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A Remix of Anselm’s Conceptual Ontological Argument

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D1. God is defined as the x such that there is not something, y, where y is conceivably greater than x.
P1. For all x, if x is conceivable, then there is something, y, such that either y is identical to x and y exists or there is something, z, such that z is identical to x, z does not exist, and y is conceivably greater than z.
P2. There is some x such that x is conceivable and it is not the case that there is some y such that y is conceivably greater than x.
P3. For all x and y, either x is conceivably greater than y or y is conceivably greater than x, or if it is not the case that either x is conceivably greater than y or that y is conceivably greater than x, there is some z such that z is the mereological sum of x and y, and either z is conceivably greater than x or z is conceivably greater than y.
C. God exists.1

E!x ≝ x exists
Cx ≝ x is conceivable
Gxy ≝ x is conceivably greater than y
σ<x,y> ≝ the mereological sum of x and y
g ≝ (ɿx)~(∃y)Gyx

1. (∀x){Cx ⊃ (∃y){[(y = x) ∧ E!y] ∨ (∃z)[(z = x) ∧ (~E!z ∧ Gyz)]}} (premise)
2. (∃x)(Cx ∧ ~(∃y)Gyx) (premise)
3. (∀x)(∀y){[Gxy ∨ Gyx] ∨ {~(Gxy ∨ Gyx) ⊃ (∃z)[(z = σ<x,y>) ∧ (Gzx ∨ Gzy)]}} (premise)
4. Cμ ∧ ~(∃y)Gyμ (2 EI)
5. ~(∃y)Gyμ (4 Simp)
6. (∃z)[~(∃z1)Gz1z ∧ ~(z = μ)] (IP)
7. ~(∃z1)Gz1ν ∧ ~(ν = μ) (6 EI)
8. (∀y){[Gνy ∨ Gyν] ∨ {~(Gνy ∨ Gyν) ⊃ (∃z)[(z = σ<ν,y>) ∧ (Gzν ∨ Gzy)]}} (3 UI)
9. [Gνμ ∨ Gμν] ∨ {~(Gνμ ∨ Gμν) ⊃ (∃z)[(z = σ<ν,μ>) ∧ (Gzν ∨ Gzμ)]} (8 UI)
10. (∀y)~Gyμ (5 QN)
11. ~Gνμ (10 UI)
12. ~(∃z1)Gz1ν (7 Simp)
13. (∀z1)~Gz1ν (12 QN)
14. ~Gμν (13 UI)
15. Gνμ ∨ [Gμν ∨ {~(Gνμ ∨ Gμν) ⊃ (∃z)[(z = σ<ν,μ>) ∧ (Gzν ∨ Gzμ)]}] (9 Assoc)
16. Gμν ∨ {~(Gνμ ∨ Gμν) ⊃ (∃z)[(z = σ<ν,μ>) ∧ (Gzν ∨ Gzμ)]} (11,15 DS)
17. ~(Gνμ ∨ Gμν) ⊃ (∃z)[(z = σ<ν,μ>) ∧ (Gzν ∨ Gzμ)] (14,16 DS)
18. ~Gνμ ∧ ~Gμν (11,14 Conj)
19. ~(Gνμ ∨ Gμν) (18 DeM)
20. (∃z)[(z = σ<ν,μ>) ∧ (Gzν ∨ Gzμ)] (17,19 MP)
21. (ζ = σ<ν,μ>) ∧ (Gζν ∨ Gζμ) (20 EI)
22. Gζν ∨ Gζμ (21 Simp)
23. ~Gζμ (10 UI)
24. Gζν (22,23 DS)
25. ~Gζν (13 UI)
26. Gζν ∧ ~Gζν (24,25 Conj)
24. ~(∃z)[~(∃z1)Gz1z ∧ ~(z = μ)] (6-23 IP)
25. (∀z)~[~(∃z1)Gz1z ∧ ~(z = μ)] (24 QN)
26. (∀z)[~~(∃z1)Gz1z ∨ ~~(z = μ)] (25 DeM)
27. (∀z)[~(∃z1)Gz1z ⊃ ~~(z = μ)] (26 Impl)
28. (∀z)[~(∃z1)Gz1z ⊃ (z = μ)] (27 DN)
29. {Cμ ∧ ~(∃y)Gyμ} ∧ (∀z)[~(∃z1)Gz1z ⊃ (z = μ)] (4,28 Conj)
30. Cμ ∧ {~(∃y)Gyμ ∧ (∀z)[~(∃z1)Gz1z ⊃ (z = μ)]} (29 Assoc)
31. {~(∃y)Gyμ ∧ (∀z)[~(∃z1)Gz1z ⊃ (z = μ)]} ∧ Cμ (30 Comm)
32. (∃x){~(∃y)Gyx ∧ (∀z)[~(∃z1)Gz1z ⊃ (z =x)]} ∧ Cx} (31 EG)
33. Cg (32 theory of descriptions)
34. Cg ⊃ (∃y){[(y = g) ∧ E!y] ∨ (∃z)[(z = g) ∧ (~E!z ∧ Gyz)]} (1 UI)
35. (∃y){[(y = g) ∧ E!y] ∨ (∃z)[(z = g) ∧ (~E!z ∧ Gyz)]} (33,34 MP)
36. [(ξ = g) ∧ E!ξ] ∨ (∃z)[(z = g) ∧ (~E!z ∧ Gξz)] (35 EI)
37. (∃z)[(z = g) ∧ (~E!z ∧ Gξz)] (IP)
38. (ν = g) ∧ (~E!ν ∧ Gξν) (37 EI)
39. ~E!ν ∧ Gξν (38 Simp)
40. Gξν (39 Simp)
41. (ν = g) (38 Simp)
42. Gξg (40,41 ID)
43. (∃x){~(∃y)Gyx ∧ (∀z)[~(∃z1)Gz1z ⊃ (z = x)]} ∧ Gξx} (42 theory of descriptions)
44. {~(∃y)Gyζ ∧ (∀z)[~(∃z1)Gz1z ⊃ (z = ζ)]} ∧ Gξζ (43 EI)
45. ~(∃y)Gyζ ∧ (∀z)[~(∃z1)Gz1z ⊃ (z = ζ)](44 Simp)
46. ~(∃y)Gyζ (45 Simp)
47. (∀y)~Gyζ (46 QN)
48. ~Gξζ (47 UI)
49. Gξζ (44 Simp)
50. Gξζ ∧ ~Gξζ (48,49 Conj)
51. ~(∃z)[(z = g) ∧ (~E!z ∧ Gξz)] (37-50 IP)
52. (ξ = g) ∧ E!ξ (36,51 DS)
53. (ξ = g) (52 Simp)
54. E!ξ (52 Simp)
55. E!g (53,54 ID)

