B O OK REVIEWS AND NOTICES TIM PAWL University of St. Th omas Paul Weingartner. God's Existence. Can it be Proven?: A Logical Commentary on the Five Ways of Th omas Aquinas. Frankfurt: Ontos Verlag, 2010. Paul Weingartner lists three tasks for this book: 1. "to show that the Five Ways of Th omas Aquinas can be presented in a form in which all fi ve ways are logically valid arguments." 2. "to off er a detailed and critical discussion of the premises used in the arguments including important defi nitions used as premises." 3. "to examine the two preliminary questions of Th omas Aquinas, 'Whether the existence of God is self-evident?' and 'Whether it can be demonstrated that God exists'" (1). Th e book has the following structure: the fi rst two questions (from task 3 above) are presented then commented on extensively. Th e commentary on these two questions takes the reader halfway through this short book (116 pages, from cover to cover). In the fi nal fi ft y pages of the book, each of the Five Ways is presented in the following manner. First the original Latin text is presented. Th en the English translation from the Fathers of the English Dominican Province is given. At this point, for the sake of completing his fi rst task, Weingartner takes the following two steps. "Th e fi rst step is a preliminary interpretation under the title 'the premises and conclusions of the text' which attempts to concentrate all the relevant parts into natural language and making [sic] them as precise as possible. Th e second step translates this into the symbolic language of First Order Predicate Logic" (2). Finally, Weingartner provides a commentary on the terms, premises, and inferences of the Way in question. Th e book is well formatted, and it is easy to navigate. We have seen some very helpful treatments of the Five Ways in the last decade or so.1 Unfortunately, this book does not rise to their level. In what follows, I will present three problems, along with illustrations of 1 See, for instance, Bochenski, Joseph M. (2000) "Th e Five Ways" in Th e Rationality of Th eism, ed. Adolfo García de la Sienra (Atlanta: Rodopi), 61-92; Wippel, John (2000), Th e Metaphysical Th ought of Th omas Aquinas (Washington: Catholic University of America Press), Chapter 12. 244 B O OK REVIEWS AND NOTICES each. Th ey are: (i) the commentary discusses too few topics, and does so in too shallow a manner; (ii) Weingartner's interpretation of many key concepts in the Five Ways is mistaken; (iii) the two-step translation process outlined above from the preliminary interpretation of the arguments to the First Order Predicate Logic (FOPL) reconstruction is done poorly. Consider the fi rst problem. Weingartner's second task in the book is "to off er a detailed and critical discussion of the premises" of the Ways. Th is is not done. Take the discussion of the First Way as an example. Th e commentary on the First Way is a mere fi ve pages, with three of those fi ve pages spent discussing how one should defi ne the term "First Mover." Th ere are only two other topics on which Weingartner comments. Th e fi rst is whether step 6 in the formalization should be presented as following from prior premises, or presented as a premise itself. Th e second concerns the important question of how one should understand the meaning of the Latin word, movetur. Th e cluster of important questions concerning movetur receives little more than a page of commentary, though the questions here are myriad and complex. Should movetur be translated intransitively, as a one-place predicate-x is in motion-or passively, as a two-place predicate-x is moved by y? What is the scope of motion in the First Way? Does he mean simply local motion? Or does it extend beyond local motion to qualitative and quantitative change as many claim? In addition to questions about the meaning of movetur, there are many other points where a reader desires commentary in the First Way. For instance, premise (4) says "Whatever moves the other is in actuality in that respect" (54). Beside the diffi culties in phrasing here (the other what?; in what respect?), a common objection looms. Th ere are many instances when something is not actual in a certain respect but moves things in that respect. What the reader needs here, and does not receive, is a commentary on how one ought to interpret this premise. Furthermore, since Weingartner reads movetur in the First Way as referring only to movement of physical bodies through space (see page 57), one wonders what sense it makes to talk about actuality in respect of movement across space. Even more diffi cult to understand is how God could be in actuality in respect of the movement of material bodies in space. And furthermore, even in mundane examples, I can push things rather than pulling them. Th at is, I can be potentially in my 245B O OK REVIEWS AND NOTICES offi ce, though push the chair to be actually in my offi ce. I needn't pull the chair through the threshold of the door so that I am in actuality towards being in my offi ce before my chair is. Commentary on this premise and the surrounding issues would have been helpful for the reader. Similar points can be made for the other Ways. Th e Fift h Way, for instance, receives a mere two and a half pages of commentary (the Second Way receives the most commentary with eleven pages). On a related point, the commentary in the book is not well informed by the secondary literature on the Ways. Th e index lists fewer than fi ve secondary sources that deal with the Five Ways in any detail, and only two works, from my count, that give a thorough examination of the Ways. Th e book would have greatly benefi ted from deeper and more prolonged commentary on the Ways. Th e second diffi culty I fi nd in this book is that Weingartner's interpretation of some salient concepts of the Five Ways is faulty. For instance, I have already discussed his treatment of movetur in the First Way. Weingartner reads the scope of movetur narrowly, as only applying "to movement of material bodies in space" (57). Th e text, however, does not bear this interpretation out, since an example of motion that Aquinas uses in the very text of the First Way is that of fi re moving wood to be hot, which is itself qualitative change, and not movement of a material body through space. An example from the Second Way comes from Weingartner's interpretation of effi cient causation. He says, writing about the premise "To take away the cause is to take away the eff ect", that "it should be underlined that it is very important that effi cient cause is described or even defi ned there as a necessary condition" (66, Weingartner's italics). Th ere are many problems with this interpretation of effi cient causation. For