An Argument Against Subjective Morality

P1. If morality is relative to the subject, then morality is a domain that is a  matter of personal opinion.

P2. All domains that are matters of personal opinion, are domains where facts and evidence cannot determine correct belief.

P3.  All domains where facts and evidence cannot determine correct belief are domains that lack propositions for which it is worth dying before giving assent under coercion.

P4.  Morality is a domain with propositions for which it is worth dying before giving assent under coercion.

C. Morality is not relative to the subject.

P1 and P2 are not too objectionable.  That is just what we mean when we say that morality is subjective.  I think that if you are going to object to the argument, you will object to P3 or P4.

A Remix of Anselm’s Conceptual Ontological Argument

st-20anselm20weninger

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.

Calvin’s basket is full

Domino Logic

Here are some really interesting videos in which dominos simulate logical reasoning and computing:

 

Novena Prayer Challenge

rosary

(Photo Credit: Sign.org)

There are many intentions for which I have been asked to pray. While I do offer a moment of prayer for these requests, I think I can do better. So I am would like to pray the rosary for the next nine days (starting September 19) for all of these intentions.

The Rosary is the most excellent form of prayer and the most efficacious means of attaining eternal life. It is the remedy for all our evils, the root of all our blessings. There is no more excellent way of praying (Pope Leo XIII).

I found a beautiful recitation of the rosary sung in Latin, so this will be what I will be listening to as I pray:

Sign of the Cross:

In nomine Patris, et Filii, et Spiritus Sancti. Amen

Apostles’ Creed:

Credo in Deum Patrem omnipotentem, Creatorem caeli et terrae. Et in Iesum Christum, Filium eius unicum, Dominum nostrum, qui conceptus est de Spiritu Sancto, natus ex Maria Virgine, passus sub Pontio Pilato, crucifixus, mortuus, et sepultus, descendit ad infernos, tertia die resurrexit a mortuis, ascendit ad caelos, sedet ad dexteram Dei Patris omnipotentis, inde venturus est iudicare vivos et mortuos. Credo in Spiritum Sanctum, sanctam Ecclesiam catholicam, sanctorum communionem, remissionem peccatorum, carnis resurrectionem, vitam aeternam. Amen.

The Lord’s Prayer:

PATER NOSTER, qui es in caelis, sanctificetur nomen tuum. Adveniat regnum tuum. Fiat voluntas tua, sicut in caelo et in terra. Panem nostrum quotidianum da nobis hodie, et dimitte nobis debita nostra sicut et nos dimittimus debitoribus nostris. Et ne nos inducas in tentationem, sed libera nos a malo. Amen.

The Hail Mary:

AVE MARIA, gratia plena, Dominus tecum. Benedicta tu in mulieribus, et benedictus fructus ventris tui, Iesus. Sancta Maria, Mater Dei, ora pro nobis peccatoribus, nunc, et in hora mortis nostrae. Amen.

Glory Be:

GLORIA PATRI, et Filio, et Spiritui Sancto. Sicut erat in principio, et nunc, et semper, et in saecula saeculorum. Amen.

Oratio Fatimae (The Fatima Prayer)

Domine Iesu, dimitte nobis debita nostra, salva nos ab igne inferiori, perduc in caelum omnes animas, praesertim eas, quae misericordiae tuae maxime indigent.

Hail, Holy Queen:

SALVE REGINA, Mater misericordiae. Vita, dulcedo, et spes nostra, salve. Ad te clamamus exsules filii Hevae. Ad te Suspiramus, gementes et flentes in hac lacrimarum valle. Eia ergo, Advocata nostra, illos tuos misericordes oculos ad nos converte. Et Iesum, benedictum fructum ventris tui, nobis post hoc exsilium ostende. O clemens, o pia, o dulcis Virgo Maria.

V. Ora pro nobis, Sancta Dei Genitrix.
R. Ut digni efficiamur promissionibus Christi.

caelum omnes animas, praesertim eas, quae misericordiae tuae maxime indigent.