QED

1 Some aspects of this argument are influenced by Oppenheimer & Zalta (1991), i.e. the existential quantifier carries no existential import and is analogous to Anselm’s existence in intellectu whereas E! is a predicate that indicates existence in re. One weakness of Oppenheimer & Zalta’s argument is that it depends on a non-logical axiom regarding Gxy such that it is connected. In other words, either Gxy or Gyx or (x = y). This requires all individuals to stand in a greater than relationship. It is plausible, though, that two non-identical individuals could share equal greatness. I am able to derive the uniqueness of the being than which none greater can be conceived by appealing to the notion that the merelogical composite of two equally great individuals is at least greater than one of its proper parts, which I take to be a modest premise. The interesting thing about my formulation is the first premise, which distinguishes in intellectu from in re existence, and captures Anselm’s claim that a greater could be conceived than a being that exists in the understanding alone without begging the question that this greater thing actually exists—it is merely conceptually greater.  See P.E Oppenheimer & E.N. Zalta. (1991). “On the Logic of the Ontological Argument.” In Philosophical Perspectives. Vol. 5. 509-529.

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A Formal Version of the Third Way

I believe by using mereological sums, I avoid the charge of the quantifier shift fallacy.

D1: God is the x such there is not some y by which x receives the necessity it has, and x is a member of the essentially ordered causal series by which things receive their necessity .
P1. For all x, if it is possible that x does not exist, then there is a time at which x does not exist.
P2. If there is a time at which the mereological sum of everything does not exist, then there does not exist now the mereological sum of everything.
P3. If there exists now some x, then there exists now the mereological sum of everything.
P4. I exist now.
P5. If necessarily there exists the mereological sum of everything, then there is some x that necessarily exists, and x is a part of the mereological sum of everything.
P6. If there is some x that necessarily exists, then if for all x, x necessarily exists, then there is some y such that x receives the necessity it has from y, only if there is an essentially ordered causal series by which things receive their necessity and it does not regress finitely.
P7. For all z it is not the case that there is an x, such that both x is a member of the essentially ordered causal series by which things receive z and it is not the case that z regresses finitely.
P8. For all x, if x necessarily exists, then x is a member of the essentially ordered causal series by which things receive their necessity.
P9. For all x, if there is not some y by which  x receives the necessity it has, and x is a member of the essentially ordered causal series by which things receive their necessity, then for all z, there is not some y by which z receives the necessity it has, and z is a member of the essentially ordered series by which things receive their necessity, and z is identical to x.
C1. God necessarily exists.

Note: D1 tells us that God does not receive his necessity from any other cause, but, being a part of the causal series by which things receive their necessity, is the cause of necessity in other things.

Let:
E!x ≝ x exists
E!t ≝ x exists at time t
Fx ≝ x regresses finitely
Oxy ≝ x is a member of essentially ordered causal series y
Rxy ≝ x receives the necessity it has from y
σ<x,P> ≝ the mereological sum of all x that P.
σ<e,E!> ≝ (∀x)[E!x ⊃ (x ≤ e)] & (∀y)[(y ≤ e) ⊃ (∃z)(E!z & (y ⊗ z)]1
e ≝ everything
g ≝ (ɿx)[~(∃y)Rxy & Oxl]
i ≝ I (the person who is me)
l ≝ the causal series by which things receive their necessity
n ≝ now

1. (∀x)[♢~E!x ⊃ (∃t)~E!tx] (premise)
2. (∃t)~E!tσ<e,E!> ⊃ ~E!nσ<e,E!> (premise)
3. (∃x)E!nx ⊃ E!nσ<e,E!>(premise)
4. E!ni (premise)
5. ☐E!σ<e,E!> ⊃ (∃x)[☐E!x &(x ≤ e)] (premise)
6. (∃x)☐E!x ⊃ {(∀x)[☐E!x ⊃ (∃y)Rxy] ⊃ (∃x)[Oxl & ~Fl]} (premise)
7. (∀z)~(∃x)[Oxz & ~Fz] (premise)
8. (∀x)[☐E!x ⊃ Oxl] (premise)
9. (∀x){[~(∃y)Rxy & (Oxl & Fl)] ⊃ (∀z)[(~(∃y)Rzy & Ozl) ⊃ (z = x)]} (premise)
10. ♢~E!σ<e,E!> (IP)
11. ♢~E!σ<e,E!> ⊃ (∃t)~E!tσ<e,E!> (1 UI)
12. (∃t)~E!tσ<e,E!> (10,11 MP)
13. ~E!nσ<e,E!> (2,12 MP)
14. (∃x)E!nx (4 EG)
15. E!nσ<e,E!> (3,14 MP)
16. E!nσ<e,E!> & ~E!nσ<e,E!> (13,15 Conj)
17. ~♢~E!σ<e,E!> (10-16 IP)
18. ☐E!σ<e,E!> (17 ME)
19. (∃x)[☐E!x &(x ≤ e)] (5,18 MP)
20. ☐E!μ & (μ ≤ e) (19 EI)
21. ☐E!μ (20 Simp)
22. (∃x)☐E!x (21 EG)
23. (∀x)[☐E!x ⊃ (∃y)Rxy] ⊃ (∃x)[Oxl & ~Fl] (6,22 MP)
24. ~(∃x)(Oxl & ~Fl)] (7 UI)
25. ~(∀x)[☐E!x ⊃ (∃y)Rxy] (23,24 MT
26. (∃x)~[☐E!x ⊃ (∃y)Rxy] (25 QN)
27. (∃x)~[~☐E!x ∨ (∃y)Rxy] (26 Impl)
28. (∃x)[~~☐E!x & ~(∃y)Rxy] (27 DeM)
29. ~~☐E!ν & ~(∃y)Rνy (28 EI)
30. ☐E!ν & ~(∃y)Rνy (29 DN)
31. ☐E!ν (30 Simp)
32. ☐E!ν ⊃ Oνl (8 UI)
33. Oνl (31,32 MP)
34. ~(∃x)[Oxl & ~Fl] (7 UI)
35. (∀x)~[Oxl & ~Fl] (34 QN)
36. ~[Oνl & ~Fl] (35 UI)
37. ~Oνl ∨ ~~Fl (36 DeM)
38. ~~Oνl (33 DN)
39. ~~Fl (37,38 DS)
40. Fl (39 DN)
41. ~(∃y)Rνy (30 Simp)
42. Oνl & Fl (33,40 Conj)
43. ~(∃y)Rνy (Oνl & Fl) (41,42 Conj)
44. [~(∃y)Rνy & (Oνl & Fl)] ⊃ (∀z)[(~(∃y)Rzy & Ozl) ⊃ (z = ν)] (9 UI)
45. (∀z)[(~(∃y)Rzy & Ozl) ⊃ (z = ν)] (43,44 MP)
46. ~(∃y)Rνy & Oνl (33,41 Conj)
47. [~(∃y)Rνy & Oνl] & (∀z)[(~(∃y)Rzy & Ozl) ⊃ (z = ν)] (45,46 Conj)
48. [~(∃y)Rνy & Oνl] & (∀z)[(~(∃y)Rzy & Ozl) ⊃ (z = ν)] & ☐E!ν (31,47 Conj)
49. (∃x){[~(∃y)Rxy & Oxl] & (∀z)[(~(∃y)Rzy & Ozl) ⊃ (z = x)] & ☐E!x} (48 EG)
50. ☐E!g (49 Theory of Descriptions)

