Author Archives: Daniel Vecchio

Anselm via Camestros

Consider the following conditionally valid categorical syllogism:


P1) All [fictional beings] are [things of which a greater can be conceived].
P2) No [beings that are identical to the being than which none greater can be conceived] are [things of which a greater can be conceived].
C) Some [beings that is identical to the being than which none greater can be conceived] are not [fictional beings] (from 1,2 by Modus Camestros)

Defense of Premises:
P1 is intuitively true in that fictional beings are such that we can always conceive of something greater, including the fact that we could conceive of such a being as having a robust actual or real existence.

P2 is simply analytically true.

However, more needs to be said about the logic of this argument, i.e. is it valid:

Camestros (AEO-2) is conditionally valid on the existence of the minor term (S), which in this case is “beings that are identical to the being than which none greater can be conceived”. This is very interesting because it may help us understand why the ontological argument is thought to “beg the question” of the Anselmian God’s existence. However, I think Anselm would want us to grant that the minor term exists (at least in the understanding). For Anselm, the question is not whether God exists, that much is already certain for anyone who understands his apophatic definition of God that he provides. The question is one of determining the mode of God’s existence.

In this case, I am contrasting a “fictional” and “not fictional” modes. Anselm would contrast “in intellectu, not in re” with “in intellectu and in re“. If we are willing to grant that the minor term, the Anselmian God, exists on some very “thin” notion of existence (e.g. to be the value of a bound variable, or to be the subject of particular quantification), then we should also conclude that the Anselmian God exists in a very thick sense, i.e. exists in reality, or in actuality, or whatever robust way one prefers. That is, if you are prepared to grant that God exists to at least the same degree as Sherlock Holmes or Elsa of Arendelle, then you are committed to a robust theistic position.

A Response to R.T. Mullins’s Argument Against Divine Simplicity

R.T.Mullins raises an interesting argument against classical theism in his article The Doctrine of Divine Simplicity. In the following, I break the argument down into chunks and address some ambiguities that I think are central to assessing the soundness of his argument.  I conclude that, if these ambiguities are resolved in light of a proper exegesis of Thomas Aquinas’s claims about Divine Freedom, the argument is unsound.

First Step:

1) If God is free, then God can refrain from acting to give grace.
2) God is free.
3) Therefore, God can refrain from acting to give grace.
I think we must be careful about what we mean by “can” in (1). From a Thomistic perspective, God’s freedom is not to be construed as a passive potency, but as a possibility grounded in that it is not absolutely necessary, nor impossible. Thomas is clear that the possibilities relevant to God’s creation are not potentials.
God wills this effect, this statement is clearly not necessary but possible, in the same way as a thing is said to be possible, not in reference to a potentiality, but because it is neither necessary nor impossible for it to be, as the Philosopher teaches (6 Metaph.) (Summa Contra Gentiles I.82).
Words like “can” indicate a kind of modality pertaining to δύναμις, which is commonly translated as “power”.  The reference to Aristotle’s philosophical lexicon, i.e. Metaphysics Δ clarifies that we should not think of what God can do in terms of potency at all.  Aristotle writes:
Some things are said to be “impotent” in accordance with this meaning of “impotence,” but others in a different sense, namely “possible” and “impossible.” “Impossible” means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie.And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. “Possible,” then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true. (Metaphysics V.1019b)
With this in mind, let us proceed.

Second Step:

