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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

William Lane Craig lectures on naturalistic alternatives to the Big Bang

This is a must see…

WINTERY KNIGHT

Here’s the lecture, which was given in 2004 at the University of Colorado, Boulder. A very liberal university!

This lecture is suitable for intermediate and advanced Christian apologists.

The description of the video states:

This is quite simply one of the best lectures William Lane Craig (a philosopher of science) has given. Craig explores the origins of the universe. He argues for a beginning of the universe, while refuting scientific models like the Steady State Theory, the Oscillating Theory, Quantum Vacuum Fluctuation Model, Chaotic Inflationary Theory, Quantum Gravity Theory, String Theory, M-Theory and Cyclic Ekpyrotic Theory.

And here is the description of the lecture from Reasonable Faith:

A Templeton Foundation lecture at the University of Colorado, Boulder, laying out the case from contemporary cosmology for the beginning of the universe and its theological implications. Includes a lengthy Q & A period which features previous critics and debate opponents of Dr…

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Formalizing Aquinas’ Fourth Way

A “less obese” Thomas for a bare-bones formal representation of the 4th way!

I am interested in Aquinas’ Fourth Way, but I find that he lays out the argument so succinctly in the Summa Theologiae that it’s hard to see a valid proof at first blush:

The fourth way is taken from the gradation to be found in things. Among beings there are some more and some less good, true, noble and the like. But “more” and “less” are predicated of different things, according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest and, consequently, something which is uttermost being; for those things that are greatest in truth are greatest in being, as it is written in Metaph. ii. Now the maximum in any genus is the cause of all in that genus; as fire, which is the maximum heat, is the cause of all hot things. Therefore there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God (ST I, 2.3).

I would like to eventually work out a stronger version of the argument–stronger, that is, by weaken some of the premises and show that they still lead to the conclusion that God exists. But, my first step is to try and properly depict the essence of the argument in its purest logical form. I think I have to quantify over predicates to capture what I think Aquinas is saying. Also, I’ve used the transcendental of “Truth” as the particular perfection in this formulation of the argument. I chose “Truth” because I didn’t want this to come off as a moral argument by using “Goodness”, and I didn’t want to use “Being” because I fear being slowed down by the “existence is not a real predicate” objection, though I think there are very good responses to that objection. Finally, I confess that I might have tripped up over some of my brackets, so forgive the crudeness of this draft, if crudeness you should find. I happily admit that the errors and misrepresentations are all my own, and not poor Thomas’ fault! So…

Let:
Πxy – x has a greater degree of predicate Π than y
ExΠy –x is the eminent cause of y being Π
Θx – x has godhood
Txy – x has a greater degree of truth than y
ExTy – x is the eminent cause of y being true
(NB: I use x, y, and z as variables and u, v, and w as pseudonyms)

1. (∀x){Θx ≡ (∀y)[(x≠y) → (Txy & ExTy)]} (definition)
2. (∀Π){(∀x)[(∀y)[Πxy → (∃z)[((z≠x) → (Πzx & EzΠx))]]]} (premise)
3. (∃x)(∃y)Txy (premise)
∴(∃x)Θx
Deduction:
4. (∃y)Tuy (3 EI)
5. Tuv (4 EI)
6. (∀x){(∀y)[Txy → (∃z)[(z≠x) →( Tzx & EzTx)]]} (2 UI)
7. (∀y)[Tuy → (∃z)[(z≠u) → (Tzu & EzTu)]] (6 UI)
8. Tuv → (∃z)[(z≠u) → (Tzu & EzTu)] (7 UI)
9. (∃z)((z≠u) → (Tzu & EzTu) (5,8 MP)
10. (w≠u) → (Twu & EwTu) (9 EI)
11. Θw ≡ (∀y)[(w≠y) →(Twy & EwTy)] (1 UI)
12. {Θw → (∀y)[(w≠y) → (Twy & EwTy)]} & { (∀y)[(w≠y) → (Twy & EwTy)] → Θw} (11 Equiv)
13. (∀y)[(w≠y) → (Twy & EwTy)] → Θw (12 Simp)
14. [(w≠u) → (Twu & EwTu)] → Θw (13 UI)
15. Θw (10,14 MP)
16. (∃x)Θx (15 EG)

If you see any problems, let me know in the comments! On a lighter note, here is another version of the Fourth Way that I did with the help of lyrics from the 1980’s classic Higher Love, because if you think about it, there must be higher love…

[Update: My very bright and patient friend, Damon Watson, noticed some problems with the brackets and I have made changes accordingly]

Good Reasons to Believe: Daniel Vecchio & Marc Belcastro

Here is my interview of Marc Belcastro and his defense of the Contingency Argument.