QED

1Formulation of definition for everything based influenced by Filip, H. (n.d.) “Mereology”. Online: https://user.phil-fak.uni-duesseldorf.de/~filip/Mereology.pdf

The Modesty of Maydole’s Temporal Contingency Argument

In a recent discussion that I had, my interlocutor claimed that “contingency” was an outdated scholastic concept. Really it is just a modal property. Sometimes it is called “two-way” possibility, i.e. x is contingent iff possibly and possibly not x. Temporal contingency the possibility of existing at some point in time and not existing at some point in time. We experience temporal contingency all the time. Anyways, I promised to explain how contingency is still relevant today in the philosophy of religion. In fact, I think it is relevant in one of the most powerful arguments for God’s existence. I can’t really imagine a good reason to deny any of the premises, and it is of course logically valid. So I am compelled to conclude that it is a sound argument for the existence of a supreme being, which I call “God”.

In a sense, The argument originates with Thomas Aquinas’s third way, but is developed by Robert Maydole, who fuses it with a modal ontological argument to devise an ingenious new argument.

Maydole defines a supreme being as follows:

D1. A supreme being is such that it is not possible that there exists anything greater than it and it is not possible that it is not greater than anything else that is non-identical to it.

He then proves the following, which we will call T1:

T1. If possibly a supreme being exists, then a supreme being exists.

Maydole does this by making use of a few theorems, like Barcan Formula, and other theorems in modal logic (I will reproduce the argument below, for those who are interested, see the conditional proof on lines 4-19 for the exact proof). Then Maydole constructs an argument for the possibility of a supreme being. He lists the following premises (but don’t attack them straight off, something interesting happens):

P1. Something presently exists.
P2. Only a finitely many things have existed to date.
P3. Every temporally contingent being begins to exist at some time and ceases to exist at some time.
P4. Everything that begins to exist at some time and ceases to exist at some time exists for a finite period of time.
P5. If everything exists only for a finite period of time, and there have been only a finitely many things to date, then there was a time when nothing existed.
P6. If there was a time when nothing existed, then nothing presently exists.
P7. A being is temporally necessary if and only if it is not temporally contingent.
P8. Everything has a sufficient reason for its existence.
P9. Anything that has a sufficient reason for its existence also has a sufficient reason for its existence that is a sufficient reason for its own existence.
P10. No temporally contingent being is a sufficient reason for its own existence.
P11. Every temporally necessary being that is a sufficient reason for its own existence is a being without limitations.
P12. A being without any limitations is necessarily greater than any other being.
P13. It is not possible for anything to be greater than itself.
P14. It is necessarily the case that “greater than” is asymmetric.

From P1-P14 one can prove C1:

C1. A supreme being exists.

The proof from P1-P14 to C1 is a bit long, and I believe Maydole even made a few typographical mistakes along the way. Here is my adaptation of this part of the argument, if you are interested.

Next consider what was said, before, that if it is possible that a supreme being exists, then a supreme being exists, i.e. T1. Maydole’s argument is surprisingly modest. What he does is argue that POSSIBLY (P1-P14) is true. Since C1 is provable from (P1-P14), we can say POSSIBLY C1 is true, which is to say that possibly a supreme being exists. Given T1 and the possibility that a supreme being exists, we can conclude that a supreme being exists (which is rightly called God)!

