premises. They say that (E) only has a conditional sense, not implying the existence of the antecedent: "if X is an existent thing in this box..."; while (O) has a decidedly existential character, affirming that "there exists an X ..." that is so and so.

Now, it happens that I do not share such critics to Aristotle's logic. Following Maritain ("L'ordre des concepts"), and making economy of a long explanation, I think that either (E) or (O) can have existential or not existential character, depending on the "suppositio" with which they are affirmed in each case. So, they may have both existential character, or they may both lack it, and in such cases there is not fault in deducing (O) from (E), as Aristotle made.

It is true that if we re-write the sentences as we have made above, that is, as modern simbolic logic does, the conclusion from (E) to (O) seems to be illicit. But such re-writing of a categorical proposition as the aristotelian (E) as a conditional proposition can be, precisely, the responsible of such a situation.

But I don't think that from this we can conclude, as Carrier does, that if (E) is true, then there exists something in the box.

Even if we put (E) in a categorical way:

"No existent thing in this box is a crow" (E)

we are not necessarily affirming, neither implicitly, that there exists something in the box. We cannot, then, deduce from such a sentence that there is something in the box, or that there is something in the box that is not a crow.

If (E) did imply the affirmation of some existent thing in the box, then it would be logically incompatible with a sentence like:

"The box is empty".

But we cannot deduce the non-emptiness of the box from the non existence of crows in the box.

Of course, the clue is that Carrier includes into "some existent thing in the box" also the absence of every existent thing in the box. But this doesn't seem correct. "Something" is not "nothing". And "nothing" is not "vacuum". Rather, is the absence of any "vacuum", as of every other thing. And if we said that "vacuum" is not a thing, then it is not "something", either, but only "nothing".

Then, the sentence that follows from "There are no crows in this box" is:

"Either there is something different from a crow in the box, or there is nothing".

which is not properly an "affirmative" sentence, but a disjunction.

If "something" is "a set restricted only by excluding crows" (Carrier), in the sense of "a set containing everything but crows", then we cannot say that "there are no crows in this box" implies "this box contains something other than crows", because that would mean that by the sole fact of denying the existence of crows in the box we are affirming that the box contains the whole rest of the Universe.

Or we can say that "a set restricted only by excluding crows" means "a set whose only character is the exclusion of crows", not having nothing more in its description. But then, it is clear from that very fact that from such sentence we can deduce nothing, because there is nothing "implied" in it different from the mere absence of crows.

So, it is true that finally Carrier escapes the objection that could be brought from classic predicate calculus, at least if we accept Maritain's interpretation. And he finally does not say really that the non existence of crows implies the existence of "something" in the box. So, up to here we are finally in accordance.

The positive statement then will be: "Either this box contains only some positive thing different from a crow, or it contains nothing".

And it is true that this proposition can be verified by looking into the box.

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But all this doctrine has nothing to do with the proving of negatives, as Carrier exposes it. Because what he finally shows as the way to prove a negative is not this:

"If there are no crows in this box, then, either this box contains only some positive thing different from a crow, or it contains nothing. But it contains only some positive thing different from a crow, (or else): But it contains nothing. Then, there are no crows in this box".

Although this argument is not valid in the sintactic (formal) level, it is valid in the semantic (material) one, because it happens that the first premise is true also the other way round. But this is not the argument as Carrier exposes it. Rather, is this:

"If there are crows in this box, we must see them when looking into the box. But we do not see crows when looking into the box. Then, there are no crows in this box."

This is a thoroughly correct way of reasoning. It is just the method of proving "ab absurdum". The general argument employed here is this:

"If A is true, then B is true. But B is not true. Then, A is not true.",

where "A" and "B" are propositions. This is what the medieval schoolmen called the "modus tollens", and is a valid way of reasoning.

As Carrier says:

2) "And to test the negative proposition one merely has to look in the box: since crows being in the box (p) entails that we would see crows when we look in the box (q), if we find q false, we know that p is false."

But then, I do not see the function of the positive statement implied by the negative one in this way of proving a negative. The tested positive sentence here is "We see crows when looking into the box". It is not entailed by the negative sentence we want to prove, that is, "There are no crows in this box", but by the positive sentence contrary to that: "There are crows in this box".