Marc was an excellent guest and helped me through as a first time host. Excellent job, Marc!

“Good Reasons to Believe” Interview of Marc Belcastro Tomorrow (2/10)

MarcB

Tomorrow I will be interviewing Marc Belcastro on “Good Reasons to Believe”.  Marc’s talk is entitled “The Contingency Argument for God’s Existence”.  He will be explaining the Leibnizian Cosmological argument, and I get to grill him a little!  Marc is an excellent and careful philosopher, so this should be good.  Also, it will be my birthday, so the best gift to me would be for you to tune in (I am not sure that that would be a sufficient reason to tune in, but it’s some sort of reason)!

Bio: Marc Belcastro is a Christian theist, of the Anselmian Trinitarian variety. His primary philosophical interests include philosophy of religion and philosophical theology. Concerning philosophy of religion, his attention has lately been occupied by two contemporary versions of the cosmological argument as well as by divine command theory. Concerning philosophical theology, he’s recently been attempting to develop some work on the respective Christian doctrines of the Trinity and of final punishment. Marc also has an affection for metaphysics and coffee, together or apart. He intends to pursue a PhD in philosophy in the near future, and he also aspires to become a father, a novelist, and a better cook. Marc, his excellent wife Shelly, and their pretty cute dog Tibby live in Dayton, Ohio.

Details: the show streams through Ustream live (Sunday 2/10  4pm UK time,  11am EST, 10 am CST).  You should be able to find the show through this link NCG Studios: The Place.  Hope you’ll tune in!

P.S. If you miss the show, I’ll post the YouTube archive when it becomes available.

Steve Winwood’s Higher Love and Aquinas’ Fourth Way

One of my favorite songs from the 1980’s is Steve Winwood’s Higher Love.  Here are some of the lyrics:

Think about it,
There must be higher love.
Down in the heart or hidden in the stars above.
Without it,
Life is wasted time.
Look inside your heart and I’ll look inside mine.

Things look so bad everywhere.
In this whole world what’s fair?
We walk the line and we try to see.
Falling behind of what could be? (Winwood & Jennings 1986).

To me, this song describes the kind of yearning Saint Augustine describes when he wrote:

You arouse us so that praising you may bring us joy, because you have made us and drawn us to yourself, and our heart is unquiet until it rests in you (Conf. 1,I).1

The song also calls to my mind 1 John 4:8:

He that loveth not knoweth not God; for God is love.

So I wonder if Winwood’s song contains something of an argument for God’s existence.  Perhaps we could apply Winwood’s insights to a version of Aquinas’ fourth way.  Here is how Aquinas argues:

Among beings there are some more and some less good, true, noble and the like. But “more” and “less” are predicated of different things, according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest and, consequently, something which is uttermost being; for those things that are greatest in truth are greatest in being, as it is written in Metaph. ii. Now the maximum in any genus is the cause of all in that genus; as fire, which is the maximum heat, is the cause of all hot things. Therefore there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God (Sum I, 2, iii).2

Just for fun, here is a Winwood inspired version of a cosmological argument:

1.  If I can love, there must be higher love.

2.  If there is a higher love, there is highest love, which is the cause of  all lesser loves and is called God.

3.  I can love.

4.  Therefore, there is a highest love, which is the cause of all lesser loves and is called God (1 John 4:8).

Further, we might argue:

5.  If life is wasted time, there is no highest love.

6.  Therefore, life is not wasted time.

Who says that pop music can’t be profound?

1 Augustine. (1998). The Confessions. Trans. M. Boulding, O.S.B. New York: Vintage Spiritual Classics. 3.

2Thomas Aquinas. (1947). Summa Theologica. Trans. Fathers of the English Dominican Province. Retrieved August 6, 2011.

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