The Five Ways and Quantifier Shift Fallacies

In the recent debate hosted on the Pints with Aquinas show between Fr. Gregory Pine and Real Atheology host Ben Watkins, Watkins presented some objections to the quinque viae or five ways of St. Thomas Aquinas. One of the objections was that at least the first three viae commit a quantifier shift fallacy. A quantifier shift fallacy occurs when a quantifier Q from a primary item A is improperly shifted with respect to a secondary item B in two distinct statements. For example:

Proposition P1: Every giraffe has one neck

Proposition P2: Every giraffe has one (and the same) neck.

P1 states that every giraffe individually has exactly one neck. P2 however shifts the meaning such that all giraffes share exactly one neck. For P1, there is one neck for each giraffe individually; for P2 there is one neck for all giraffes taken together. Notice that, in these two propositions, the same quantifier (“one”) is used for both; but the meaning or sense of the quantifier is shifted. As such, if both propositions are used in a single syllogism, a kind of equivocation occurs. From the fact that every giraffe has one neck, it does not follow that there is one total neck which all giraffes have together.

Watkins’s objection is that the first three viae make a similar error. The objection is that even if the arguments work, all they show is that there is a first cause for every causal chain, not that there is exactly *one* first cause for all causal chains together. I.e., if there are three causal chains X, Y, and Z, and each has one first cause (CX, CY, and CZ, respectively), it does not follow that there is one total first cause for all three chains (that CX, CY, and CZ are all identical and hence constitute one overall cause).

I hope here to explain why this object is incorrect. For the sake of discussion, I will be focusing on the secunda via, but what I have to say equally relates to all three of the first three viae. The secunda via argues that there are ordered efficient causes in nature, and that all series of ordered efficient causes must terminate in a prima causa efficiens, a first efficient cause. But in order to succeed, all the argument needs is that a) there is at least one series of ordered efficient causes, and b) there is at least one first efficient cause. If there is at least one prima causa, then the next step of the argument is to show that there is exactly one prima causa, i.e. that there is one and only one. This step of the argument, the shift from there being at least one prima causa to there being exactly one prima causa, is not given explicitly in the text of the secunda via as it is presented in the Summa Theologiae. But it is given in following sections of the Summa. The secunda via is located in prima pars Q. 2, art. 3. In prima pars Q. 3 Saint Thomas argues that God is absolutely simple; and in prima pars 11.3 he argues that God is one. So there is valid argumentation which Saint Thomas gives in conjunction with the secunda via in support of the conclusion that there is only one prima causa for all causal series; and this argumentation is not guilty of a quantifier shift fallacy.

Perhaps a more salient critique would be, not that the secunda via commits a quantifier shift fallacy, but that the secunda via alone does not give explicitly the full argumentation which leads to the conclusion that there is exactly and only one prima causa. But this objection too misses the mark, because it seems to misunderstand the relevant points that 1) the secunda via, as presented in the Summa Theologiae, is meant only as a summary (it is in a summa, after all); and 2) that the text of the secunda viae is improperly read in isolation from the following texts.

To conclude, I’d like to give a brief outline of the argumentation which begins with the secunda via and leads to the conclusion that there is exactly one first cause, quam omnes Deum nominant.

  1. There is at least one first cause (the conclusion of the secunda via).
  2. If there is at least one first cause, there is at least one first cause which is actus purus (conclusion given in prima pars 3.1).
  3. If there is at least one first cause which is actus purus, there is exactly one first cause which is actus purus (conclusion given in prima pars 11.3).
  4. Therefore there is exactly one first cause which is actus purus. QED.

2 thoughts on “The Five Ways and Quantifier Shift Fallacies

  1. I just looked at question three article one in the Summa Theologiae, and I’m not sure I saw an argument for a first cause being actus purus. Could you elaborate on this for me, as the problem of getting to pure actuality seems to be the most looming one for the First and Second Ways.

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    1. The argument in effect is that whatever is composed of act and potency is caused in being, and hence cannot be the first member of a causal series.

      To draw this out a bit, in the De Ente et Essentia Aquinas shows that if the existence of a thing is distinct from the essence or nature of the thing, than the existence is non-subsistent and hence is dependent upon a cause. Now, the causal activity of something depends upon its existence (if it didn’t exist, it couldn’t exercise causal activity). So if an agent is not subsistent being (actus purus), then its existence will be caused existence, and hence it cannot be the first member of a causal series. The first member of a causal series must be absolutely uncaused, and hence must be subsistent being or actus purus

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