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Carrier also says:

4) "Even if it is less certainly true than propositions which are actually irrefutable, such as mathematical truths or "I am thinking, therefore I am,"

Then, at least, we get the conclusion that there are necessary truths, or , if you want, irrefutable truths which have the maximum of certainty, not solely in arithmetic, geometry, calculus, and the like, and that those truths can be found too in affirmations referred to factual reality, as is the case with "I am thinking, therefore, I am."

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Now we have the following problem: Can we apply this line of reasoning to the proof of general statements? . This is, as Carrier says, the problem of induction: we cannot prove general affirmations or negations because of the limited character of all experience.

For example:

"there are no big green Martians in this or any universe,"

"there is gravity on every planet in every universe"

Here Carrier makes recourse to the "method of the best bet". "Given insufficient evidence, then deny".

6) "In computers this sort of proof (of the positive or negative variety) results in an infinite loop (or quasi-infinite loop), and clever programmers can give software the tools to recognize such routines before executing them. Then, instead of executing them, they have them execute a simpler subroutine that equates to a "best guess." Not surprisingly, we all do the same thing: since we have neither the ability nor the desire to devote a dangerous proportion of our time and resources to testing every proposition of this kind, we adopt a simpler rule: given insufficient evidence, then no belief. This is the same thing as "given sufficient evidence, then belief," since insufficient evidence is the same thing as sufficient evidence for denial. "

The reason that he gives is then the following: We must decide. But if evidence is not sufficient, then we must decide by whim, which is not reasonable, or we must consider something true, without enough evidence, which is not reasonable either. Then, we must deny, providing that we are ready to examine every new evidence.

As he says:

7) "Consider the negative case. When it comes time to decide what to believe, if we did not assume such "unprovables" were false, we would either have to choose which unprovables to believe by some totally arbitrary means, which amounts to a ridiculous "belief by whim" method, or else we have to assume that all such statements are true. Of course, we only have to believe true those unprovables that do not contradict other proven statements or that do not contradict each other, but even in the latter case we have no grounds for choosing which of two contradictory unprovables we will believe, and this is the same "belief by whim" dilemma. But even with these provisions, this policy would result in a great number of absurd beliefs (like "there are big green Martians in the universe"). Thus, when finally deciding what to believe, it is clear that the best policy is to assume that all unprovables are false, until such time as they are proved. In other words, it is reasonable to disbelieve a proposition when there is no evidence."

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Our answer to this reasoning is that we do not need to decide in every case.

Nothing compels us to "decide what to believe" in every case. I can live a good life without deciding nothing about whether there is life outside the solar system or not. More still, I must not decide, if I want to respect the laws of good thinking, before having sufficient evidence for the affirmative or the negative.

There are occasions in which we are in doubt, that is, there is not enough evidence nor to accept, nor to reject a proposition. For example ¿is there life in other galaxies? I don't see the advantage of believing that there is not, even if we haven't been able to prove that yes.

It seems that the computer cannot doubt. It has to take a route, this or that. At least, this kind of program is one that leaves not place for doubt. But we humans have the chance of doubt.

The alternative is not "affirm or deny". The real logical alternatives are "affirm or not affirm", and "deny or not deny". Either we do not affirm, but we do deny, or we do not affirm and we do not deny: this last is the case of doubt.

But if the method of the "best guess" is not a valid one, we do have anyhow the means to prove a universal negative, by using the reasoning above mentioned, in cases in which the nexus between "A" and "B" is a necessary one. Because necessity implies universality. If given A, of absolute necessity must be given B (because B, as Carrier says, is part of the meaning of A), and B is not given, then A is not given. And that, with absolute necessity, and so, in every possible case.

It is true, then, that if we make recourse only to induction, that is, to experience, there is no way to prove a negative statement as "God does not exist". The most that somebody could say is: "I have never found God in my experience". But his experience is always limited. In fact, he could only say: "I have not found God in my experience up to now". He should not have reasons to affirm God's existence, but neither to deny it. As to finding or not God in our experience, Carrier has an argument, as we shall see below. But it is not based solely or mainly on induction.