Hail, Holy Queen:

SALVE REGINA, Mater misericordiae. Vita, dulcedo, et spes nostra, salve. Ad te clamamus exsules filii Hevae. Ad te Suspiramus, gementes et flentes in hac lacrimarum valle. Eia ergo, Advocata nostra, illos tuos misericordes oculos ad nos converte. Et Iesum, benedictum fructum ventris tui, nobis post hoc exsilium ostende. O clemens, o pia, o dulcis Virgo Maria.

V. Ora pro nobis, Sancta Dei Genitrix.
R. Ut digni efficiamur promissionibus Christi.

(EWTN, Latin Prayers).

My Intentions:

1) The continued health of my daughter, my wife, and myself.
2) Full employment and financial stability for my family.
3) The health of my Aunt Laura.
4) The health of my grandmother, Clare.
5) The speedy recovery of my cousin’s husband, Mark.
6) For the recovery of my compadre, Armando.
7) For my sister and her family.
8) The requests of Michael Shenigo.
9) The requests of Helen Marple-Horavt.
10) For those who doubt God.
11) For the victims of recent violent attacks.
12) For defenseless children absused by their parents and adults.
13) For the unborn and the victims of abortion.
14) For the United States in the election of candidates who truly seek to bring justice and peace to the world.
15) For the souls of my mother, Matthew, Lupe, Tia Socorro, and Carol who recently passed.

If you would like to participate in this challenge, post your intentions in the comments below and I will include them in my intentions as I pray over the next nine days. You don’t have to be a Catholic or believer to pray or join in this challenge, in fact, it might make sense to pray even if you don’t believe.

The Outsider’s Test Passed

A Cosmological Argument

The following Cosmological Argument is based on the arguments of Alexander Pruss and Richard M. Gale1, and Jerome Gellman2.

D1. God is the timeless, immaterial, personal, omnipotent, omniscient, omnibenevolent, free being who is worthy of worship, and is the explanation for why the big conjunctive contingent fact is true in the actual world.
P1. For all propositions p, if proposition p is contingent, then there is a possible world where something explains why the proposition is true.
P2. The big conjunctive contingent fact is contingent.
P3. The big conjunctive contingent fact is the conjunction of all actual contingent atomic facts true at the actual world.
P4. For all worlds w, and all things x, if x explains the big conjunctive contingent fact is true at w and the big conjunctive contingent fact is the conjunction of all actual contingent atomic facts true at the actual world, then world w is identical to the actual world.
P5. For all propositions p, and things x, if x explains why p is true in the actual world and p is contingent, then x exists necessarily.
P6. For all propositions p, and things x, if x explains why p is true in the actual world, and the proposition “Matter Exists” is an element of p, then x is immaterial.
P7. For all propositions p, and things x, if x explains why p is true in the actual world, and the proposition “Time exists” is an element of p, then x is eternal.
P8. For all propositions p, and things x, if x explains why p is true in the actual world, and the set of all atomic propositions describing natural laws that exists is an element of p, then x is not natural.
P9. For all propositions p, and things x, if x explains why p is true in the actual world, x is either natural or personal.
P10. For all propositions p, and things x, if x explains why p is true in the actual world and p is contingent and x exists necessarily, then x is free.
P11. For all things x, if x is free, then it is not the case that there is something z such that the actions of x entirely depend on z.
P12. For all propositions p1 and all things x1, if x1 explains why p1 is true in the actual world and there is a world w and a proposition p2 such that p2 is the conjunction of all actual contingent atomic facts at w, and there is some y that explains why p2 is true at world w, and x is not identical to y, then there is something z such that the actions of x entirely depends upon z.
P13. For all propositions p1 and things x, if x explains why p1 is true at the actual world, and it is not the case that there is a world w and a proposition p2 such that p2 is the conjunction of all actual contingent atomic facts at w, and there is some y that explains why p2 is true at world w, and x is not identical to y, then x is omnipotent.
P14. For all x, if x is omnipotent and x is personal, then x is all knowing.
P15. For all x, if x is omnipotent, x is all-knowing, and x is free, then x is omnibenevolent.
P16. For all x, if x is omnibenevolent, and x is personal, and x is omnipotent, then x is worthy of worship.
P17. For all x, if x is timeless, immaterial, personal, omnipotent, omniscient, omnibenevolent, free, worthy of worship, and explains why the big conjunctive contingent fact is true in the actual world, then if anything y is timeless, immaterial, personal, omnipotent, omniscient, omnibenevolent, free, worthy of worship, and explains why the big conjunctive contingent fact is true in the actual world, then x is identical to y.
P18. The proposition “Matter exists” is an element of the big conjunctive contingent fact.
P19. The proposition “Time exists” is an element of the big conjunctive contingent fact.
P20. The set of all atomic propositions that describe the natural laws that exist is an element of the big conjunctive contingent fact.
C. God necessarily exists.