4) If God’s act to give grace is absolutely necessary, then God cannot refrain from acting to give grace.
5) God can refrain from acting to give grace.
6) Thus, God’s act to give grace is not absolutely necessary.
Here, the ambiguities in (4) multiply. A Thomist would say that the act by which God’s grace is given is absolutely necessary, as its end is the Goodness of God. However, within this one act, we can conceptual distinguish the means, which are not absolutely necessary, but are willed only by the necessity of supposition, which is a sort of necessity that is compatible with the contingency of the object and with the freedom of God’s will. In other words, God wills by absolute necessity, but the things that are willed which are other than God are not by absolute necessity. So, if we understand the antecedent in (4) to suppose that the giving of God’s grace is, itself, absolutely necessary, then it would follow that God cannot refrain from it, as the antecedent would be false. Understood this way, a Thomist can grant 4-6.
However, we could also construe the premise this way: (4′) If God’s act, by which he gives grace, is absolutely necessary, then God cannot refrain from acting to give grace. Understood this way, the antecedent is true while the consequent is false, and so the Thomist would deny the premise.
Now, if we understand “cannot” in terms of modalities not pertaining to potency, the premise could be, again, understood as true. For, when the consequent is true, the conditional is true.  However, the Thomist would say that God’s will is absolutely necessary and would even be able to grant that there is no passive potential for God to will otherwise. Yet, if “cannot” is understood in terms of a modality apart from passive potency, i.e. change or motion, as mentioned above, the Thomist would disagree, and the consequent would be false. God wills by absolute necessity, by which grace is given as a means to the end. The “means” is not absolutely necessary nor impossible, thus creation and grace remain possible. We might put it this way: ‘that God wills’ is absolutely necessary, but ‘what God wills’ is not absolutely necessary.
Wherefor since God wills Himself as end, and other things as means to the end, it follows that in regard to Himself He has will only, but in respect of other things choice.  Now choice is always an act of free-will.  Therefore free-will is befitting God (SCG I.88).
Conceptually, Thomas distinguishes the absolute necessity of God willing Himself and God wills things other than himself. Though both are in the totality of His one act of will, those other things are only willed by suppositional necessity (see SCG I.83).
Thus, we cannot determine the truth-value of (4) without these clarifications, and that is sufficient to say the argument is unsound as it stands.

Third Step:

7) God’s existence is absolutely necessary.
8) Anything that is identical to God’s existence must be absolutely necessary.
9) All of God’s actions are identical to each other such that there is only one divine act.
10) God’s act to give grace is identical to God’s one divine act.
11) God’s one divine act is identical to God’s existence.
12) Therefore, God’s one divine act is absolutely necessary.
Again, with the distinctions drawn out above, we should proceed with caution. We can say that God’s one divine act is identical to God’s existence, which is absolutely necessary. However, again, that God knows and wills things other than himself does not mean that he is things other than himself, thus the object of God’s intellect and will can be other-directed, just as God can conceive of things other than Himself precisely because God conceives of His own Essence, which is the cause of all things. So, that God has one divine act is absolutely necessary, but the content of that act, as it pertains to things other than God, is not absolutely necessary, as seen above.  Perhaps this is just to point out that the de dicto necessity that God wills does not entail the de re necessity of what God wills.  A modal fallacy occurs when one attempts to infer necessity through identity and substitution runs the risk of modal fallacies, as pointed out by Christoper Tomaszewski.

Fourth Step:

13) If God’s one divine act is absolutely necessary, then God’s act to give grace is absolutely necessary.
14) Therefore, God’s act to give grace is absolutely necessary.
15) Therefore, God cannot refrain from acting to give grace.
16) Therefore, God is not free.
This is where the problem becomes apparent.  We can grant, in (13) that there is one divine act, and this one divine act is absolutely necessary. We can also say that the content of this divine act includes God’s election to give grace (SCG I.88). But we cannot infer from this that God’s election to give grace is absolutely necessary, but only that the act by which he has elected to give grace was an absolutely necessary act. God had to will, but he did not have to will grace. Could God have refrained? In one sense, yes. It is neither absolutely necessary nor impossible that God provides grace, but there is no sense in which God could have been moved or changed to refrain from providing grace.

Conclusion:

So, my overall assessment is that once these ambiguous premises are clarified, it becomes clear that God can be free, in a sense, while also willing by absolute necessity.  With clarifications in place, premises like (4) and (13) render Mullins argument unsound 1, at least as an internal critique of Thomistic doctrines.  I have said very little about the doctrine of divine simplicity, in this write-up, but I think the problems lie elsewhere.

Further Thoughts on Divine Freedom and Classical Theism:

  1. The free will of God should not be construed like a counterfactual of creaturely freedom where the possibility of doing otherwise = the potential to do otherwise.
  2. Therefore, we should not literally think of God’s freedom to create our world, or alternative possible worlds means that God, in other possible worlds, actualizes a different set of potentials in his will.
  3. Modality, with respect to God, should be understood apophatically, or perhaps analogically. God freely wills creation because he is not necessitated a) by anything external to God, or b) by the end to which God’s will is necessarily directed, viz. God’s own Goodness. Hence, creation is not necessitated. Also, creation is not impossible for God to will, as nothing prevents it. Moreover, if it is insisted that it is impossible for God to will anything contingent, this is only to beg the question, since “contingent” in this context has nothing to do with potentials in God, but the lack of necessity or impossibility for God to will creation.
  4. Thus, for Aquinas, there is a kind of possibility which extends beyond potentiality (which may be a lower grade of possibility). There is the possible, which is neither necessary nor impossible. Aquinas uses de dicto mathematical statements as instances of this: “Possibly, a triangle is isosceles”. This is true even if the de re possibility of a given triangle (the potential) does not exist. So there may not be a possible world where a given triangle is isosceles, but there is no impossibility or necessity that a triangle be isosceles. Likewise, it is possible that God creates our world, or another world, but given God’s actual will, there is no potential.
  5. So, does this mean that creation is contingent or necessary? It seems that creation is necessary, on the supposition of God’s given will. There is no potential that God wills an alternative. Nonetheless, Aquinas thinks that it is illicit to conclude that there is absolute necessity in creation, since there is no antecedent necessity in what God wills with respect to creation. The problem of modal collapse seems to involve a collapse in thinking that “no potential for alternatives” = impossibility of alternatives, and this is just to collapse a level of divine modality relevant in discussing divine freedom.
  6. According to Aquinas (see SCG I.82), God’s will does not have potency (passive potency) with respect to the alternatives of creation. Instead, the alternatives of creation as possibilities with respect to the objects of God’s will (active potency) because God’s will can attain its end perfectly while willing an infinite variety of possible creations.  I suspect that a possibility that is extra-mental must be a passive potency, but a possibility, as it exists in the mind, exists in the activity of the mind and the actual mental object.  Thus, I strongly suspect that without God, a necessarily existing omnipotent mind that is actively aware of all possibilities, the only alternatives are brute facts or modal collapse.
  7. Aquinas’s reference to Aristotle (Metaphysics Δ.1019b) in order to talk about the δύναμις of God shows that we are not talking about motion or chance, both of which Aquinas denies are a part of creatio ex nihilo (see SCG II.17).  This non-potency δύναμις is more of a manifold of logical/conceptual space wherein an object is not necessitated nor impossible, so this does not threaten God’s pure actuality.
  8. Can we still use the semantics of possible worlds?  Here is a suggestion, if we must use possible worlds: we ought to recognize that it is a way to model modal relations.  Relative to creatures, we could grant that there are accessibility relations among possible worlds, as this is just to model the way in which actualities have powers in this world.  Relative to God, we might say that there is no potential world, i.e. possible world accessible to the actual world, where God wills otherwise, though it is possible, with respect to the object of God’s will that creation could have been otherwise. Thus, there are possible worlds were God elects differently (granting the logical/conceptual space that follows from God’s active potency, or omnipotence), but there are not accessibility relations, so these possible worlds are not possible from the vantage-point of the actual world, because there is no potency in God’s active-power to will otherwise.  This, of course, is not due to a limitation in God, but because nothing can move God to will otherwise than he would.
  9. The solution I offer here might, then, block the need to argue that God can will in an exactly identical manner across possible worlds, but with radically different effects.  This preserves the principle of sufficient reason, even in a very strong, contrastive, form (if one chooses to adopt such a strong version of the principle).  However, I suspect some will still insist that the solution is a kind of modal collapse in that there is only one potential world, and that is the actual world.  This, I am willing to grant, because I think it is consistent with Aquinas, fits with apophatic theology, and still provides a way to say that God is free.

1A sound argument is both valid and any premises that it has are true. I would determine this argument as unsound because the ambiguities in the premises make it impossible to judge the truth of the premises. Moreover, it is likely that 13-16 involve a modal fallacy.

Three normative theories overly simplified…

Consequentialism: maximize happiness, even if it means compromising your moral integrity.

Deontology: be worthy of happiness, and damn the happiness for yourself and the world around you.

Virtue Ethics: realize that true happiness is found in pursuing worthiness of happiness.

Anselm without Defining God

One of the most common objections that I hear to my ontological arguments is that they use definitions that beg the question.  However, I am careful to note four things that I think block the charge that I “define God into existence”: 1) I require that stipulated definitions be defended as coherent, 2) I specify that I am setting my arguments within the context of free logic, 3) my definitions cannot directly entail, or be semantically equivalent to the conclusion, and 4) I must provided at least one premise that is justified independently from any definition of God, or from the conclusion.