The same happens with materialism. "All I have found in my experience is matter", even if it were true, it does not mean that only matter exists. Again, we could only say: "All that I have found up to now in my experience is matter". To go further, we must add some kind of deduction, based on some kind of principle, that is, on some kind of analytical, necessary relation between concepts.

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The way to prove a negative, finally, is always an application of the "reductio ad absurdum" argument: "If A is true, then B is true. But B is not true. Then, A is not true", being "A" and "B" propositions.

A special case of this is to obtain a contradiction from the supposition that A is true. One way of doing this is to show that the very concept of a thing is contradictory, as happens with the square circle.

Applying this to the religious problem, we must distinguish then between two different cases: 1) atheism 2) materialism.

In none of the two instances we can use induction. The fact that we have not yet encountered a certain thing does not prove that such a thing does not exist, and the fact that all things we have so long found are of a certain quality does not prove that we are not able to find tomorrow something not possessing that quality.

So we must use deduction, assuming as an hypothesis the existence of God, or the existence of something that is not material, and deducing some false consequence.

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In the case of atheism, then, the job consists in finding a contradiction in the very concept of an existent "God", or drawing contradictory of false consequences from that concept. And certainly, most of the atheist's arguments point in that direction. But the difficulty here is, then, to show that there exists really an analytical relation between the concept of "God", and the other concept that is used to form the contradiction. And the difficulty is that the concept of "God" is by definition the concept of a transcendent being, to which we cannot apply in an identical sense what we know about the beings in our experience.

This rule is not an arbitrary expedient of the theist to escape from objections. There are certain pairs of affirmations about God that are really contradictory, for example: "There is only one God", "There are three Gods". Because in this case it is not a question about the specific nature of God, but only about the specific nature of numbers.

That is why it is not true that the Christian faith could not be refuted. If the Christian faith said that "there is one God", and "there are three Gods", and insisted on the fact that "God" means exactly the same in those two sentences, then the Christian faith would be false.

But if we say: "There is only one individual nature of God", and "There are three divine Persons", the matter is different. To say that this pair of affirmations is contradictory, we must previously have the certainty that in God "person of God" and "individual nature of God" are identical in every respect. Now, that is too much knowing about a subject transcendent by definition as God, and in any case, such a knowledge cannot be drawn from experience.

Of course, in our experience of men, if there is one person, then there is also one individual nature. But then, our experience of men is not an experience of God.

And again, as to the concept of "God", it is by definition the concept of a transcendent being.

And if we say that since God does not exists, neither does "transcendency", then we are begging the question. Such non-existence was precisely the but of our demonstration as atheists.

It can be retorted that then we cannot know anything about God, because then all our words mean something totally different when applied to Him.

But this need not be the case. If God is on one side Infinite, and so, transcendent, He is on the other side, "per hypothesis", the Cause of the world. Now, it is impossible that between cause and effect there be no relation at all. The world cannot be something totally strange to the Creator form which it derives all its being. We must affirm, then, at the same time a great difference, and some resemblance. That is what is meant by the word "analogy" in metaphysics.

Consider for example the relation between a man and his portrait. Of course that they are different things. But not totally. And the man has exerted a sort of causality upon the portrait, by means of the painter. This is more clear, if instead of the portrait we put a photograph.

Again, the relation between this example and the reality of God and his creatures is also an analogy.

So, the notions we use to think about God, that we have obtained from this finite world, are neither identical in their meaning, when applied to God, nor completely equivocal. They are analogous, in the sense just mentioned, that has nothing to do with the "analogous reasoning" that is sometimes mentioned in logic.

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In the case of materialism, we should have to be able to show in a deductive way that the concept of "matter" is implied in the concept of "existence", and so, a non material existence would be contradictory.

The job will be then to deduce the notion of "matter" from the notion of "existence". The syllogism will be: "Every existent is X. Every X is material. Then, every existent is material." Then, will follow the negation looked for: nothing that is not material exists.

But the problem here is to find that "X".