Let

P ∈ Q ≝ proposition P is an element of proposition Q
E!x ≝ x exists
Fx ≝ x is free
Gx ≝ x is omnibenevolent
Kx ≝ x is omniscient
M̅x ≝ x is immaterial
Nx ≝ x is natural
Ox ≝ x is omnipotent
Sx ≝ x is personal
T̅x ≝ x is eternal
Wx ≝ x is worthy of worship
Bpw ≝ p is the conjunction of all actual contingent atomic facts is true at world w
Dxy ≝ the actions of x entirely depends upon y
Expw ≝ x explains that p is true at world w
a ≝ the actual world
β ≝ the big contingent conjunctive fact
g ≝ (ɿx){[(T̅x ∧ M̅x) ∧ (Sx ∧ Ox)] ∧ [(Kx ∧ Gx) ∧ (Fx ∧ Wx)] ∧ Exβa}
M ≝ Matter exists.
T ≝ Time exist.
ℕ ≝ the set of all atomic propositions describing natural laws that exist.

1. (∀p)[(◊p ∧ ◊~p) ⊃ (∃w)(∃x)Expw] (premise)
2. ◊β ∧ ◊~β (premise)
3. Bβa (premise)
4. (∀w)(∀x)[(Exβw ∧ Bβa) ⊃ (w = a)] (premise)
5. (∀p)(∀x){[Expa ∧ (◊p ∧ ◊~p)] ⊃ □E!x} (premise)
6. (∀p)(∀x){[Expa ∧ (M ∈ p)] ⊃ M̅x} (premise)
7. (∀p)(∀x){[Expa ∧ (T ∈ p)] ⊃ T̅x} (premise)
8. (∀p)(∀x){[Expa ∧ (ℕ ∈ p)] ⊃ ~Nx} (premise)
9. (∀p)(∀x)[Expa ⊃ (Nx ∨ Sx)] (premise)
10. (∀p)(∀x){{[Expa ∧ (◊p ∧ ◊~p)] ∧ □E!x} ⊃ Fx} (premise)
11. (∀x)(Fx ⊃ ~(∃z)Dxz) (premise)
12. (∀p1)(∀x){{Exp1a ∧ (∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (x ≠ y)]} ⊃ (∃z)Dxz} (premise)
13. (∀p1)(∀x){{Exp1a ∧ ~(∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (x ≠ y)]}} ⊃ Ox} (premise)
14. (∀x)[(Ox ∧ Sx) ⊃ Kx] (premise)
15. (∀x){[(Ox ∧ Kx) ∧ Fx] ⊃ Gx} (premise)
16. (∀x){[(Gx ∧ Sx) ∧ Ox] ⊃ Wx} (premise)
17. (∀x){{[(T̅x ∧ M̅x) ∧ (Sx ∧ Ox)] ∧ [(Kx ∧ Gx) ∧ (Fx ∧ Wx)] ∧ Exβa} ⊃ (∀y){[(T̅y ∧ M̅y) ∧ (Sy ∧ Oy)] ∧ [(Ky ∧ Gy) ∧ (Fy ∧ Wy)] ∧ Eyβa ⊃ (x = y)]} (premise)