However, I think the concern over the definition is overblown, and we could just derive the conclusion that there is at most one being such that it is not conceivable that there is something greater.  Call it “God” or “Banana Smoothie”.  It really doesn’t matter.  A term like God is emotionally loaded anyways, so maybe there is some rhetorical strategy in abandoning the word “God” altogether.

Here is the argument:

P1) For all x, if x is that than which none greater can be conceived, and there is some other z, which is that than which none greater can be conceived, and x and z are not the same, then  it is conceivable that there is something that can be combined with x as a mereological sum to make a composite whole of it and x as proper parts.

P2) For all x, and all z1, if it is conceivable that there is some mereological sum, which is the whole composed of x and z1 as proper parts, then conceivably there is some thing greater than x (namely the whole, out of which x is a proper part).

P3) All things that are not fictional beings are things that exist in reality.

P4) All fictional beings are things of which a greater can be conceived.

P5) There is something than which none greater can be conceived and either it is fictional or it is not fictional.

C) There is exactly one being in reality such that it is not conceivable that there is something greater.

We have to at least define some predicates, so let,

Fx ≝ x is a fictional being
Rx ≝ x exists in reality
Gxy ≝ x is greater than y
∑xyz ≝ x is the mereological sum of  the proper parts, y and z
©… ≝ it is conceivable that…

1. (∀x){~©(∃y)Gyx ∧ (∃z)[~©(∃y)Gyz ∧ ~(z = x)]} ⊃ ©(∃z1)(∃y)∑yxz1} (premise)
2. (∀x)(∀z1){©(∃y)∑yxz1] ⊃ ©(∃y)Gyx}(premise)
3. (∀x)(~Fx ⊃ Rx) (premise)
4. (∀x)(Fx ⊃ ©(∃y)Gyx) (premise)
5. (∃x)[~©(∃y)Gyx ∧ (Fx ∨ ~Fx)] (premise)
6. (∃x){~©(∃y)Gyx ∧ (∃z)[~©(∃y)Gyz ∧ ~(z = x)]} (IP)
7. ~©(∃y)Gyμ ∧ (∃z)[~©(∃y)Gyz ∧ ~(z = μ)] (6 EI)
8. {~©(∃y)Gyμ ∧ (∃z)[~©(∃y)Gyz ∧ ~(z = μ)]} ⊃ ©(∃z1)(∃y)∑yμz1 (1 UI)
9. ©(∃z1)(∃y)∑yμz1 (7,8 MP)
10. ©(∃y)∑yμν (9 EI)
11. (∀z1)[©(∃y)∑yμz1 ⊃ ©(∃y)Gyμ (2 UI)
12. ©(∃y)∑yμν ⊃ ©(∃y)Gyμ (11 UI)
13. ©(∃y)Gyμ (10,12 MP)
14. ~©(∃y)Gyμ (7 Simp)
15. ©(∃y)Gyμ ∧ ~©(∃y)Gyμ (13,14 Conj)
16. ~(∃x){~©(∃y)Gyx ∧ (∃z)[~©(∃y)Gyz ∧ ~(z = x)]} (6-15 IP)
17. (∀x)~{~©(∃y)Gyx ∧ (∃z)[~©(∃y)Gyz ∧ ~(z = x)]} (16 QN)
18. (∀x){~~©(∃y)Gyx ∨ ~(∃z)[~©(∃y)Gyz ∧ ~(z = x)]} (17 DeM)
19. (∀x){©(∃y)Gyx ∨ ~(∃z)[~©(∃y)Gyz ∧ ~(z = x)]} (18 DN)
20. (∀x){©(∃y)Gyx ∨ ~(∃z)~[©(∃y)Gyz ∨ (z = x)]} (19 DeM)
21. (∀x){©(∃y)Gyx ∨ (∀z)[©(∃y)Gyz ∨ (z = x)]} (20 QE)
22. (∀x){©(∃y)Gyx ∨ (∀z)[~~©(∃y)Gyz ∨ (z = x)]} (21 DN)
23. (∀x){©(∃y)Gyx ∨ (∀z)[~©(∃y)Gyz ⊃ (z = x)]} (22 Impl)
24. (∀x)(~©(∃y)Gyx ⊃ Fx) (IP)
25. ~©(∃y)Gyμ ∧ (Fμ ∨ ~Fμ) (5 EI)
26. ~©(∃y)Gyμ ⊃ Fμ (24 UI)
27. Fμ ⊃ ©(∃y)Gyμ (4 UI)
28. ~©(∃y)Gyμ ⊃ ©(∃y)Gyμ (26,27 HS)
29. ~©(∃y)Gyμ (25 Simp)
30. ©(∃y)Gyμ (28,29 MP)
31. ©(∃y)Gyμ ∧ ~©(∃y)Gyμ (29,30 Conj)
32. ~(∀x)(~©(∃y)Gyx ⊃ Fx)(24-31 IP)
33. (∃x)~(~©(∃y)Gyx ⊃ Fx)(32, QN)
34. (∃x)~(~~©(∃y)Gyx ∨ Fx) (33 Impl)
35. (∃x)~(©(∃y)Gyx ∨ Fx)(34 DN)
36. (∃x)(~©(∃y)Gyx ∧ ~Fx) (35 DeM)
37. ~©(∃y)Gyμ ∧ ~Fμ (36 EI)
38. ~Fμ ⊃ Rμ (3 UI)
39. ~Fμ (37 Simp)
40. Rμ (38,39 MP)
41. ~©(∃y)Gyμ (37 Simp)
42. ©(∃y)Gyμ ∨ (∀z)[~©(∃y)Gyz ⊃ (z = μ)] (23 UI)
43. (∀z)[~©(∃y)Gyz ⊃ (z = μ)] (41,42 DS)
44. ~©(∃y)Gyμ ∧ (∀z)[~©(∃y)Gyz ⊃ (z = μ)] (41,43 Conj)
45. ~©(∃y)Gyμ ∧ (∀z)[~©(∃y)Gyz ⊃ (z = μ)] ∧ Rμ (40,44 Conj)
46. (∃x){~©(∃y)Gyx ∧ (∀z)[~©(∃y)Gyz ⊃ (z = x)] ∧ Rx} (45 EG)