It will not do, as we have said, to say that every existent in our experience is material. First, we have experience of our own inner world not in terms of materiality. I talk of experience, not of philosophical theories about the inner world, or even about the non existence of the inner world.

Second, the conclusion then could only be: "Then, every existent in our experience is material", which is not a true expression of materialism, since materialism is a thesis about the whole of existence, not only about the existence found in our experience.

And if we said that the whole of existence is the existence found in our experience? Well, that should have to be proved, also. Of course induction is of no use here, that would beg the question. It would be like saying that there is not more being or reality that which is found in our experience, because we have not found in our experience a being that were not part of our experience. We would be proving that experience is everything on the basis that experience is everything.

As to the syllogism, it would have to be: "Every existent is Y. Every Y is found in our experience. Then, every existent is found in our experience".

Now the difficulty is to find the "Y".

Again, the nexus between "existent" and "Y" cannot be based only on experience. That would lead us again to an inductive argument disguised as a deductive one. And the same is true for the nexus between "Y" and "found in our experience".

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As to the continuation of the article, Carrier says, following the above mentioned method of "reductio ab absurdum":

7) "Christian Theism in its most basic sense entails observations that would necessarily be made by everyone everywhere and at all times, and thus it is as easily disproven as the alien in the bathtub. For instance, God is theoretically omnipresent, and granted us the ability to know him (to feel his loving presence, etc.), yet I have absolutely no sensation of any God or anything that would be entailed by a God, even though the theory states that he is within me and around me wherever I go."

Here the "prediction" does not follow from the "theory". The "ability to know God" such as the "theory" exposes, does not include necessarily "to feel his loving presence". That is left, on the whole, to the mystics. We ordinary human beings, says the "theory", can know God either by philosophical reasoning, or by faith in His words. Now, faith to a witnessing doesn't need to imply an emotional response, as it doesn't imply it in the law - courts, and even if it did, the "feeling" is not the reason that validates the witnessing.

Finally, the possibility of experiencing the love of God is closely related to our own attitude of love and humble respect towards Him, and has not the form of a physic law, as could be expected in a relation between personal beings.

If we are to drive "predictions" from the "theory", then we must take as starting point the theory itself, and as a whole, and not a part of it, or a part of another thing. Now, the "theory" now in case says that God is not subject to sense perception. Then, the precedent "prediction" does not follow from it.

Carrier adds:

8) "Likewise, God is theoretically the epitome of compassion, and also all-knowing and all-powerful and beyond all injury, yet I know that what demonstrates someone as compassionate is the alleviation of all suffering known to them and safely within their power to alleviate. All suffering in the world must be known and safely within the power of God to alleviate, yet it is still there, and since the Christian theory entails the opposite observation, Christianity is false."

Here, one of the premises of the "prediction" is wrong:

"what demonstrates someone as compassionate is the alleviation of all suffering known to them and safely within their power to alleviate."

The dentist doesn't alleviate all suffering to its patients, and is within his power to do it: he can just leave medicine and start another job. But this does not allow us to say that he is not compassionate.

A father who does not allow his son to go to play because he has to do his homework could safely alleviate his son's suffering by forgetting all about school. But if he does not do so, we do not call him uncompassionate.

Carrier will say that nor the father nor the dentist are Omnipotent. But then his premise should be:

"What demonstrates someone as compassionate is that he, in case of being at the same time Omnipotent, alleviates all suffering known to him, which is safely within his power to alleviate".

But now the premise is not any more an empirical truth. It expresses only Carrier's personal theory of Omnipotence, that is, Carrier's personal theory of Divinity. Since we have not an empirical knowledge of Omnipotence, as we have of dentists and fathers, we cannot state with the same assurance the relation between Omnipotence, Compassion, Wisdom, and Alleviation, and the conclusions that follow from it.

Specially because, "per hypothesis", we cannot know completely God's wisdom. Now, to say that a certain mode of behaving is the only adequate one, even to God, is to forget that. How many times we have been mistaken in our interpretation of the conduct of other men as we are? How much more peril of such a mistake is in the case of the transcendent God? A child could think that the dentist is a bad man, because he makes him suffer. But at least the child and the dentist are into the limits of the same human species, while God transcends all created things.