18. m ∈ β (premise)
19. t ∈ β (premise)
20. ℕ ∈ β (premise)
21. (◊β ∧ ◊~β) ⊃ (∃w)(∃x)Exβw (1 UI)
22. (∃w)(∃x)Exβw (2,21 MP)
23. (∃x)Exβω(22 ΕΙ)
24. Eμβω (23 ΕΙ)
25. (∀x)[(Exβω ∧ Bβa) ⊃ (ω = a)] (4 UI)
26. (Eμβω ∧ Bβa) ⊃ (ω = a) (25 UI)
27. Eμβω ∧ Bβa (3,24 Conj)
28. (ω = a) (26,27 MP)
29. Eμβa (24,29 ID)
30. Eμβa ∧ (◊β ∧ ◊~β) (2,29 Conj)
31. (∀x){[Exβa ∧ (◊β ∧ ◊~β)] ⊃ □E!x} (5 UI)
32. [Eμβa ∧ (◊β ∧ ◊~β)] ⊃ □E!μ (31 UI)
33. □E!μ (30,32 MP)
34. Eμβa ∧ (M ∈ β) (18,29 Conj)
35. (∀x){[Exβa ∧ (M ∈ β)] ⊃ M̅x} (6 UI)
36. [Eμβa ∧ (M ∈ β)] ⊃ M̅μ (35 UI)
37. M̅μ (34,36 MP)
38. Eμβa ∧ (T ∈ β) (19,29 Conj)
39. (∀x){[Exβa ∧ (T ∈ β)] ⊃ T̅x} (7 UI)
40. [Eμβa ∧ (T ∈ β)] ⊃ T̅μ (39 UI)
41. T̅μ (38,40 MP)
42. Eμβa ∧ (ℕ ∈ β) (20,29 Conj)
43. (∀x){[Exβa ∧ (ℕ ∈ β)] ⊃ ~Nx} (8 UI)
44. [Eμβa ∧ (ℕ ∈ β)] ⊃ ~Nμ (43 UI)
45. ~Nμ (42,44 MP)
46. (∀x)[Exβa ⊃ (Nx ∨ Sx)] (9 UI)
47. Eμβa ⊃ (Nμ ∨ Sμ) (46 UI)
48. Nμ ∨ Sμ (29,47 MP)
49. Sμ (45,58 DS)
50.(∀x){{[Exβa ∧ (◊β ∧ ◊~β)] ∧ □E!x} ⊃ Fx} (10 UI)
51. {[Eμβa ∧ (◊β ∧ ◊~β)] ∧ □E!μ} ⊃ Fμ (50 UI)
52. [Eμβa ∧ (◊β ∧ ◊~β)] ∧ □E!μ (30,33 Conj)
53. Fμ (51,52 MP)
54. Fμ ⊃ ~(∃z)Dμz (11 UI)
55. ~(∃z)Dμz (53,54 MP)
56. (∀x){{Exβa ∧ (∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (x ≠ y)]} ⊃ (∃z)Dxz} (12 UI)
57. {Eμβa ∧ (∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (μ ≠ y)]} ⊃ (∃z)Dxz (56 UI)
58. ~{Eμβa ∧ (∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (μ ≠ y)]} (55,57 MT)
59. ~Eμβa ∨ ~(∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (μ ≠ y)]} (58 DeM)
60. ~~Eμβa (29 DN)
61. ~(∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (μ ≠ y)]} (59,60 DS)
