One of the relatively new formalizations of prima via is in (Nieznański 2006). Its logical base is first-order classical predicate calculus with identity.
Abbreviations:
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‘MAD(x, y, e)’ means ‘y causes x to exist’
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‘xPOe’ means ‘x is in potency to esse (“existence”)’
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‘xACe’ means ‘x is in act to esse’
Definitions:
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where R is a binary relation: xR*y :=∃ n xRn
y. In turn, Rn is defined recursively as R1 :=R ∧ ∀ k (Rk + 1 :=RkoR), where RoR is superposition, i.e.: xRoRy :=∃z (xRz ∧ zRy)
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v(y) :=∃ x MAD(y, x, e)
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yMOx :=MAD(y, x, e) (that shows that ternary relation is not necessary)
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MO is unfounded :=∀ x, y (yMO*x ∧ x ≠ y → v(x))
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x is (one of?) the first unmoved mover(s?)Footnote 4 :=∃ y (yMO*x ∧ x ≠ y ∧ ¬ v(x))
According to Nieznański, Thomas assumes the following six axioms:
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1.
∃ y v(y)
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2.
∀ x, y (yMOx → yPOe)
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3.
∀ x, y (yMOx → xACe)
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4.
¬ ∃ x (xPOe ∧ xACe)
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5.
∀ x, y (yMOx → (v(x) → (x ≠ y → ∃ z (xMOz ∧ x ≠ z))))
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6.
∀ y (v(y) → ∃ x (yMO*x ∧ x ≠ y ∧ ¬ v(x)))
They imply that:
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7.
∀ x, y (yMOx → yPOe ∧ xACe) (from 2, 3)
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8.
¬ ∃ x xMOx (from 4, 7)
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9.
∀ x, y (yMOx → x ≠ y) (from 8)
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10.
∃ x, y (yMO*x ∧ x ≠ y ∧ ¬ v(x)) (from 1, 6)
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11.
∃ x (x is (one of?) the first unmoved mover(s?)) (from 10 and definition)
It becomes apparent that four axioms are in fact superfluous: it suffices to assume 1 and 6 to prove the existence of (one of?) the first unmoved mover(s?). But then the proof seems trivial: from the very strong axiom 6 (that can be called after B. Bolzano “the principle of foundation”) we almost immediately have the conclusion. Therefore, applying the principle of charity to Thomas’ argument, I believe that in fact Nieznański did not reconstruct the prima via.
One could argue here: “never mind, we need the premise that there is no potency in God, and the argument shows that this is the case”. But from 3 and 4 it follows that every cause of existence has no potency to esse and even if 3 may be true in the case of esse substantiale (substantial existence, or the existence of substance), it is not obvious in the case of esse accidentale (accidental existence, or the existence of accident): suppose that I freely decide to write this sentence. The esse of my decision has a (ultimate) cause (if we believe in free will) in me. But I was not in act to this esse, yet in potency.Footnote 5 Therefore, even if Thomas had in mind here esse substantiale, the truth of 3 is compatible with being in potency to esse accidentale.
I take J. Bocheński’s last formalization (Bocheński 2003, 49–57), as corrected by Nieznański due to several logical errors (see Nieznański 2006, 30f), as more adequate. The logical basis is the same.
Abbreviations:
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‘MAD(x, y, z)’ means ‘x is moved (in the Aristotelian sense of change) by y to z’
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‘xPOy’ means ‘x is in potency to y’
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‘xACy’ means ‘x is in act to y’
Definitions:
-
where R is a binary relation (or a ternary one provided that its third argument is hidden because it is unessential): xR*y :=∃ n xRn
y. In turn, Rn is defined recursively as R1 :=R ∧ ∀ k (Rk + 1 :=RkoR), where RoR is superposition, i. e. xRoRy :=∃ z (xRz ∧ zRy).
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MAD is unfounded (in Aquinas’ words: procedit in infinitum – “proceeds in infinity”):= ∀ x, y (yMAD*x ∧ x ≠ y → v(x))
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v(x) :=∃ y, z MAD(x, y, z)
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M(x) :=x is (one of?) the first unmoved mover(s?)
According to Bocheński, Aquinas assumes seven axioms:
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1.
∀ x, y (MAD(x, y, z) → xPOz)
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2.