But now 46 say that there is exactly one being than which none greater exists and it exists in reality.

QED

Suppose we add to our lexicon:

g ≝ (ɿx)~©(∃y)Gyx

Then we could easily reach:

47. Rg (46 theory of descriptions given the def of “g”)

And this is precisely the conclusion I reach here.  So using a definite description at the outset saves space, but requires additional defenses for the premise that are made explicit here.

Vecchio’s Variation on Anselm’s Ontological Argument (VVAOA)

P1) All things that are not fictional are things that exist in reality.
P2) All things that are fictional are such that it is conceivable that there is something greater.
C) God, i.e. the being of which it is not conceivable that there is a greater, exists in reality.

Defense of P1: Fictional and non-fictional are complementary classes, and non-fictional is definitionally synonymous with real. So, if something is not fictional, it is non-fictional, and, thus, real.

Defense of P2: For anything fictional, one can conceive of a concrete correlate. For instance, Platonism is a conceivable metaphysical system in which entities that non-Platonists might conceive of as abstracta are conceived as concrete extra-mental realities that have causal powers. So it is for anyone who conceives of God as a fictional object of thought. One can also conceive God to be a concrete extra-mental reality that has causal powers. Given that one can conceive of a concrete correlate of a fictional being, these correlates will be similar in description except that the latter would be conceived to have causal powers, while the former, as an abstract fiction, would not. Ceteris paribus, if one thing lacks causal powers while the latter has causal powers, the latter is greater than the former, in as much as by ‘greatness’ one should understand ‘greater in capacity, ability, or power’.

The following formal proof shows the above to be valid.
Let,

Fx ≝ x is a fictional being
Rx ≝ x exists in reality
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)~©(∃y)Gyx