62. (∀x){{Exβa ∧ ~(∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (y ≠ z)]} ⊃ Ox} (13 UI)
63. {Eμβa ∧ ~(∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (μ ≠ y)]}} ⊃ Oμ (62 UI)
64. Eμβa ∧ ~(∃w)(∃p2){Bp2w ∧ (∃y)[Eyp2w ∧ (μ ≠ y)]} (29,61 Conj)
65. Oμ (63,64 MP)
66. (Oμ ∧ Sμ) ⊃ Kμ (14 UI)
67. Oμ ∧ Sμ (49,65 Conj)
68. Kμ (66,67 MP)
69. [(Oμ ∧ Kμ) ∧ Fμ] ⊃ Gμ (15 UI)
70. Oμ ∧ Kμ (65,68 Conj)
71. (Oμ ∧ Kμ) ∧ Fμ (53,70 Conj)
72. Gμ (69,71 MP)
73. [(Gμ ∧ Sμ) ∧ Oμ] ⊃ Wμ (16 UI)
74. Gμ ∧ Sμ (49,72 Conj)
75. (Gμ ∧ Sμ) ∧ Oμ (65,74 Conj)
76. Wμ (73,75 MP)
77. {[(T̅μ ∧ M̅μ) ∧ (Sμ ∧ Oμ)] ∧ [(Kμ ∧ Gμ) ∧ (Fμ ∧ Wμ)] ∧ Eμβa} ⊃ (∀y){[(T̅y ∧ M̅y) ∧ (Sy ∧ Oy)] ∧ [(Ky ∧ Gy) ∧ (Fy ∧ Wy)] ∧ Eyβa ⊃ (μ = y)} (17 UI)
78. T̅μ ∧ M̅μ (37,41 Conj)
79. Sμ ∧ Oμ (49,65 Conj)
80. (T̅μ ∧ M̅μ) ∧ (Sμ ∧ Oμ) (78,79 Conj)
81. Kμ ∧ Gμ (68,72 Conj)
82. Fμ ∧ Wμ (53,76 Conj)
83. (Kμ ∧ Gμ) ∧ (Fμ ∧ Wμ) (81,82 Conj)
84. [(T̅μ ∧ M̅μ) ∧ (Sμ ∧ Oμ)] ∧ [(Kμ ∧ Gμ) ∧ (Fμ ∧ Wμ)] (80,83 Conj)
85. [(T̅μ ∧ M̅μ) ∧ (Sμ ∧ Oμ)] ∧ [(Kμ ∧ Gμ) ∧ (Fμ ∧ Wμ)] ∧ Eμβa (29,84 Conj)
86. (∀y){[(T̅y ∧ M̅y) ∧ (Sy ∧ Oy)] ∧ [(Ky ∧ Gy) ∧ (Fy ∧ Wy)] ∧ Eyβa ⊃ (μ = y)} (77,85 MP)
87. {[(T̅μ ∧ M̅μ) ∧ (Sμ ∧ Oμ)] ∧ [(Kμ ∧ Gμ) ∧ (Fμ ∧ Wμ)] ∧ Eμβa} ∧ (∀y){[(T̅y ∧ M̅y) ∧ (Sy ∧ Oy)] ∧ [(Ky ∧ Gy) ∧ (Fy ∧ Wy)] ∧ Eyβa ⊃ (μ = y)} (85,86 Conj)
88. {[(T̅μ ∧ M̅μ) ∧ (Sμ ∧ Oμ)] ∧ [(Kμ ∧ Gμ) ∧ (Fμ ∧ Wμ)] ∧ Eμβa} ∧ (∀y){[(T̅y ∧ M̅y) ∧ (Sy ∧ Oy)] ∧ [(Ky ∧ Gy) ∧ (Fy ∧ Wy)] ∧ Eyβa ⊃ (μ = y)} ∧ □E!μ (33,87 Conj)
89. (∃x){{[(T̅x ∧ M̅x) ∧ (Sx ∧ Ox)] ∧ [(Kx ∧ Gx) ∧ (Fx ∧ Wx)] ∧ Exβa} ∧ (∀y){[(T̅y ∧ M̅y) ∧ (Sy ∧ Oy)] ∧ [(Ky ∧ Gy) ∧ (Fy ∧ Wy)] ∧ Eyβa ⊃ (x = y)} ∧ □E!x} (88 EG)
90. □E!g (89 theory of descriptions)