∀ x, y (MAD(x, y, z) → yACz)
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3.
¬ ∃ x, z (xPOz ∧ xACz)
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4.
∃ x, y, z (MAD(x, y, z) ∧ v(y))
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5.
∀ x, y, z (MAD(x, y, z) ∧ x ≠ y ∧ v(y) → ∃ t, u (MAD(y, t, u) ∧ y ≠ t))
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6.
∃ x, y, z (MAD(x, y, z) ∧ x ≠ y ∧ v(y) ∧ ∃ t, u (MAD(y, t, u) ∧ y ≠ t)) → ¬ MAD is unfounded
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7.
¬ MAD is unfounded → ∃ M(x)
From these we can infer what follows:
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8.
∀ x, y, z (MAD(x, y, z) → x ≠ y) (from 1, 2, 3)
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9.
∃ x, y, z (MAD(x, y, z) ∧ x ≠ y ∧ v(y)) (from 4, 8)
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10.
∃ x, y, z (MAD(x, y, z) ∧ x ≠ y ∧ v(y) ∧ ∃ t, u (MAD(y, t, u) ∧ y ≠ t)) (from 5, 9)
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11.
∃ M(x) (from 6, 7, 10)
Philosophers who criticize “the five ways” usually reject 6 but – being aware that 6 is not obvious from the point of view of pure logic – I personally do not find anything unreasonable in maintaining this version of the principle of foundation.Footnote 6 Instead, I believe that Thomas should refute 2 (and – for the same “libertarian” reason – 5 as well), because I need not be in act to what I intend to do.Footnote 7 Similarly, to change the spatial location (z in 5) of the stick (x) freely, I (y) need not be moved by anything else (t). That is why I find this way of proving that God is a pure act unconvincing.
After this digression let us return to the main thread, i. e. arguments from q. 3, a. 6.
Argument 2): quia Deus est suum esse (q. 3, a. 4) (“for God is [identical with] His existence”). But on the contrary, Thomas at most proved that God’s essence is His existence (another question is whether something, being its own existence, is deprived of accidents). It would indeed follow if, for example, God were His own essence, but this is equivalent to the thesis that is yet to be proved.
Thomas’ advocate can suggest a more charitable interpretation. Namely, let us analyze q. 3, a. 4 (and later, if needed, the parallel text from SCG, i. e. c. 22). The first argumentFootnote 8 is invalid, since Thomas neglects the possibility that existence can be a part of essence. The second one is erroneous, since it invokes premises from the prima via, which we have just undermined.Footnote 9 In the third one he claims: …illud quod habet esse et non est esse, est ens per participationem. (…) Si igitur non sit suum esse, erit ens per participationem, et non per essentiam. Non ergo erit primum ens, quod absurdum est dicere (“something that has existence and is not identical with the existence, is a being through participation. (…) So if God is not [identical with] His existence, He will be being through participation, not through His essence. Hence, He will not be the first being, and it is an absurd to say so”). ‘Primum ens’ denotes here the first cause (from “the second way”) or the being necessary through itself (from “the third way”). Nevertheless, assuming that these “ways” are sound arguments,Footnote 10 I can see no inference from “there is the first cause (or being necessary through itself)” to “this being is identical with its existence”.Footnote 11
Argument 3): …omne quod est per se, prius est eo quod est per accidens. Unde, cum Deus sit simpliciter primum ens, in eo non potest esse aliquid per accidens. Sed nec accidentia per se
Footnote 12
in eo esse possunt, sicut risibile est per se accidens hominis. Quia huiusmodi accidentia causantur ex principiis subiecti, in Deo autem nihil potest esse causatum, cum sit causa prima (“Everything, which is by itself, is prior to what is by accident. Hence, since God is by His own nature the prime being, nothing can be in Him by accident. Neither can any proper accidents be in Him, as, for example, being able to laugh is a man’s proper accident; because accidents of that kind have their cause in the subject’s principles. Yet nothing, which is in God, can have any cause, since God is the first cause”).