1. (∀x)(~Fx ⊃ Rx) (premise)
2. (∀x)(Fx ⊃ ©(∃y)Gyx) (premise)
3. Fg (Assumption Indirect Proof)
4. Fg ⊃ ©(∃y)Gyg (2 by Universal Instantiation)
5. ©(∃y)Gyg (3,4 by Modus Ponens)
6. (∃x){[~©(∃y)Gyx ∧ (∀z)[~©(∃y)Gyz ⊃ (z = x)] ∧ ©(∃y)Gyx} (5 by theory of descriptions)
7. [~©(∃y)Gyμ ∧ (∀z)[~©(∃y)Gyz ⊃ (z = μ)] ∧ ©(∃y)Gyμ (6 by Existential Instantiation)
8. [(∀z)[~©(∃y)Gyz ⊃ (z = μ)] ∧ ~©(∃y)Gyμ] ∧ ©(∃y)Gyμ (7 by Commutation)
9. (∀z)[~©(∃y)Gyz ⊃ (z = μ)] ∧ [~©(∃y)Gyμ ∧ ©(∃y)Gyμ] (8 by Association)
10. ~©(∃y)Gyμ ∧ ©(∃y)Gyμ (9 by Simplification)
11. ~Fg (3-10 by Indirect Proof)
12. ~Fg ⊃ Rg (1 by Universal Instantiation)
13. Rg (11,12 by Modus Ponens)
QED

An Ontological Argument Using Aristotelian Logic

The following argument should receive an Aristotelian interpretation for existential import, but neutral on the question of whether one is discussing fictional or non-fictional existence. This is in-line with the Anselmian point that the question isn’t whether God exists, but the mode of God’s existence, i..e in reality or in the understanding alone:

1) All fictional beings are things of which a greater can be conceived (premise).

2) No being that is identical to the being than which none greater can be conceived is a thing of which a greater can be conceived (premise).

3) No being that is identical to the being than which none greater can be conceived is a fictional being (from 1,2 by Modus Camestres).

4) Some beings that are identical to the being than which none greater can be conceived are not fiction beings (from 3 by Sub-Alternation).

5) Some beings that are identical to the being than which none greater can be conceived are non-fictional beings (from 4 by Obversion).

6) There is some x, such that x is identical to the being than which none greater can be conceived and x is non-fictional (from 5 by Semantic Equivalence).

QED

The Aptness of the Ontological Argument

There is a kind of abductive argument from aptness, or fittingness, that some philosophers and theologians have employed in the past.  For example, Bl. Duns Scotus develops an argument for the Immaculate Conception from its fittingness.

What is aptness?  It seems to be an explanatory feature like parsimony, or conservativeness.  It is something that, were we to discover its truth, we would not be surprised, given what we presently understand of the topic.  Moreover, in contemplating the aptness of a hypothesis, one has a sense that such a truth, though unsurprising, is nonetheless illuminating.

Now, the aptness of a hypothesis, insofar as it seems to be an abductive explanatory feature, does not appear to be the intuition of merely an analytical or tautological truth, even, say, within counterfactual contemplation.  For example, I wouldn’t really say that it is apt that, should there be a sound proof that the Goldbach conjecture be true, that the proof would be mathematical in nature.  For, to say that is just really to state the implicit tautology that if there is a sound mathematical proof for x, then there is a sound mathematical proof for x, and tautologies like that are not, in any way, illuminating, which is at least part of what we mean by “apt.”

I have explained aptness through a kind of subjunctive conditional, i.e. ‘if x were true of y, it would be apt that x is true of y.’  That alone might be some reason to think it is probable that x is true of y.  However, if there is also evidence that is consistent with the claim of aptness, it would be reasonable, all the more, to increase the likelihood that x is true of y.

So, what of the ontological argument?  Or more precisely, what of a priori arguments that purport to establish the existence of God, i.e. a maximal great, supreme, or perfect being.  It seems apt that if any concrete object should be established solely through a priori considerations, then God would be a candidate.  Nay, given the supposed chasm between creature and creator, it is apt that, among concreta, God alone should be proved to exist solely by a priori considerations.

Put in terms of our formula, we could say, “If God alone, among concreta , could be proved to exist solely by a priori considerations, then it would be apt that God alone, among concreta, can be proved to exist solely by a priori considerations.”  And this might be some reason to think a version of the ontological argument is plausible.  Now consider the evidence in support of the hypothesis — i.e. the lack of ontological arguments for any other concrete objects (leaving aside the possibility of ontological arguments for objects in an abstract realm), and the plethora of candidate ontological arguments for a supreme being.  These facts of philosophical history, that ontological arguments seem only to be suited to establish the existence of God, I would contend, a good abductive reason to think it is plausible that there be a sound ontological argument.

