debate with g. oppy 1

8/9/2019 Debate with G. Oppy 1

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Dear professor Oppy,

I have crafted this "a priori " argument that aims to prove the necessary existence of God. I submit it to your consideration, so any critique is welcome.

Best regards,

Daniel

* * *

Definition 1

Possible is what can be thought without contradiction.

Thought by whom? Surely there should be no mention of thought in this definition.

Thought by any rational being. Even if I didn't mention thought expressly in my definition, it would beobvious that when I state that some proposition is non-contradictory (i.e., self-consistent) I imply that itis such for anyone who is able to think about it.

I think that what you have said is ambiguous; more importantly, I think that it fails to meet an importantcondition on definitions.

Perhaps you mean this: p is possible iff for any x, if x is a rational being, then it is possible that x believesthat p without contradiction.

Or perhaps you mean this: p is possible iff for some x, x is a rational being and it is possible that x believes that p without contradiction.

Either way, the definition is improper, because the term to be defined on the LHS of the definition is usedon the RHS of the definition.

The advantage of omitting mention of rational beings is that you drop modal talk from the RHS of thedefinition. (p is possible iff p is not a contradiction.) Of course, as I go on to note, the resulting definitionis still unacceptable. But at least it doesn't violate one of the formal conditions on proper definitions.

I must admit that you are right here. Then, let's say: "Possible is what entails no self-contradiction".

There are other advantages in not invoking rational beings.

Suppose, for example, that there are rational beings that necessarily lack certain concepts (e.g. becausethose concepts are too complicated from them to grasp). In particular, let's suppose that we lackconcepts of God's intrinsic properties. Suppose, further, that we let "F" stand for one of God's intrinsic

properties. Consider the proposition God is F. Since we cannot grasp this proposition, it is not possiblefor us to believe it without contradiction. So, it is not possible that God is F. That's a very quick proof of the claim that God's nature is perfectly and completely accessible to us, on the first of thedisambiguations given above. Moreover, the second disambiguation won't help unless we suppose thatthere *is* a rational being that possesses all concepts. But to suppose that is surely to go almost all of the way to the conclusion that is supposed to be established by the argument. (By my naturalist lights, itis necessary that there is no rational being that possesses all concepts.)

Ok.

There are well-known objections to the suggestion that "p is possible iff p is not a contradiction".That water is not H20 is no contradiction; but many contemporary philosophers follow Kripke in



thinking that it is necessary that water is H20.

But, since "water " is the layman's name for "H2O ", stating that "it is necessary that water is H2O "equals to say that "it is necessary that water is water ". This would be undeniably true, like everytautology is, according to the principle of non-contradiction.

It isn't true that "water" is just the layman's name for "H2O". The word "water" was in common useamong scientists long before it was discovered that water is H20. If water were just the layman's name for H2O, then it could not have been a substantive scientific discovery that water is H2O. (Instead, everyone

would have recognised this to be a tautology.) If your view of modality turns substantive scientificdiscoveries into tautologies, then your view of modality is just wrong.

I meant that "water " is nowadays the layman's name for "H2O ". But I still don't see how "that water is not H2O " can't be a contradiction even in the past. Water has always been H2O, regardless of what we thoughtof it. Thus, you could only assert that at some time our idea of what water was didn't match its currentdefinition as H2O. Summing up, it is necessary that water is H2O (since water must be water), but it is notnecessary that water exists.

Definition 2

Impossible is what cannot be thought without contradiction.

Definition 3

Necessary is that whose denial cannot be thought without contradiction.

Definition 4

Nothingness is the total absence of matter or energy.

Nothingness would be the total absence of everything (not just the absence of mass-energy).

I disagree. Nothingness, as I define it , is the total absence of matter or energy. If you don't like the word"nothingness" for this definiens, you could commute it for any other one ("absolute lack of a universe",for instance) and the demonstration would still keep all its power.

It is always dangerous to give novel definitions to words in common use. It would have been better tomake up a new word, or else to just use the defining expression -- 'total absence of mass-energy" --throughout.

Really it is not that novel. When Saint Augustine wrote on the "creatio ex nihilo" of the universe, by "nihilo"he meant "total absence of matter ", but not "total absence of anything ", since he assumed God as anecessary being.

Definition 5

The universe is the set of all matter and energy.

(Quibble): The universe is not a set. Sets are abstract entities; the universe is not an abstract entity.

I mean the elements of this set.