Now, the argument is very strong, because it is plausible that P1-P14 are actually true. However, Maydole only requires that the premises be possibly true rather than actually true, which is to say that they are not logically or metaphysically incoherent, or that they are true in some metaphysically possible world (as contemporary modal logicians would say). The deduction is valid, and it is very hard for me to think any of the premises are false. So I am compelled to think that this is, indeed, a sound argument for God’s existence.
So the proof looks something like this:

Let

Gxy ≝ x is greater than y
Sx ≝ (~◊(∃y)Gyx & ~◊(∃y)(x≠y & ~Gxy))

1. ◊(P1-P14) (premise)
2. (P1-P14) ⊢ C1 (premise that C1 is provable from P1-P14)
3. {◊(P1-P14) & [(P1-P14) ⊢ C1]} ⊃ ◊C1 (premise)
4. ◊(∃x)Sx (Assump CP)
5. ◊(∃x)Sx ⊃ (∃x)◊Sx (BF theorem)
6. (∃x)◊Sx (4,5 MP)
7. ◊Su (6 EI)
8. ◊(~◊(∃y)Gyu & ~◊(∃y)(u≠y & ~Guy)) (7, df “Sx”)
9. ◊(~◊(∃y)Gyu & ~◊(∃y)(u≠y & ~Guy)) ⊃ (◊~◊(∃y)Gyu & ◊~◊(∃y)(u≠y & ~Guy)) (theorem)
10. ◊~◊(∃y)Gyu & ◊~◊(∃y)(u≠y & ~Guy) (8,9 MP)
11. ◊~◊(∃y)Gyu (10 Simp)
12. ◊~◊(∃y)(u≠y & ~Guy) (10 Simp)
13. ◊~◊(∃y)Gyu ⊃ ~◊(∃y)Gyu (theorem, by “S5”)
14. ◊~◊(∃y)(u≠y & ~Guy) ⊃ ~◊(∃y)(u≠y & ~Guy) (theorem, by “S5”)
15. ~◊(∃y)Gyu (11,13 MP)
16. ~◊(∃y)(u≠y & ~Guy) (12,14 MP)
17. ~◊(∃y)Gyu & ~◊(∃y)(u≠y & ~Guy) (15,16 Conj)
18. Su (17, df “Sx”)
19. (∃x)Sx (18 EG)
20. ◊(∃x)Sx ⊃ (∃x)Sx (4-19 CP, which proves T1)
21. {◊(P1-P14) & [(P1-P14) ⊢ C1] (1,2 Conj)
22. ◊C1 (3,22 MP)
23. ◊(∃x)Sx (22, def “C1”)
24. (∃x)Sx (20,23 MP)

QED

To me, it is P11 that needs more explanation. It certainly seems right that a temporally necessary being who is the sufficient reason for its own existence has the sort of existence that is not limited by time nor by the existence of any other thing. But to say that the existence of x is not limited by time nor any thing seems a bit different from saying thag such a being is essentially without limitations. I believe the idea is that if there is no time nor state of affairs in which such a being would cease to exist or lack a reason for existing, then it is not limited by anything at all, and must be greater than every other thing.

Another person noted that P5 did not make sense to him because time is something that exists, so there could never be a time when nothing exists. Maydole, however, is quantifying over things in a way that is distinct from moments (in his “Modal Third Way” you see a more careful distinction between moments and things). With the right qualifications, and stipulations, this worry can be alleviated, e.g. one might say “no concrete things” or “no subsitent things” rather than “nothing”.

Reference:
Maydole, R. 2012. “The Ontological Argument”. In The Blackwell Companion to Natural Theology. Ed. W.L. Craig & J.P. Moreland. Malden, MA: Blackwell Publishing, pp. 580-586.

Vexing Links (5/25/2015)

Some recent links of note:

  • Robin Smith has recently updated the SEP article on Aristotle’s Logic
  • Tuomas Tahko updates an entry at the SEP on Ontological Dependence originally authored by the late great E.J. Lowe
  • Peter Adamson’s History of Philosophy without any Gaps has a new podcast episode  on 13th century Logic
  • Massimo Pigliucci took the New Atheists to the woodshed (almost feel sorry for them)
  • Jeffery Jay Lowder notes that David Wood took John Loftus to the woodshed on the question “Did Jesus Rise from the Dead?” (I agree with Lowder and couldn’t help but get the impression that Loftus knew he had been whipped by the end of the debate—granting that he failed to address 1 Cor 15)
  • Messianic Drew constructs a similar argument for God from Fitch’s paradox as I did previously on this blog.  One difference is that I use the BCF (Big Conjunctive Fact) to explicitly argue for an omniscient mind (which isn’t a big slice of God, but certainly troubling for naturalism)
  • Alex Pruss as a nice neat argument for God from life (I list biogenesis as evidence that supports theism, though that is always subject to new discoveries)
  • Speaking of which, a new theory of abiogenesis is being lauded by internet atheists as putting God on the ropes (Should theists be sweating? It might be worth noting that the scientist who has devised the theory, Dr. England, is an observant Jew who prays to God three times a day.  Classical theists don’t require that the creation of life to be a miraculous intervention, but the general order of nature points to a living source of creation)
  • I recently found an interesting clip of evolutionary biologist, Ken Miller (who testified against ID in the Dover case) defend Aquinas’s fifth way (though the fifth way is a teleological argument, it is not the same as the sorts of arguments ID theorists put forward, as Ed Feser likes to point out)
  • Inspiring Philosophy has a great video response to the question of whether the Trinity is a pagan concept
  • Bill Vallicella and Dale Tuggy are discussing God’s relationship to being (this is the latest from Vallicella, but it all started from this interview on Tuggy’s superb Trinities podcast)
  • Lastly, and most importantly, if you are wondering which superhero would win in a one-on-one battle, wonder no more

Bernstein/Ahmed debate on Unbelievable?

Unbelievable? hosted a great debate between C’Zar Bernstein and Arif Ahmed on the Argument from Consciousness for God’s existence: listen here.

A rough outline for Bernstein’s argument was something like:
1. There are non-physical minds.
2. The explanation for (1) is either personal or natural.
3. The explanation is not natural.
4. Therefore, the explanation is personal.

Fleshed out, Bernstein defended an evidential argument, where consciousness doesn’t logically entail the God of classical theism, but that consciousness provides evidential support for classical theism. Most of the debate came down to the first premise, which Bernstein defended by way of the modal argument for the soul.

Ahmed focuses on an eliminativist/Humean response and basically just denied there were persons, and fell back on the claim that we should really only admit into our ontology whatever is strictly needed for science (so no need to talk about conscious persons or moral properties).  A good deal of the discussion focused on whether we have good reason to think persons exist, and I think Bernstein got the better of Ahmed in the end (pointing out how Ahmed couldn’t even really talk about pain without referencing his own awareness of it).  However, this meant that little time was focused on showing why consciousness is good evidence in support of classical theism.  Indeed, I agree with Bernstein that it is good evidence.  However, I think more needs to be said for why this is so.