Perhaps, though, you are not moved that the aptness of the ontological argument should makes us think that such an argument is probably sound.  Aptness may still be sufficient to establish the soundness of an ontological argument.  How so?  Well, it seems to me that if we should think that a feature increases the probability of a hypothesis this entails not that it is broadly logically possible, but that we should think it is broadly logically possible.  That is, if our considered judgment is that we think there is evidence for a hypothesis, which increases the likelihood of that hypothesis, then we are committed to thinking the prior probability of the hypothesis is not 0.  This does not establish that a sound ontological argument is, in fact, possible, but that one who is committed to their being evidence for a sound ontological argument is, in fact, committed to the real possibility for it.  But then, if one thinks such an argument is possible, one should also think such an argument, in fact, exists.

We might reason as follows:

P1. If one should think there is good evidence to support the claim that it is apt that God alone, among concreta, can be proved to exist solely by a priori considerations, then one should think that the probability of the hypothesis ‘God alone, among concreta, can be proved to exist solely by a priori considerations’ has increased.
P2. If one should think that the probability of the hypothesis ‘God alone, among concreta, can be proved to exist solely by a priori considerations’ has increased, then one should think that it is broadly logically possible that God alone, among concreta, can be proved exist solely by a priori considerations.
P3. If one should think that it is broadly logical possible that God alone, among concreta, can be proved exist solely by a priori considerations, then one should think that, in fact, God alone, among concreta, can be proved exist solely by a priori considerations.
P4. One should think there is good evidence to support the claim that it is apt that God’s existence alone, among concreta, can be proved to exist solely by a priori considerations.
C.  So, one should think that, in fact, God alone, among concreta, can be proved to exist solely by a priori considerations.

Defense of the premises:

In defense of P1, one can say that to have good evidence to support the explanation for a hypothesis just is to make that hypothesis more likely than it otherwise would be.  We can simply stipulate that this is what we mean by good evidence, i.e. it is sufficient to imply the plausibility of the hypothesis in question.

In defense of P2, we are not actually, as some might fear, shifting from epistemic possibility to broad logical possibility, strictly speaking.  We are couching this implication within what one should think, given one’s epistemic duties. Whether or not something is, in fact, broadly logically possible, if one thinks something is not, a priori impossible, one cannot, rationally, at the same time remain agnostic to its broad logical possibility.  To think that a hypothesis might become more likely, given the evidence, entails that one, thinking appropriately, also thinks the hypothesis is inherently possible.  Otherwise, no evidence would improve the probability.  Hence, the rational person who thinks there is evidence that is suggestive some sound ontological argument, that person ought to think that such an argument is really possible, in a robust sense.

For P3, I would simply note that, given the fact that a priori ontological arguments derive modally necessary conclusions, from a priori necessary truths.  Such an argument would, in effect, be sound across possible worlds.  Indeed, the very counterfactual I have contemplated in this post “If God alone, among concreta , can be proved to exist solely by a priori considerations, then it would be apt that God alone, among concreta, can be proved to exist solely by a priori considerations” could be assessed as true, like other subjunctive conditionals, in terms of possible worlds, e.g. in the nearest possible world where God alone, among concreta, can be proved to exist solely by a priori considerations, it is explanatorily fitting and apt that such is the case, and that is just to affirm P3.

Finally, P4 is based on the above considerations.  I think it is basically intuitive that it should be apt that the ontological argument should work only for God, and for no other concrete object.  The fact that there have been dozens of formulations of the ontological argument that are, at the very least, plausibly sound, and no ontological argument for any other concrete thing only goes to support this aptness, and so make this aptness not only likely, but provide abductive support for one to embrace the possibility of some sound ontological argument for God.  Now, one might say that there are evidential matters to consider, but I am not compelled to think so.  If Plantinga’s own version of the argument is correct, then the possibility of a maximally great being is at least reasonable to believe on its own.  Moreover, there appears to be substantive responses to arguments for the incoherence of theism, and I take that to be the primary counter-evidence to the ontological argument.  Given that, I think the aptness of the ontological argument, and the evidential support for it, is sufficient to make it plausible that there is sound ontological argument.

From this, it follows that we should think God exists.

QED

De Ente and the Falsity of Naturalism

Thomas Aquinas writes:

…[E]verything that is in a genus has a quiddity beyond its existence, since the quiddity or nature of the genus or species is not in the order of nature distinguished in the things of which it is the genus or species, but the existence is diverse in diverse things (De Ente V.).