Or Carrier will say that to alleviate the patient's suffering is not within the power of the dentist, nor alleviating his son's suffering with homework is in the father's power, supposed that they want the end, that is, health or education.

But this is just another way of referring to Omnipotence. If they were Omnipotent, they could get the end, without such means. And then, the compassion would lead them to alleviate all suffering. But here we are again building a theory of Omnipotence, that is not any more an empirical truth, as we have said.

And again the author says:

9) "Likewise, God theoretically designed the universe for a moral purpose, but the universe lacks moral features-animals thrive by survival of the fittest, not survival of the kindest, and the laws of physics are no respecter of persons, they treat the good man and the bad man equally."

Here also one of the premises of the "prediction" is wrong. In the most possibly moral universe, animals and laws of nature would not be moral agents. As to God, of course he is a moral agent, but then we are carried back to the argument from compassion, alleviation, and omnipotence.

He keeps on arguing that:

10) "Moreover, the universe behaves like a mindless machine, and exhibits no intelligent action of its own accord, and there are no messages or features of a linguistic nature anywhere in its extra-human composition or behavior, such as we would expect if a thinking person had designed it and wanted to communicate with us."

Again the "prediction" does not follow from the "theory".

The fact of a machine being intelligently made does not imply that the machine be intelligent .

The fact of a machine being "mindless" does not imply, as Carrier wants to make us think, that his maker is mindless, or that the machine has no maker. All machines that I know are at the same time mindless, very intelligently made, and made by an intelligent being.

A machine is not in need of exhibiting "intelligent action of its own accord" in order to show that it is intelligently made. No intelligently made machine that I know possesses that fantastic quality.

But Carrier says that:

11) "There are no messages or features of a linguistic nature anywhere in its extra-human composition or behaviour, such as we would expect if a thinking person had designed it and wanted to communicate with us".

One wonders why the linguistic messages should came only from the extra-human composition of the Universe. There are linguistic messages from within humanity, that pretend to be the messages of the Divine Revelation by human intermediaries.

Of course, Carrier will say that such pretended Revelation is false. ¿On which grounds? The complete argument now in question would be:

"If there were a God, there would be a linguistic message. Now, there is not such linguistic message, because Revelation is false. So, Revelation is false and there is not a God."

But we cannot use the fact of Revelation being false as a proof of Revelation being false. And if we said that Revelation must be false, since we have proved that there is not a God, we must remember that such a "proof" was made here on the ground of Revelation being false.

This is then a circular argument that, left to itself, doesn't prove anything.

More still: there is a non-linguistic message coming from the extra-human part of the Universe, and is exactly the character of an intelligently made, mindless machine that the Universe has. Precisely, if the Universe is "mindless", then the superb intelligence of its design does not came from itself, nor from us, but from the Supreme Mind of the Creator.

I think that this last has not reply.

Here Carrier asks for something that is not necessary (that the message be "linguistic") or asks for it where it is not necessary to ask for it (in the "extra - human" part of the Universe). The most curious thing is that both things exist, only in another place or way different from that which Carrier wants. It looks exactly as if the requirements of his argument had been carefully arranged in order to make impossible the affirmation of God.

He then says that:

12) "Christians attempt to preserve their theory by moving it into the set of unprovables that lack all evidence. They do this arbitrarily, and for no other reason than to save the theory, by creating impassable barriers to observation, just as requiring us to look in every corner of every universe creates an impassable barrier for one who is asked to decisively disprove the statement "there are big green Martians."

There do exist impassable barriers to observation, that are not arbitrary. For example, we cannot observe the past, nor the future. For the past we have memory and reconstruction, for the future, forecast and speculation, but for none of them do we have observation. We cannot observe all the simultaneous facts that occur a given instant in the Universe. We can only observe a very little part of the present, that immediately becomes past.