It’s worth a listen, that is for sure.

An Ontological Argument from Actuality

Here is a refinement on my ontological argument from actuality:

1. Something is an Anselmian God if and only if it is conceivable, nothing can be conceived of which is more actual, and it necessarily exists (definition Θ).

2. There is something conceivable such that nothing can be conceived of which is more actual (premise).

3. For all x, if the possibility of failing to conceive of x implies the possibility that x doesn’t exist, x is mentally dependent (premise).

4. For all x, if x is mentally dependent, there is something conceivable that is more actual than x (premise).

Therefore,

5. An Anselmian God exists.

I start out with a definition of an Anselmian God, which is a stipulation, but is rooted in the idea that a Being of Pure Actuality is arguably perfect and possesses a good number of divine attributes.  

As I noted in a previous post, the traditional argument uses a “greater than” relation, which some find suspect.  “Greatness” would have been understood by Anselm as something that can be evaluated objectively on a scale, as in the Neo-Platonic notion of the Great Chain of Being.  To the contemporary ear, “greatness” seems subjective and vague.  I think “actual” in the Thomistic-Aristotelian sense is a fair approximation of greatness, but we can have a better sense of what “actual” means.  Thomas is able to derive the divine attributes from a being of Pure Actuality, so “most actual” is plausibly a divinely loaded superlative.  Moreover, it seems to me that the act-potency distinction is not something the contemporary ear would take to be dependent on subjective opinions.  So, I think (2) is fairly impeccable.  

I think (3) is a bit clunky, but it basically means that if something is merely a concept, then it is mentally dependent.  So, in the case of God, if God is merely a concept in the mind, then the possibility that God could fail to be conceived by all minds that exist implies that God, as a mere concept, could fail to exist, and so depends upon minds to continue to exist.  Put another, if God is merely a concept, then there was no God in the Jurassic period, as William Lane Craig once suggested to John Dominic Crossan.

Finally, (4) says that if something is mentally dependent, then something is conceivable that is more actual than it.  Some people think, for instance, that moral values are mind-dependent.  So, for instance, the actuality of the value of human life, VHL, depends on there being an actual community of minds that actually conceive of human life as valuable.  Were such a community to cease to exist, the VHL would only potentially exist, even if humans existed.  If the VHL were an objective fact grounded in human nature, then the actuality of the VHL would obtain whenever humans actual exist.  There is a certain assymetry that suggests that grounding the VHL in human nature is to view VHL as more actual than grounding VHL in the subjective opinions of a community of minds.  For the VHL to be actual in one case, there need only be actual humans exemplifying human nature, where as in the latter, there needs to be actual humans exemplifying human nature and an actual community of minds that actually is of the opinion that human life is valuable.  For, without the humans, a community of minds that endorses the VHL would really just be saying that VHL potentially exists and would be actual upon the occassion of human life.  We could say, then, that x is more actual than y iff the existence of x depends upon the actualization of fewer potentials than y depends upon.  VHL grounded in the actuality of human nature depends upon the actualization of fewer potentials than VHL grounded in subjective opinions about humans. So (4) just tells us that for any x that depends upon the mental for its actuality, it is conceivable that there is something that is more actual (and less dependent) than x, e.g. to conceive that x can actually exist independent of mentally conceiving of x.

Let

Cx – x is conceived
Mx – x is mentally dependent
Axy – x is more actual than y
Θx- x is an Anselmian God, 

that is: 

1. (∀x){Θx ≝ ([♢Cx & ~(∃y)(Ayx & ♢Cy)] & ☐(∃z)(z=x))} (Def Θ)
2. (∃x)[♢Cx & ~(∃y)(Ayx & ♢Cy)] (premise)
3. (∀x){[♢~Cx ⊃ ♢~(∃z)(z=x)] ⊃ Mx} (premise)
4. (∀x){Mx ⊃ [(∃y)(Ayx & ♢Cy)]} (premise)
5. (∀x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (IP)
6. ♢Cu & ~(∃y)(Ayu & ♢Cy) (2 EI)
7. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ Mu (3 UI)
8. Mu ⊃ [(∃y)(Ayu & ♢Cy)] (4 UI)
9. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ [(∃y)(Ayu & ♢Cy)] (7,8 HS)
10. [♢Cu & ~(∃y)(Ayu & ♢Cy)] ⊃ [♢~Cu ⊃ ♢~(∃z)(z=u)] (5 UI)
11. ♢~Cu ⊃ ♢~(∃z)(z=u) (6,10 MP)
12. (∃y)(Ayu & ♢Cy) (9,11 MP)
13. Avu & ♢Cv (12 EI)
14. ~(∃y)(Ayu & ♢Cy) (6 Simp)
15. (∀y)~(Ayu & ♢Cy) (14 QN)
16. ~(Avu & ♢Cv) (15 UI)
17. (Avu & ♢Cv) & ~(Avu & ♢Cv) (13,16 Conj)
18. ~(∀x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (5-17 IP)
19. (∃x)~{[♢Cx & ~(∃y)(Ayx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (18 QN)
20. (∃x) ~{~[♢Cx & ~(∃y)(Ayx & ♢Cy)] ∨ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (19 Impl)
21. (∃x){~~[♢Cx & ~(∃y)(Ayx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (20 DeM)
22. (∃x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (21 DN)
23. (∃x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] & ~[~♢~Cx ∨ ♢~(∃z)(z=x)]} (22 Impl)
24. (∃x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] & ~[☐Cx ∨ ♢~(∃z)(z=x)]} (23 ME)
25. (∃x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] & [~☐Cx & ~♢~(∃z)(z=x)]} (24 DeM)
26. (∃x){[♢Cx & ~(∃y)(Ayx & ♢Cy)] & [~☐Cx & ☐(∃z)(z=x)]} (25 ME)
27. [♢Cu & ~(∃y)(Ayu & ♢Cy)] & [~☐Cu & ☐(∃z)(z=u)] (26 EI)
28. ~☐Cu & ☐(∃z)(z=u) (27 Simp)
29. ☐(∃z)(z=u) (28 Simp)
30. [♢Cu & ~(∃y)(Ayu & ♢Cy)] (27 Simp)
31. [♢Cu & ~(∃y)(Ayu & ♢Cy)] & ☐(∃z)(z=u) (29,30 Conj)
32. Θu (1,31 “Def Θ”)
33. (∃x)Θx (32 EG)

A Quick Argument against Christian Unitarianism from Love

This hymn sets up some of the themes of my argument, so please listen to it first!