QED

Footnotes:

1 A.R. Pruss & R.M. Gale. (1999). “A New Cosmological Argument.” In Religious Studies. Vol. 35. 461-476

2 J. Gellman. (2000). “Prospects for a Sound Stage 3 of Cosmological Arguments.” In Religious Studies. Vol. 36 159-201

Vexing Links (8/5/2016)

Apologies for the hiatus. I am hoping to put some arguments out there soon. But in the meantime, here are some links of note:

1. My Ph.D. dissertation is now on ProQuest.

2. My review of Modality & Explanatory Reasoning by Boris Kment was recently published by the Polish Journal of Philosophy.

3. I’m currently reading Structure and the Metaphysics of Mind: How Hylomorphism Solves the Mind-Body Problem by William Jaworski.  I’m hoping to do a presentation on hylomorphism this fall, so this will really help.

4. Wisecrack has some great videos on the Philosophy of  Daredevil, and the Philosophy of the Joker.

5.  Looking forward to the Ultimate Game of Thrones and Philosophy, especially as it will feature contributions from Max Andrews and Tyler Dalton McNabb.

6. Dale Tuggy interview Timothy Pawl on Trinities Podcast: Pt 1 and P2.

7. Appropriate for our current political climate, the SEP has a new article out on the Ethics and Rationality of Voting.

8.  Illustrates the problem of semantics for AI: the Domino Computer.

9. The History of Philosophy without any Gaps has some great recent podcasts on the Trinity: Episodes 258 and  259.

10. Justin Brierley of the Unbelievable? Podcast explains the argument from Fine-Tuning.

Hebrews 3, Proving the Minor, and the Divinity of Christ

I was recently reading the Letter to the Hebrews and came upon an interesting passage:

Therefore, holy brethren, partakers of a heavenly calling, consider Jesus, the Apostle and High Priest of our confession; He was faithful to Him who appointed Him, as Moses also was in all His house. For He has been counted worthy of more glory than Moses, by just so much as the builder of the house has more honor than the house. For every house is built by someone, but the builder of all things is God. Now Moses was faithful in all His house as a servant, for a testimony of those things which were to be spoken later; but Christ was faithful as a Son over His house—whose house we are, if we hold fast our confidence and the boast of our hope firm until the end (Hebrews 3:1-6, NASB).

The logic of the passage jumped out at me, as I have been keen to find passages that affirm the divinity of Christ in light of my interactions with Biblical Unitarians.  This passage is concerned with demonstrating that Christ is worthy of more glory than Moses.  Thomas Aquinas dissects the passage in the following manner:

161. – But the Apostle’s reason is that more glory is due Him Who built the house, than to him that dwells in it. But Christ built the house: ‘You have made the morning light and the sun’ (Ps. 73:16); ‘Wisdom has built herself a house’, i.e., the Church (Pr. 9:1). For Christ by Whom grace and truth came, built the Church, as legislator; but Moses, as promulgator of the Law: therefore, it is only as promulgator that glory is due Moses. Hence, his face became bright: ‘So that the children of Israel could not steadfastly behold the face of Moses for the glory of his countenance’ (2 Cor. 3:7). Therefore, the sequence of thought is this: You say that Christ is faithful as Moses was. Why then overlook Him? Certainly this man was counted worthy of greater glory than Moses, by so much as he that has built the house has greater honor than the house. As if to say: Even though Moses deserves mention, Christ is more honorable, because He is the builder of the house and the chief lawgiver: ‘Behold, God is high in his strength, and none is like him among the lawgivers’ (Jb. 36:22). Therefore, if Moses is deserving of glory, Christ is more deserving: ‘For is the ministration of condemnation be in glory, much more the ministration of justice abounds in glory’ (2 Cor. 3:9).

162. – Then he proves the minor premise of his reason when he says: For every house is built by some man. But the minor is that Christ built that house. He proves this, first, because every house needs a builder; secondly, because the house of which he speaks was built by Christ, the builder of all things is God.