Again, nothing makes it urgent for me to disprove that "there are big green Martians". But if I put myself to it, and there is not a deductive argument at hand (for example, that the concept of "big green Martian" were contradictory), then I have no other way to do it that to look in the whole Universe. And that is not enough, because the Martian could take care of not being precisely in the place where I am going to look at a given moment. I should have to be able to see every corner of the Universe at the same time. That is really an impassable barrier, but nobody has created it. It is just so.

As to the unobservable character of God, is one of the few things in which all philosophers, or at least, the most of them, agree. It is not an arbitrary move in order to prevent objections. It is a primary truth, logically deducible from the supreme excellence of the divine Being. But of course, that implies metaphysics. Let us only say that the Absolute, and the Infinite, cannot be caught from a perceptive standpoint.

Carrier goes on saying:

13) "For instance, the advanced theory holds that God alleviates suffering in heaven, which we conveniently cannot observe, and he has reasons for waiting and allowing suffering to persist on Earth, reasons which are also suitably unobservable to us, because God chooses not to explain them, just as he chooses, again for an unstated reason that is entirely inscrutable, to remain utterly invisible to all my senses, external and internal, despite being always around and inside me and otherwise capable of speaking to me plainly."

Here there is a mix of two different kind of things: 1) Things that depend on God's will, as communicate or not the reasons of what He does or leaves to do. Even here we could also say that some of such reasons are not accessible to our mind in our present state, and can only be communicated to us in Heaven. This would lead us to 2) Things that do not depend on God's will, as to be invisible to the human eye, and imperceptible to the other human senses, external, and internal.

The second kind of things depend, not on God's will, but on God's mode of being, on God's nature. They do not depend on a character of reality exterior to God and imposed to him. As St. Thomas teaches, God is his own nature. God is not a being between the others: He is the Being that is also the Source of being for every other being distinct from Himself. That means that the characters of created reality follow from the characters of God, even if they not always follow from the will of God. It depends on God's will if there are other things besides God, or not. But it does not depend on God's will that every other existent being be defined by its degree of likeness with God's essence.

As to Omnipotence, it means, exactly, "the power to do anything that is not contradictory and absurd". It cannot mean "the power to create the square-circle", but then I don't see why should it mean so. We talk of Omnipotence in reference to what we consider the limitations of our created power. But we do not think that the incapability of making the square-circle is one of our limitations.

Now, a God who were perceptible by the senses, or completely intelligible to the finite creature, or even completely dependent on His own free will, would be of the same kind of contradictory absurd as the square-circle.

Carrier says that:

14) "Christianity is the proposal of a theory, and like all theories, it entails predictions-but these predictions are not being born out."

First of all, "Christianity" is not the proposal of a theory, but the acknowledgment, through faith in witnessing, of a fact: the Revelation of God in human history, that is, in the history of Israel and the history of Christ.

This is important, even for unbelievers. For it is important even for those who discuss it, to know the exact nature of the Christian claim. The main claim of the Christian faith is not that the Universe is such and such (that is what is commonly understood by a "theory"). The main claim of our faith is that something has happened in this planet: God has come between us, to talk with us, in the person of Jesus Christ. Of course, this main statement implies a lot of statements about the Universe; the first of them is that there is a God.

A fact like this must be accepted or rejected on the grounds of the testimonies we have about it, but it can never be a question of wanting to understand it perfectly before accepting o rejecting it. That is not the way with facts, nor with alleged facts. Electricity was an accepted fact much before being an explained fact. And facts have the power to sometimes change our ideas about reality.

The existence of the Universe is an undeniable fact, but is not a completely understood fact. As someone once said: "Things would be more scientific if nothing existed". With the difference of supporting his acceptance on faith and not in perception, the attitude of the Christian with respect to the Christian fact is much the same as the attitude of the scientist with respect to the Universe.

In second place, even if we choose to consider it a "theory" in order to discuss it, we must be sure of having drawn correctly the predictions, which has not been the case up to now.