This is a compact version of the first argument from q. 3, a. 4 – to see this, it suffices to modify this proof from q. 3, a. 4, so as it concerns accidents, instead of esse:
…quidquid est in aliquo quod est praeter essentiam eius, oportet esse causatum vel a principiis essentiae, sicut accidentia propria consequentia speciem, ut risibile consequitur hominem et causatur ex principiis essentialibus speciei; vel ab aliquo exteriori, sicut calor in aqua causatur ab igne. Si igitur aliquid (scilicet accidens) sit in Deo
, necesse est quod vel sit causatum ab aliquo exteriori, vel a principiis essentialibus eiusdem rei. (…) Hoc autem non potest dici de Deo, quia Deum dicimus esse primam causam efficientem (“it is necessary that everything which is in something, and outside of the essence of that in which it is, is caused either by the principles of essence, as proper accidents following from the species, as being able to laugh belongs to a man, and the essential principles of the species are its cause, or by something external to this thing, as, e.g. fire is the cause of heat in water. So if there is something (that is, an accident) in God, it will be necessary that it is caused either by something external to God, or by His essential principles. (…) But we cannot say it about God, since God is the first efficient cause”).
But on the contrary, that God does not have a cause (assuming that the secunda via is sound), does not imply that God cannot be the cause of the proper accident. Moreover, it does not exclude the possibility of existing of two Gods, one of them being the cause of the (improper) accident in another. The reason is that Thomas proved neither that God is unique (the attempts to prove it are in q. 11, a. 3) nor that He is the cause of everything.
To sum up, arguments from ST are inconclusive.
Summa Contra Gentiles
* c. 21 (Quod Deus est sua essentia – “That God is His essence”).
Argument 1): Ostensum est autem in Deo nullam esse compositionem (c. 18). Deus igitur est sua essentia (“It has been shown that there is no composition in God (in Chapter 18). Hence, God is [identical with] His essence”). Let us analyze then c. 18:
Argument 1): …in omni composito oportet esse actum et potentiam. (…) Quae enim actu sunt, non uniuntur nisi quasi colligata vel congregata, quae non sunt unum simpliciter. In quibus etiam ipsae partes congregatae sunt sicut potentia respectu unionis: sunt enim unitae in actu postquam fuerint in potentia unibiles. In Deo autem nulla est potentia (“there must be an act and a potency in every composite. (…) For [these] things which are in act are not unified unless, so to say, bound or aggregated, as not being one in and of itself. And in these things, their aggregated parts are in potency to being unified: for they are actually unified, after having been potentially unified. Yet, there is no potency in God”).
But on the contrary: it has not been established that there is no potency in God, and even if it has, partes congregatae refer obviously to common mereological wholes, such as heaps, not to accidents.
Argument 2): Omne compositum posterius est suis componentibus. Primum ergo ens, quod Deus est, ex nullis compositum est (“every composite is posterior to its components. So the first being, which is God, is not composed of anything”).
Here we could simply repeat the last ‘but on the contrary’ from the part devoted to the respective argument from ST.
Argument 3): Omne compositum est potentia dissolubile (…). Quod autem est dissolubile, est in potentia ad non esse. Quod Deo non competit: cum sit per se necesse-esse (“Every composition is potentially decomposable (…). What is decomposable, is potentially non-existent, which does not belong to God, since He is by Himself a necessary being [or: it is necessary by itself that He exists]”).
But on the contrary: it may not hold for the composite of essence and proper accident(s).
Argument 4): Si igitur compositus esset Deus, haberet componentem: non enim ipse seipsum componere posset, quia nihil est causa sui ipsius; esset enim prius seipso, quod est impossibile. Componens autem est causa efficiens compositi. Ergo Deus haberet causam efficientem… (“if God were composed, He would have something composing Him, for He could not compose Himself, as nothing is the cause of itself: otherwise He would exist before Himself, which is impossible. And a thing composing is the efficient cause of a thing composed. Hence, God would have an efficient cause”).
But on the contrary: as above.
Argument 5): In quolibet genere tanto aliquid est nobilius quanto simplicius: sicut in genere calidi ignis, qui non habet aliquam frigidi permixtionem. Quod igitur est in fine nobilitatis omnium entium, oportet esse in fine simplicitatis. Hoc autem quod est in fine nobilitatis omnium entium, dicimus Deum, cum sit prima causa: causa enim est nobilior effectu. Nulla igitur compositio ei accidere potest (“in every kind, the simpler something is, the more noble it is: for example, among hot things fire is such, as it is not mixed with anything cold. Thus, something that is the most noble of all beings, is the simplest. Yet, by God we mean something that is the most noble of all beings, because He is the first cause: for a cause is more noble than an effect. Hence, no composition can take place in Him”).