163. – First, therefore, he proves that this house, as any other, needs a builder, because its various parts are put together by someone. This is obvious in a structure in which the wood and stones, of which it is composed, are united by someone. But the assembly of the faithful, which is the Church and the house of God, is composed of various elements, namely, Jews and Gentiles, slaves and free. Therefore, the church, as any other house, is put together by someone. He gives only the conclusion of this syllogism, supposing the truth of the premises as evident: ‘Be you also as living stones built up, a spiritual house, a holy priesthood’ (1 Pt. 2:5); ‘Built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief cornerstone’ (Eph. 2:20).

164. – Then (v. 4b) he proves that Christ is the builder of that house, for He is God, the builder of all things. And if this is understood of the whole world, it is plain: ‘He spoke and they were made; he commanded and they were created’ (Ps. 32:9) But there is another spiritual creation, which is made by the Spirit: ‘Send forth your spirit, and they shall be created, and you shall renew the face of the earth’ (Ps. 104:30). This is brought about by God through Christ: ‘Of his own will has he begotten us by the word of truth, that we might be some beginning of his creature’ (Jas. 1:18); ‘We are his workmanship, created in Christ Jesus in good works’ (Eph. 2:10). Therefore, God created that house, namely, the Church, from nothing, namely, from the state of sin to the state of grace. Therefore, Christ, by Whom He made all things, ‘by whom also he made the world’ (Heb. 1:2), is more excellent (since He has the power to make) than Moses, who was only the announcer (Thomas Aquinas, Commentary on Hebrews).

If I understand Aquinas’s analysis of the passage correctly, the author of Hebrews is trying to prove:

C1: Christ is worthy of more glory than Moses

And the premises that support this conclusion are:

P1: For all persons p1 and p2, if p1 is the builder of the house that p2 dwells in, then p1 is worthy of more glory than p2.1

P2. Christ is the builder of the house that Moses dwells in.

Now, C does follow reasonably well from P1 and P2 (see the footnote below). Aquinas notes that further support is provided in verse 4 for the truth of the minor premise, i.e. P2. This sub-argument has massive Christological significance, and the argument looks like this:

P3: For all x, if x is a house, then there is some person who built x.

P4: For all x, if there is some person who built x, the person who built x is God.

From (P3) and (P4), we can draw the conclusion that God is the builder of all houses, or:

C2: For all x, if x is a house, the person who built x is God.

So, given that there is some house that Moses dwells in:

P5: There exists some x such that x is a house and Moses dwells in x.

We can conclude:

C3: There exists some x such that x is a house and Moses dwells in x, and the person who built x is God.

Or in more readable English: God is the builder of the house that Moses dwells in.

But wait a minute! C3 doesn’t say anything like P2. The only way that C3 could be taken to support P2 is if we add a premise, which the author of the Letter to the Hebrews has suppressed, namely:

P6: Christ is God.

The author invites the reader to reason through his enthymeme, and keep in mind the truth that Christ is God, and so the creator of all things, including the Church and all of the houses of Israel, including that of Moses. So from C3 and P6, we can draw out:

C4: There exists some x such that x is a house and Moses dwells in x, and the person who built x is Christ.

And C4 just is P2.

Now, we are also told that Jesus is the Son over the house, but that it is His house. So, we get both the idea that Jesus is the Son of God and God, the creator of all things.

Suppose, for a moment, that the author did not intend such an argument.  Instead, he merely wanted to argue that Christ is the Son of the house, whereas Moses is the servant.  If so, then his entire point about builders being more deserving of glory than members of the house would be wasted ink.  For that entire passage would only prove that God is more worthy of glory than Moses, which is hardly in dispute.  The passage only makes sense if it can lend support to the authors actual conclusion, and the only way to validly reach that conclusion is if we identify Christ as God.

1To be more precise, we should say something like, P1′: For all persons p1 and p2, if p1 is the builder of the house that p2 dwells in, and p1 is not identical to p2, then p1 is worthy of more glory than p2. We would also need to then add P3′: Christ is not identical to Moses, which is a reasonable assumption given the Transfiguration, for instance.

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

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