So, Carrier continues:

15) "So Christians invent excuses to save the theory-excuses which have absolutely no basis in any evidence or inference, except the sole fact that they rescue the theory. This is Ptolemy's hypercycles all over again: the motions of the planets and sun refused to fit the theory that they all revolve around the Earth, so Ptolemy invented numerous complex patterns of motion that had no particular reason to happen other than the fact that they rescue the theory of geocentricity. It is simply far wiser to conclude that instead of this monstrously complex and bizarre architecture of groundless saving suppositions, it makes far more sense, and uses far fewer suppositions, to simply admit that the universe doesn't revolve around the Earth after all."

The error of Ptolemy was not to try to save his theory. Every scientist does that. His error was that his theory was not worth being saved. But he probably could not know it, living so much time before Copernicus and Kepler.

If we get to have a reasonably good theory that explains the most of the facts known to us in a certain field, it would not be reasonable to throw it away at the first little and obscure difficulties. Nobody does that, nor Einstein, nor Planck, nor Mach, nor Hawkings. Of course common sense tells us that a firmly assented truth must be defended against objections, that it is much more probable that such objections came from our ignorance or lack of understanding. It is only when the fight against the difficulties becomes desperate, that good sense tells us to begin looking for another theory.

The arguments of Zeno "proving" that movement does not exist could not be answered by many of his adversaries. But he did not get much more followers for that, and that is a proof of the good sense of the Greeks.

On the contrary, Aristotle made up all his philosophy as an immense "excuse" for the "theory" of movement, because he felt that such a basic truth could not be thrown away.

And even Copernicus's theory, and indeed, every scientific theory, could be seen as an immense excuse for the primary theory that reality is understandable by the human intellect.

The important thing here is not if theories are so "excused" or not, but if the grounds to affirm the theory are good, and if the answer to the difficulties is effective.

It is true that "effectiveness", in some fields, is related to "simplicity". Ptolemy's theory revealed its falsehood in part by its complications, not directly based in evidence. But for the trained believer, the whole set of truths that is laboriously developed by philosophy and theology is like a cascade flowing from a very simple and very profound truth about God. I mean: there are no "hypothesis ad hoc" here, because even the most seemingly opposed truths about God descend logically from the concept of a First Cause, once one accepts to see it in the true light of metaphysics, and cannot be demonstrated as contradictory, even if their complete conciliation remains mysterious.

But Carrier adds:

16) "Of course, even these groundless "solutions" to the Christian theory do not really save the theory, because, to maintain it, at some point you must abandon belief in God's omnipotence-since at every turn, God is forced to do something (to remain hidden and to wait before alleviating suffering, etc.) by some unknown feature of reality, and this entails that some feature of reality is more powerful than God."

This argument supposes that the "feature of reality" in question is different from God itself. But that is not the case. The "feature of reality" that imposes some things to God's will is God Himself, His very being. Now, God is not more powerful that God.

The case is rather this: an absolute freedom of will is a contradictory concept. For it would be, for example, the freedom to be free or not to be free; the freedom to exist or not exist; the freedom to be possible, even if contradictory, and the like. It is impossible to form the concept of a "free will" without some "limitations" as these to its power.

But this does not imply the negation of freedom. It only implies that a free will is the will of a certain being with a certain nature, a nature that is prior to any free willing of the being in question. Such a being could not be free if he had not the nature of a free being. The impossibility of choosing between having been born or not does not take away from me the possibility of choosing between getting married or not.

And I cannot choose between being able to choose or not, because it is logically impossible. But this does not mean that I am not able to choose, rather, it means that I am able to choose by nature, and not by choice.

Being and nature are prior to will and freedom. Not to destroy them, but to make them possible. Nothingness cannot choose.

And Carrier concludes saying that:

17) "And this feature cannot merely be God's moral nature, since if that were his only limitation, there would then be no barrier to his speaking to me or acting immediately to alleviate suffering or designing the universe to have overtly moral or linguistic features, since any truly moral nature would compel, not prevent, such behavior."

Lets go by parts.

It is not God's moral nature, it is God's metaphysical nature. It is His being, that which makes that He be God and not another thing. My impossibility to be seen by nude sight at 10 km of distance has nothing to do with my moral character.

And as to God's "moral nature", again, it is methodologically incorrect to draw conclusions about the transcendent Being on the only basis of our knowledge (or our opinions) about non transcendent beings, as I have said above.


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