I think it would be better to view the universe as the (mereological) *fusion* of its elements. That way, itdoes not come out as an abstract entity.



Ok.

Definition 6

God is the immaterial creator of the universe.

This surely begs the question. Perhaps you might say: IF there is just one immaterial creator of theuniverse, THEN that one is God.

Just by defining God this way I'm not assuming that God exists. I simply assert that, if God existed, itwould need to meet these requirements.

From "God is the F" it follows -- in classical logic -- that there is at least one F. Had you said -- as Isuggested -- that, if there is exactly one F, then God is the F, then your definition would have been fine.

Ok, I think this is not substantial anyways.

Definition 7

Opposite is what cannot be thought of as existing alongside with its denial (Either A or ¬A).

I think that you should say: ~(A & ~A). (Of course, classically, this amounts to the same thing. But,for example, intuitionists will baulk at the inference from ~(A&~A) to (Av~A)

Ok.

Axiom 1

The opposite of what is possible is also possible (If A is possible, then ¬A is possible).

False in standard model logics.

Let A = Necc B.

If Poss A, then Poss Necc B. But, in standard modal logics, if Poss Necc B, then Necc B. And, instandard modal logics, if Necc B, then ~ Poss ~ B.

If Poss ~A, then Poss ~ Necc B. If Poss ~ Necc B, then Poss Poss ~B. But, in standard modal logics,if Poss Poss ~ B, the Poss ~ B.

So, if A = Necc B, then Poss A and ~ Poss ~A.

I think that you are misrepresenting my point. I'm stating that, if A is possible, then it is necessarythat ¬A is possible. Otherwise A would be necessary (by Definition 3, which you have accepted as avalid one).

My criticisms of Definition 1 obviously apply equally to Definition 2 and Definition 3. So, no, I did not

accept those definitions as valid. (Sorry for not spelling this out.)

I wasn't convinced by your criticisms when you used the example of water and H2O. But, in any case, couldyou please define " possible", "impossible" and "necessary " in a way that you deem acceptable?

And, no, I have not misrepresented your point. You say: if A is possible, then it is necessary that ~A is



possible. I give a counterexample. Suppose that A is of the form Necessarily B. (Suppose, for example,that A is "It is necessary that water is H2O".) For the sake of my example, grant me that it is necessarythat water is H2O. So B is necessarily true (and A is true). Since whatever is the case is possible, A ispossible. That is: it is possible that it is necessary that water is H2O. QUESTION: Is it necessary that ~Ais possible? That is, is it necessary that it is possible that it is not necessary that water is H2O? Bystandard (S5) modal logic, it is necessary that it is possible that it is not necessary that water is H2O isEQUIVALENT TO it is possible that water is not H2O. But we agreed that it is necessary that water isH2O. Contradiction. We have a counterexample to your "Axiom".

I'm a lawyer, not a logician, but I understood what you meant; hence I wrote that you were misrepresentingmy argument. The trickery of your "refutation" is pretty evident: you cannot assume that " A is of the formnecessarily B", since by " possible" I mean "non-contradictory and not necessary ", as I already clarified.

I recommend that you look up a standard textbook on modal logic. (Say: Hughes and Cresswell; or maybe Chellas.)

Thanks.

Axiom 2

What is neither possible nor impossible is necessary (quartum non datur ).

False. Every proposition is either possible or not possible (= impossible). There is no third option.Every necessary proposition is possible. (In standard modal logics, if Necc A, then Poss A.)

That's right, but not every possible proposition is necessary. Then, by " possible" I don't mean just"non-contradictory ", but "non-contradictory and not necessary ". I should specify it in Definition 1 toavoid inconsistency.

It is standard to say that it is CONTINGENT that p if (a) it is possible that p; and (b) it is possible that ~p.

I'm on my right to use my own definitions, as long as I present them with an unequivocal and consistentmeaning.

Every proposition is either necessarily true, contingently true, contingently false, or necessarily false.

If we accept this revision, then we need to go back and reconsider everything to this point.

Look at the revised version of definition 1: p is CONTINGENT iff p is not a contradiction. 2+2=4 is not acontradiction WHENCE it is contingent that 2+2=4. Oops!

I don't accept the revision. So I would say: p is POSSIBLE if p is not a contradiction and is not necessary.2+2=4 is necessary, whence it is not possible that 2+2=4. Obviously, when I say "it is not possible that 2+2=4" I don't mean that it is impossible, but that it is necessary. I use a tripartite distinction and I reach thefollowing consequences:

1) The opposite of what is necessary is impossible.