I take Christian Unitarianism to be the conjunction of the positions that Jesus of Narazerth is the Messiah by whose death and resurrection salvation entered the world, and that Jesus of Nazareth is not the same being, substance, or person as God the Father.  Christian Unitarians can take a variety of positions with respect to Christology, e.g. the view that Jesus was fully human and led a sinless life, and was elevated to a divine-like status, that Jesus was an angelic being, Michael for example, who took on flesh, or that Jesus was a lesser deity who existed prior to creation eternally or before creation began, i.e. he was the Logos, which should be construed as a demiurge who acted on behalf of an utterly transcendent higher God.

First, I should motivate some aspects of my premises regarding the nature of God.  Though we cannot understand God fully, I do believe that the Christian God is that being than which none greater can be conceived.  If Christian Unitarians reject that definition, that’s fine, but I also think that the Anselmian God actually exists, and anything that is not this “Anselmian God” is a false god who is unworthy of worship.

Second, 1 John 4:8 tells us that God is love.  Given that the Anselmian God is the greatest conceivable being, and that love is a perfection, it stands to reason that if there is an Anselmian God, that God exemplifies a love than which none greater can be had.  Otherwise, one might easily conceive of a greater God.

So the argument is this:

D1: God is that than which none greater can be conceived. [Anselmian definition]
P1: If God is that than which none greater can be conceived, God exemplifies that love than which none greater can be had.
C1: God exemplifies that love than which none greater can be had. [From D1 & P1 MP]
D2: That love than which none greater can be had is laying down one’s own life for a friend. [Definition from Jn 15:13]
P2: If Christian Unitarianism is true, it is not the case that God exemplifies laying down one’s  own life for a friend.
C2: If Christian Unitarianism is true, it is not the case that God exemplifies that love than which none greater can be had. [From D2 & P2]
C3: Christian Unitarianism is false. [From C1 & C2 DN + MT]

Some possible responses:

1: On Trinitarian Christianity, God did not exemplify that love than which none greater can be had until 33AD. Therefore, God is not the Anselmian God, since a God that has laid down his own life for a friend for a greater amount of time is greater.
R1: God is an eternal and omniscient being. In creating the World, and from His perspective, the Trinitarian God already exemplifies this love for all time. From all time, his sacrifice is exemplified. Temporally, it happened for us on a particular date in history.  Moreover, Christ laid down his life for all, including past humans.  That the act of laying down one’s life for a friend did not happen at the earliest moment of history does not cheapen the act, since an earlier sacrifice would not have been for more “friends.”

2: The Trinitarian God only laid down his life once. One could conceive of a God who lays down his life more times. So the Trinitarian God is not the Anselmian God.
R2: The quantity of times one lays down one’s life is not the issue, but when it is done for a friendship. Christ died that all may be counted as friends. And he did this in friendship and obedience to the other persons of the Trinity. Thus, there is no “friend” for whom Christ could lay down his life a second time. The fallen angels are forever enemies of God by their will, so they are not among the set of possible friends for whom God could lay down his life again.

3: John 15:13 is really about the greatest act of love a human can do, not the greatest act any “one” can do. Or Christ was using hyperbole. Or the act does not include God, who is capable of a higher act of love. Or it is logically impossible for God to exemplify this human act of love.
R3: The Greek in John 15:13 doesn’t limit the case to humans, but just uses the pronouns “οὐδεὶς,” “τις,” and “αὐτοῦ.” These are reasonably translated as “no one,” “one,” and “of him.” So it isn’t clear from the text that the case is limited to human beings. Given that Christ would go on to lay down his life for humanity, it would be strange to think that he was just being hypebolic here. If he were being hyperbolic and there is some greater act of love, what is it? What act of love does God do that would be greater than had he laid down his life for our salvation? The burden would be on the Christian Unitarian to make the case that some other act of love is greater, despite the Scripture. Finally, if it is argued that it is simply logically impossible that God lay down his life for a friend, then this puts the Christian Unitarian in the uncomfortable position of trying to demonstrate that the incarnation is a logical absurdity. Some might take up this task, but it is not an easy task.

With respect to my response to the third objection, I would like to emphasize a couple of other issues. A) It seems to me that one of the beautiful messages of Christianity is this theodicy, if it can be called a theodicy, that doesn’t seek to explain away evil, but says that God entered into this veil of tears too. God humbled himself and experienced evil directly. Christian Unitarianism seems to cheapen this “theodicy” because it tells us that God remains distant and somehow thinks sending someone on his behalf is “good enough.” Relatedly, B) Christian Unitarianism tells us that the death of one sinless human (or semi-divine being) was sufficient to atone for sin. On theories of the atonement, like the satisfaction theory, this cheapens the debt of sin. On Trinitarianism, a divine person of the Holy Trinity, laid down his life for us all. The life of the Second Person of the Holy Trinity is His own. No creature can claim to own his or her life in the same way a divine, necessary, and eternal being can. So, if Christ were just another creature, the offering of his life would be less significant. It would be offering something that, in some sense, belonged to the Father in the same way any other creaturely life belongs to the Father. If the Unitarian chooses to escape this by positing a co-eternal, necessarily existing per se, lesser divinity (polytheism), this conflicts with aseity, which is arguably a great-making property. Also, such a move seems ad hoc, since I don’t think any Christian Unitarians would say that the Logos is per se necessary, i.e. necessarily exists of itself and not by the necessity of the Father (higher God).