But on the contrary: the first sentence is not justified; the same goes for quod Deus est in fine nobilitatis omnium entium et quod causa est nobilior effectu. Even if they were warranted, they would be consistent with such object having accidents.
Argument 6): In omni composito bonum non est huius vel illius partis, sed totius: nam partes sunt imperfectae respectu totius (…). Si ergo Deus est compositus, perfectio et bonitas eius propria invenitur in toto, non autem in aliqua eius partium. Et sic non erit in eo pure illud bonum quod est proprium ei. Non est ergo ipse primum et summum bonum (“in every composite, the good does not belong to this or that part, but to the whole: since parts are imperfect as compared to the whole (…). So, if God is composite, His proper perfection and goodness is found in the whole, not in some of His parts. Thus, there will not be in Him purely this good, which is proper to Him. Therefore, He is not the first and the highest good”).
But on the contrary: it is not justified quod ipse est primum et summum bonum, and even if it were, we would have once again non sequitur.
Argument 7): Ante omnem multitudinem oportet invenire unitatem. In omni autem composito est multitudo. Igitur oportet id quod est ante omnia, scilicet Deum, omni compositione carere (”before each multiplicity one should find unity. But in every composite is multiplicity. Hence, it is necessary that this, which is before everything, namely God, is free of every composite”).
But on the contrary: it has not been proven quod Deus est ante omnia. And even if it has, we would have the same flaw as above.
Coming back to the arguments from c. 21:
Argument 2): In Deo autem non sunt aliqua accidentia, ut ostendetur (c. 23). Est igitur ipse sua essentia (“but there are no accidents in God, as it will be shown (in chapter 23). Therefore, He is [identical with] His essence”).
Once again we have to refer to c. 23:
Argument 1):=ST, q. 3, a. 6, argument 2) (see above).
Argument 2): Accidents can be either proper or improper ones. If proper, see ST, q. 3, a. 3 above. If improper, this accident is caused, but this fact implies that God changes, contrary to quod Deus est primus motor separatus, omnino immobilis (c. 13) (“that God is the first, separated mover, in no respect movable”).
But on the contrary, c. 13 is the counterpart of the prima via, but the prima via does not establish that there is no change in God.Footnote 13
Argument 3):=ST, q. 3, a. 6, argument 1) (see above)
Argument 4): Cuicumque inest aliquid accidentaliter, est aliquo modo secundum suam naturam mutabile: accidens enim de se natum est inesse et non inesse. Si igitur Deus habet aliquid accidentaliter sibi conveniens, sequetur quod ipse sit mutabilis. Cuius contrarium supra demonstratum est (“Everything in which there is something accidentally, is somehow by its nature changeableFootnote 14; for [improper] accident is by its nature being in and not being in [i. e. by its nature it has potentiality for being in something, and also for not being in something]. Hence, if God has something accidentally, it follows that He is changeable; whose opposite has been demonstrated above”).
But on the contrary, once again it is based upon the prima via.
Argument 5):=c. 18, argument 5) (see above)
Argument 6): cum Deus est simplicissimus (“that God is the simplest”, c. 18), i. e.=c. 21, argument 1) (see above)
Coming back to the arguments from c. 21:
Argument 3):=ST, q. 3, a. 3 (see above)
Argument 4): Essentia rei vel est res ipsa vel se habet ad ipsam aliquo modo ut causa (…). Sed nullo modo potest esse aliquid causa Dei (“the essence of a thing is either [identical with] this thing or is related to this thing in some way as a cause (…). Yet in no way something can be the cause of God”).
But on the contrary, both the secunda via and its counterpart from SCG talk about efficient causes, not about formal ones.
Argument 5): Quod non est sua essentia, se habet secundum aliquid sui ad ipsam ut potentia ad actum. (…) Sed in Deo nulla est potentialitas, ut supra ostensum est (c. 16) (“Something that is not [identical with] its essence, is related in some of its aspect to that essence as potency to act. (…) But there is no potency in God, as it has been shown above (in chapter 16)”).
But on the contrary, the first proposition is not justified, and neither is the second one.Footnote 15
To sum up, arguments from SCG are also inconclusive.