instance, many premises in Weingartner's formulation come out false if Aquinas meant effi cient causes to be defi ned as necessary conditions in this Way. Consider premise (2), which says "Th ere is no case in which a thing is the effi cient cause of itself " (62). Th is is false if being an effi cient cause is defi ned as being a necessary condition in this argument, since any thing is, trivially, a necessary condition for itself. Likewise, premise (3), that "In effi cient causes it is not possible to go on to infi nity" is false, since mere necessary conditions can go on to infi nity. Consider the series, "P is true;" "It is true that 'P is true;'" "It is true 246 B O OK REVIEWS AND NOTICES that 'it is true that 'P is true;''" etc. Each is a necessary condition for the other(s), and the regress carries on infi nitely. Furthermore, this example shows that effi cient causation, if defi ned as merely being a necessary condition, can be circular, since two things can be necessary conditions for one another (as is the case with the right-hand and left -hand side of any true biconditional). For another example, which I do not have space to discuss here, see the understanding of 'maximum' in the Fourth Way. Th e fi nal diffi culty with this book is that the two-step translation process outlined above from the reconstructions of the arguments to the First Order Predicate Logic (FOPL) is done poorly. Th ey are not presented in a reader friendly way. It is sometimes unclear which premises from the fi rst step are being reconstructed in the second step (see, for instance, premises 8b and 14-16 of the Th ird Way, pg 77). Th e inference rule used to derive one line from others is sometimes cited but more oft en it is not, leaving the reader to try to fi gure out which rule, or rules, were employed to arrive at the line (see, for instance, the inference from 3 and 4 to 5 in the First Way, pg 55). Th is is a signifi cant hindrance for the book, since the fi rst task Weingartner sets himself in this book is to show that the proofs are deductively valid. To show this, it is not suffi cient to name which premises are involved in the inference, the reader needs to know which deductively valid inference steps are employed as well. Weingartner uses numbers within parentheses (e.g., "(5b)") to number the lines of the fi rst step, and uses numbers without parentheses (e.g., "8a") to number the lines of the FOPL translation, which can lead to some confusion for the reader. Finally, the defi nitions of the predicates employed in the reconstruction are listed at the end of the proof with little explanation. Th e book contains numerous instances where the move from the fi rst-step to the second-step fails. For example, see the step in the Th ird Way from the natural language premise (5b) to the FOPL translation 8a. Premise (5b): (5b)because that which does not exist, only begins to exist by something already existing Is translated as 8a. ∃t∀x(¬EXtx)→¬◊∃y∃t(BEGty) where "EXtx...x exists at t (t0=present)" and "BEGty...y begins at t" (77). In English, 8a says that if there is a time at which nothing exists, 247B O OK REVIEWS AND NOTICES then it is not possible for there to exist a thing and a time such that the thing begins to exist at that time. Th is is a poor translation of (5b). Th e same existential operator does not bind both times. And so the antecedent could be about one time and the consequent about another. For instance, suppose there exists a time, say, the fi rst instant of the year 2700AD at which nothing exists. From this it would follow, given 8a, that it is not possible for a thing to begin to exist at a time. But why would it be impossible for Napoleon to begin existing at a certain time on August 15th, 1769, given that almost a millennium later at the fi rst instant of 2700AD nothing exists? Th e premise should tell the reader, instead, that if there is a time at which nothing exists, then at that very time, and for any time such that it is later than that time, it is not possible that something begin to exist. Moreover, note that even if 8a were revised to avoid this translation error, it would still be a poor translation of (5b). (5b) tells us why it is that something cannot begin existing at times aft er which nothing exists (because something already existing is required to bring the new thing into existence). But 8a leaves out this vital reason. Another example comes from the Fourth Way. Weingartner states the fourth premise of the Fourth Way (88): (4)Th e maximum in any genus is the cause of all in that genus. His translation of this premise into FOPL reads (88): 7.∀z∀r(MJzrf→Czru) where "MJxyf...x is greater than y w.r.t. perfection" and "Czru...z causes r w.r.t. being" (89). In English, 7 says that for any thing, z, and any thing, r, if z is greater than r with respect to perfection, then z causes r with respect to being. More colloquially, for any two things, if one is more perfect than the other, then the more perfect one causes the other to be. Th is is not a satisfactory translation of (4) into FOPL. As Weingartner notes (93), the levels of perfection correspond to levels of being and the levels of being correspond to the actuality of essential forms. Th erefore a rough division of levels of perfection is this: (a) non-living beings, (b) living beings without senses, (c) animals, (d) human beings, (e) angels, (f) God. So some human, Bob, is more perfect than any non-living thing, any plant, and any non-rational animal. By ∀ elimination on 7 (substituting Bob for z), we can derive, in English, that for any r, if Bob is more perfect 248 B O OK REVIEWS AND NOTICES than r, Bob is the cause of r. Th en, noting Bob's level of perfection, we can substitute in any animal or plant for r and yield that Bob causes that animal or plant. So, by 7, each individual human is the cause of each individual non-living thing, plant, and non-rational animal. (4) does not have this unfortunate entailment, and so 7 is not a satisfactory translation of 4 into FOPL. Th e error is with using two universal quantifi ers in this way. Th is same type of error appears in premises 5 and 6 of the argument as well (88). A similar error appears in the translation from (1) to 1 of the Fift h Way (95). Th is error, like the error in Way Four, infects other premises in the argument (premises 2-4). In summary, while the book is carefully laid out and there are some parts of interest, Weingartner's commentaries don't cover enough material, his understanding of some major concepts in the Five Ways is fl awed, and his formalizations contain serious errors.2 2 I thank David Clemenson, Marie Feldmeier, Sandra Menssen, Yujin Nagasawa, Michael Rota and Jonathan Stoltz for their aid in composing this review.