There is one last objection that occurs to me (though there may be others):
4: Even if God exemplifies the highest form of love through Christ’s sacrifice, on Trinitarianism, it is only one persons of the Trinity who exemplifies this love. The Father and the Holy Spirit either cannot, or do not exemplify this love.
R4: Being of one substance, God can be said to exemplify this love. And this love is exemplified to a higher degree since one being exemplified it, not merely through one person, but all three. For it is the Father who sent the Son, and it was by the Power of the Holy Spirit that the Son became incarnate. Thus the supreme act of love is one act by one Being who, being multi-personal, stands in different relations to the act. The Father sends the Son, which is the very act by which the Son is sent by the Father. And this is the act by which God so loved the World (Jn 3:16). Whether the Father or the Holy Spirit could have incarnated instead of the Son is an interesting question. But, if my earlier point is correct, it is not a supreme act of love to merely lay down one’s life. So only one of the Persons could have done this if the act was for all “friends.” A second passion via another Person of the Trinity would not affect anything more for God’s friends. So it is not necessary that God exemplify this sacrifice by all Three Persons laying down incarnated lives. Once was sufficient, and all three persons were completely involved in the event, though by different relations.

Thanks to Andrew Terrell for a conversation which helped stimulate some of these thoughts. Though, I should say that any heretical views expressed here are my own.

Reasonable Faith’s Presentations of Arguments for God

Reasonable Faith is putting out some well produced, clear, and concise presentations of classic arguments for God’s existence (as William Lane Craig typically develops those arguments).  They are definitely worth a look:

The Kalam Cosmological Argument:

The Argument from Fine Tuning:

The Moral Argument:

It seems that Dr. Craig is putting together videos that defend each one of the arguments he favors for theism.  If so, we should expect a video on the ontological argument, reformed epistemology, the historicity of the resurrection, and perhaps the applicability of mathematics to the universe (a sub-argument from fine-tuning).  At least, I hope to see such videos in the future.  If they come out, I’ll be sure to update the list.

While I don’t consider these videos to be scholarly level presentations that deal with the best objections to the arguments one might find in the literature, they are a good starting point.  They are especially good if one is more of an auditory/visual learner.

I was particularly impressed by the analogy made in the Moral Argument video to explain the response to Euthyphro’s dilemma.  Just to recall, Euthyphro’s dilemma, as it is often put by contemporary philosophers of religion, presents two untoward possibilities: either God commands the good because it is good, or God’s commands are good simply because they are commanded by God.  If it is the former, the good exists independently from God, which not only means that God is not needed to explain objective moral values and duties, but also threatens God’s aseity.  If it is the latter, then the good is arbitrary, since God could have commanded anything and it would be good because of that reason.  In other words, God would have no standard or measure of moral goodness to consider when making His commands, they would simply issue forth and become good because of God’s authority.  Murder, theft, and adultery could have been good if God chose to command them.

The response is to propose a third possibility, since the dilemma does not present perfectly dichotomous options.  Classical theists want to argue that this third option is that God’s nature somehow is the Good.  That is, God’s nature is the standard or measure by which moral values are measured and the commands issued by God are commands issued by the standard of Goodness itself.

The analogy that impressed me was to suggest that God’s nature relates to moral values and duties in the world in a similar way in which a live performance relates to a hi-fidelity recording.  The closer the recording is to capturing the sound of the live performance, the better the recording is.  The live audio is as good as can be.  The recording cannot exceed that standard (without distorting it and not being faithful to the original).  So God’s nature is the living presence of Goodness and all else is measured insofar as it is analogous to God in being good.

Intelligibility, Information, and Beauty

What is information?  Information expresses something.  It is intentional and so not random, right?  A Youtube collaboration between VSauce and Veritasium presents an interesting argument that information is random, or rather, entropy:

But is that right?  Information is random?  If so, wouldn’t it be unintelligible?

When transmitting information, you can compress all that which is a pattern or predictable.  This means that whatever cannot be reduced or compressed is pure information.  At the same time, pure information without pattern and order is meaningless.  It is just white noise.  So it seems that intelligibility is not the same thing as information, at least when it is defined as entropy (as it is in this information theory).  Meaning emerges from patterns of information.  The random must be ordered and patterned in ways that we can decode and understand.  So intelligibility or meaning is the confluence of information and order.

The video makes the neat point that our scientific theories are really just attempts to compress the information we find in nature.  It is interesting to note that scientists often prefer theories and equations that are described as “elegant” or “beautiful”.  In certain sense, the idea that intelligibility, or meaning, emerges from patterns of random information can help us to understand why we find these compressions beautiful.

In an earlier post, I had defended the beauty of the Trinitarian God over unitarian gods on the grounds that the Trinity has both unity and distinction, i.e. a simple unified divine substance that is three distinct persons.  I argued that we can objectively define that which is beautiful as that which is unified, harmonious, and ordered while admitting distinctions.

If information is maxim entropy, it contains an irreducible unity.  That unity of information becomes intelligible when it is ordered into patterns and brought into harmony with other bits of information.  It becomes meaningful.  So whatever is intelligible is inherently beautiful.  Thus, there may be something metaphysical underlying the idea that a scientifically true formula or equation is objectively “elegant” or “beautiful”.  We find that it is “elegant” or “beautiful” because it is a simple unity, yet it has the power to explain a wide variety of our data by revealing patterns.  The more unified and simple an equation is, and the greater amount of distinct phenomena it captures, the more beautiful it is.  This also hints at the fundamental unity between objective truth and beauty, which I believe we find in nature as a reflection of what is fundamental to the Godhead.