E.g.: It is necessary that I am alive or not alive; this is incompossible [=opposite] with me being neither alive nor not alive. Therefore, it is impossible that I am neither alive nor not alive.

2) The opposite of what is possible is possible.

E.g.: It is possible that I am alive; this is incompossible with me being not alive. Therefore, it is possible

that I am not alive (that is, that I die).

3) The opposite of what is impossible is necessary.

E.g.: It is impossible that I am neither alive nor not alive; this is incompossible with me being alive or not alive. Therefore, it is necessary that I am alive or not alive.



All this seems to be undeniably true.

(At this point, the "proof" has broken down completely. Of course, you may think that there is some wayof repairing it. If you try, make sure that you go back to the start, and redo the whole thing.)

Now that my definitions are clear, I don't think I need to redo it.

Axiom 3

What is neither impossible nor necessary is possible (quartum non datur ).

True, but unnecessarily complicated. What is not impossible is possible.

Axiom 4

What is neither possible nor necessary is impossible (quartum non datur ).

True, but unnecessarily complicated. What is not possible is impossible.

Proposition 1

Any universe is the opposite of nothingness.

Any universe is AN opposite of nothingness. (As is God. As is anything at all.)

God is not the opposite of nothingness if you define "nothingness" as I did.

Demonstration:

Nothingness is the total absence of matter or energy (by Definition 4). The universe is the set of all matter and energy (by Definition 5). Opposite is what cannot be thought of as existing alongside with its denial (by

Definition 7). Therefore, any universe is the opposite of nothingness.

Proposition 2

Nothingness is possible.

Some think so; many do not. Those who believe in a necessarily existent God CANNOT believe this.

See previous comment.

Demonstration:

Any universe is the opposite of nothingness (by Proposition 1). The opposite of what is possible is alsopossible (by Axiom 1). Any non-contradictory universe is possible (by Definition 1). Therefore, nothingnessis possible.

Proposition 3

An opposite of a possible case cannot be necessary.

Demonstration:

The opposite of what is possible is also possible (by Axiom 1). The possible and the necessary aremutually exclusive in the same event (by Definitions 1, 3 and 7). Therefore, the opposite of a possible casecannot be necessary.

Proposition 4



Any universe is not necessary.

Not if there is just one possible universe. Some determinists believe this.

They surely believe it, but they cannot prove it.

True enough. But there is (almost) nothing substantive in philosophy for which there is proof. Wherethere is serious dispute between philosophers, it is at least London to a brick that there are no proofs.

I think that you are aware of this: your statement "Where there is serious dispute, etc." is a philosophicalone too, and not everyone is disposed to accept it (not me, for instance).

Demonstration:

Nothingness is possible (by Proposition 2). Any universe is the opposite of nothingness (by Proposition 1).The opposite of a possible case cannot be necessary (Proposition 3). Therefore, any universe is notnecessary.

Proposition 5

If the universe is necessary, God is impossible.

Not if it is necessary that God creates the best possible world. (This was Leibniz's view.)

This necessity derives from God's own necessity and perfection. So, even admitting that it is necessarythat God creates such a world, it follows that this world is not necessary by itself, but by God (andtherefore not necessary "strictu sensu ", since it was produced "ex nihilo", from non-existence toexistence, which means that its denial doesn't imply any contradiction at all).

What you say here seems not to make sense, given the earlier definition of "necessity".

Clearly, you can disagree with Leibniz, and deny that it is necessary that God creates the best possibleuniverse (and no other). But, if you grant that it is necessary that God creates the best possible universe(and no other), then you grant that it is necessary that there is just one universe (the best possible one).

Leibniz statement was that, if God created any world, it would be necessary that such world was the bestpossible one. He didn't believe AT ALL that God was metaphysically forced to create the world, sincenothing can force God, which is the greatest power and remains totally unconditioned by any externalfactor. Thus, God is only compelled in some way by his own nature, that is, by his supreme perfection, that

doesn't allow him to produce a world which is not the best.

Leibniz's view is hardly popular; it leaves no room for either divine or human freedom, on standardlibertarian accounts of freedom.

I've been a Leibnizian for the last 13 years, since I am 22, so I don't see myself apostatizing now. Despite of your claim, I can guarantee that his philosophy leaves enough room for a reasonable notion of freedom.

debate with g. oppy 1

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