Given some basic modal theorems and axioms, and the above considerations, the following argument occurred to me:

P1. If naturalism is true, everything is in the genus “nature”.
P2. If everything is in the genus “nature”, then everything has a quiddity beyond its existence.
P3. Necessarily, if there is some x such that its quiddity is nothing other than its existence, then necessarily there is some x such that its quiddity is nothing other than its existence.
P4. If there is something x such that its quiddity is nothing other than its existence, then not everything has its quiddity beyond its existence.
P5. Possibly, there is some x such that its quiddity is nothing other than its existence.
C. It is not the case that naturalism is true.

Defense of P1: Naturalism just is the thesis that everything that exists is natural, and so belongs to the generic class “nature”.

Defense of P2: According to Aquinas, if the quiddity, or essence, of a thing is in a genus, then its quiddity cannot be its existence, since a genus admits of more than one instance, and whatever has its existence as its quiddity cannot admit of more than one instance.

Defense of P3: If something has its existence as its quiddity, then it has existence per se and so necessarily so.  This is necessarily implied, since it is analytically true.

Defense of P4: This would be based on the notion that if a quiddity is the same as its existence, then its quiddity would not also be beyond its existence, for then the quiddity and existence could not be the same.

Defense of P5: This is just to say that it is at least metaphysically possible that something’s quiddity and facticty are the same.  There does not appear to be anything impossible about such a notion, at least prima facie.

Formal Proof:

Let,

N ≝ Naturalism is true
Gxy ≝ x is in the genus y
Q(F,x) ≝ F is ths quiddity of x
B(F,G,x) ≝ F is beyond G for x
E! ≝ existence
n ≝ nature
Theorem of K: ☐(p → q) → (♢p → ♢q)
Theorem of S5: ♢☐p → ☐p
Axiom M: ☐p → p

1. N → (∀x)Gxn (premise)
2. (∀x)Gxn → (∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (premise)
3. ☐{(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)} → ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}} (premise)
4. (∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)} → ~(∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (premise)
5. ♢(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)} (premise)
6. N → (∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (1,2 HS)
7. ☐{(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)] → ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}} → {♢(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}} (Theorem of K)
8. ♢(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (3,7 MP)
9. ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (5,8 MP)
10. ♢☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (Theorem of S5)
11. ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}(9,10 MP)
12. ☐(∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} → (∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]} (Axiom M)
13. (∃x){[Q(E!,x)∧(∀F)~(F = E!)]→ ~Q(F,x)]}(11,12 MP)
14. ~(∀x)(∀F)[(Q(F,x) → B(F,E!,x)] (4,13 MP)
15. ~N (6,14 MT)

QED

Physicalism v. Hylomorphism

3jqqon.jpg

Well, he didn’t

Let

Fx ≝ x is a financier
Rxy ≝ x ran a sex trafficking ring out of y
Kxy ≝ x killed y
j ≝ (ɿx)(Fx ∧ Rxl)
l ≝ Little St. James Island

1. ~(∃x)[(Fx ∧ Rxl) ∧ Kxx](premise)
2. Kjj (Assumption for Indirect Proof)
3. (∃x){[(Fx ∧ Rxl) ∧ (∀y)[(Fy ∧ Ryl)→ (y = x)] ∧ Kxx} (2 theory of descriptions)
4. [(Fμ ∧ Rμl) ∧ (∀y)[(Fy ∧ Ryl)→ (y = μ)] ∧ Kμμ (3 EI)
5. (∀x)~[(Fx ∧ Rxl) ∧ Kxx] (1 QN)
6. ~[(Fμ ∧ Rμl) ∧ Kμμ] (5 UI)
7. [(Fμ ∧ Rμl) ∧ (∀y)[(Fy ∧ Ryl)→ (y = μ)] (4 Simp)
8. Fμ ∧ Rμl (7 Simp)
9. Kμμ (4 Simp)
10. (Fμ ∧ Rμl)∧ Kμμ (8,9 Conj)
11. [(Fμ ∧ Rμl)∧ Kμμ] ∧ ~[(Fμ ∧ Rμl) ∧ Kμμ] (6,10 Conj)
12. ~Kjj (2-11 Indirect Proof)

QED