How is this fundamental to the Godhead? If God is Being itself, or Being must truly, then God must be perfect, simple, and irreducible.  Whatever is perfect in Being must be truly Good, and indeed, the Father is Good. Goodness is opposed to ignorance, as ignorance is a source of evil, so if the Father is Good, he must know His own Nature, and so must be thought thinking itself.  Since the Divine Substance is absolutely simple, the Father cannot abstract a genus or species to comprehend His Nature propositionally.  Instead, He must comprehend or grasp the Divine Nature Itself in a concrete way, or else He grasps nothing.  And in doing this, conceives of the Divine Substance distinctly from the One who is conceiving.  If God’s knowledge is accurate, he must conceive of the same exact concrete Substance that He is.  So his eternal conception of the Divine Substance is the same substance that He is, it is the grasp of the Truth of God’s Goodness.  And we call this eternal conception, or this eternally begotten grasp of the Divine Substance, the Son, who is the Truth itself.  As the Father knows the Divine Substance, the Divine Substance is essentially intelligible to the Father.  There is a distinction between knower and known and a pattern of sameness that makes the Divine Substance knowable to itself.  Thus, Beauty is intrinsic to Divine Substance in its self-intelligibility.  Since Beauty is that which is desirable in itself, the Will of God is directed towards the Divine Substance.  So another relationship exists between God’s Will and the Divine Substance, which is desirable because of the intrinsic beauty of the Divine Substance as a Self-Intelligible unity.  So the Divine Substance, which is the object of the Divine Will, proceeds from the Father (as Knower) and the Son (as Known), and must be distinct from these Two.  We call the object of the Divine Will, which is God, the Holy Spirit.  The Holy Spirit is true Beauty.  And so there is a Trinity of Persons that is the Godhead.

If the Divine Substance is Being itself, it is also the representative of the transcendentals of Being: Goodness, Truth, and Beauty.  Interestingly, those three transcendentals are convertible with Being but remain distinct from one another.  So we find that the Persons of the Trinity are convertible with God, but are distinct from one another.  This is not to say that the Son is not Good or Beautiful, or that the Holy Spirit is not True or Good.  Rather, I am saying that the Persons of the Trinity relate to one another in terms of Goodness, Truth, and Beauty.  But they are far more than these transcendentals.  I think it is a helpful way of understanding the relationships among the Persons in the ontological structure of their relationships (unbeggotten, begotten, and proceeding). The relationship among the Persons of the Trinity and the Divine Substance is ultimately mysterious, but an analogy to the trinity of transcendentals is a helpful image to have in mind.

Of course, whenever I reflect on the Trinity, I fear that I might stumble into heresy.  Nonetheless, I am drawn to thinking about it, like a moth to the flame.  How could I not?  There is nothing more mysterious, more beautiful, and more true.  So, if my comments are in error, I humbly submit them as a mere reflection that is subject to revision.

The Ontological Argument From Transcendence 2.0

I’ve presented my own version of Anselm’s ontological argument here and I’ve also argued for an ontological argument using “more transcendent” rather than “greater” here. Combining the two, and refining the argument, I got this:

1. Something is an Anselmian God if and only if it is conceivable, nothing can be conceived of which is more transcendent, and it necessarily exists (definition Θ).

2. There is something conceivable such that nothing can be conceived of which is more transcendent (premise).

3. For all x, if the possibility of failing to conceive of x implies the possibility that x doesn’t exist, x is mentally dependent (premise).

4. For all x, if x is mentally dependent, there is something conceivable that is more transcendent than x (premise). Therefore,

5. An Anselmian God exists.

Let

Cx – x is conceived
Mx – x is mentally dependent
Txy – x is more transcendent than y
Θx- x is an Anselmian God, that is: (∀x){Θx ≝ ([♢Cx & ~(∃y)(Tyx & ♢Cy)] & ☐(∃z)(z=x))} (Def Θ)

1. (∃x)[♢Cx & ~(∃y)(Tyx & ♢Cy)] (premise)
2. (∀x){[♢~Cx ⊃ ♢~(∃z)(z=x)] ⊃ Mx} (premise)
3. (∀x){Mx ⊃ [(∃y)(Tyx & ♢Cy)]} (premise)
4. (∀x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (IP)
5. ♢Cu & ~(∃y)(Tyu & ♢Cy) (1 EI)
6. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ Mu (2 UI)
7. Mu ⊃ [(∃y)(Tyu & ♢Cy)] (3 UI)
8. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ [(∃y)(Tyu & ♢Cy)] (6,7 HS)
9. [♢Cu & ~(∃y)(Tyu & ♢Cy)] ⊃ [♢~Cu ⊃ ♢~(∃z)(z=u)] (4 UI)
10. ♢~Cu ⊃ ♢~(∃z)(z=u) (5,9 MP)
11. (∃y)(Tyu & ♢Cy) (8,10 MP)
12. Tvu & ♢Cv (11 EI)
13. ~(∃y)(Tyu & ♢Cy) (5 Simp)
14. (∀y)~(Tyu & ♢Cy) (13 QN)
15. ~(Tvu & ♢Cv) (14 UI)
16. (Tvu & ♢Cv) & ~(Tvu & ♢Cv) (12,15 Conj)
17. ~(∀x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (4-16 IP)
18. (∃x)~{[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (17 QN)
19. (∃x) ~{~[♢Cx & ~(∃y)(Tyx & ♢Cy)] ∨ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (18 Impl)
20. (∃x){~~[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (19 DeM)
21. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (20 DN)
22. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[~♢~Cx ∨ ♢~(∃z)(z=x)]} (21 Impl)
23. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[☐Cx ∨ ♢~(∃z)(z=x)]} (22 ME)
24. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & [~☐Cx & ~♢~(∃z)(z=x)]} (23 DeM)
25. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & [~☐Cx & ☐(∃z)(z=x)]} (24 ME)
26. [♢Cu & ~(∃y)(Tyu & ♢Cy)] & [~☐Cu & ☐(∃z)(z=u)] (25 EI)
27. ~☐Cu & ☐(∃z)(z=u) (26 Simp)
28. ☐(∃z)(z=u) (27 Simp)
29. [♢Cu & ~(∃y)(Tyu & ♢Cy)] (26 Simp)
30. [♢Cu & ~(∃y)(Tyu & ♢Cy)] & ☐(∃z)(z=u) (28,29 Conj)
31. Θu (30 Def Θ)
32. (∃x)Θx (31 EG)

[Update 11/9/204] I’ve noticed that some did not understand why if possibility that failing to conceive x implied that x possibly didn’t exist, then a greater could be conceived than x.  I’ve tried to make this more explicit by explaining this in terms of mental dependence.  Here, a concept is not an abstract object, but an object in the mind.

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