A Commentary on Stephen Puryear's response to Andrew Loke and Travis Dumsday

Puryear's response essay is called Finitism, Divisibility, and the Beginning of the Universe: Replies to Loke and Dumsday. 

In this commentary, we'll see if Puryear's response to Loke and Dumsday holds up, but I also want to see if what I said in the previous blog is still defensible. 

Puryear says:

My argument has elicited replies from Andrew Ter Ern Loke [2016] and Travis Dumsday [2016]. Here I address the three basic objections to emerge from those replies.

The first two, due to Dumsday, concern the distinction between infinite magnitudes and infinite multitudes, and the distinction between extensively and intensively infinite progressions. 

The third objection, which both Loke and Dumsday urge in one form or another, concerns the possibility that time might be continuous yet naturally divide into smallest parts of finite duration.

That third objection I'm especially interested in. But I am very interested in the first two objections as well. Let's dive in. 

Commentary on Stephen Puryear's "Finitism and The Beginning of the Universe"

It's always exciting to read new criticisms of William Lane Craig's Kalam Cosmological Argument. In this blog, I'll be providing commentary on Stephen Puryear's "Finitism and The Beginning of the Universe". Here is the abstract: 

Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the antifinitist objection, but argue that it also subverts the very argument against an eternal past it was intended to save.

Series: Part 10 of 11: Evaluating Morriston's Criticism of Craig's Criticism of Morriston

Come, and take choice of all my library,
And so beguile thy sorrow. - William Shakespeare, Titus Andronicus

The Infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. - David Hilbert

The is a response to Wes Morriston's "Craig on the actual infinite" (2002). 

Series: Part 9 of 11: Evaluating Morriston's Criticism of Craig's Criticism of Morriston

The last reply is from Morriston against Craig called "Beginningless Past and Endless Future: Reply to Craig". The essay isn't divided into sections but I'll do my best to address ideas as they arise topically in Morriston's response. I confess that Morriston response was not a little vexatious. I wanted there to be the kind of point-counterpoint one expects after the conceptual groundwork had been laid. I make no airs about my support for Craig. He just happens to persuade me. A thrill I get when I read philosophy is when all the groundwork is taken into account in one's response: the point-counterpoint makes progress, the unfurling of the dialectic is undeniably distinct, and my intellect is impelled to take pause. Unfortunately, this didn't happen. But what I attribute to Morriston's failure may be my own and I always stand corrected from my intellectual betters. 

Series: Part 8 of 11: Craig's Usage of Tense in His Criticism of Wes Morriston regarding the Kalam

Craig published an essay called Taking Tense Seriously in Differentiating Past and Future: A Response to Wes Morriston in 2010 in response to Wes Morriston's Beginningless Past, Endless Future, and The Actual Infinite (for my response to that essay, see here). 

Series: Part 7 of 11: A response to Dr. Wes Morriston

This is a response to Dr. Wes Morriston's essay 'Beginningless Past, Endless Future, and The Actual Infinite.' Much of what I'll say I've already said in the previous six blogs of this series. But I will elaborate if needed. This essay was published in 2010. Morriston has written another essay entitled, 'Craig on the Actual Infinite', published back in 2002. Craig responded to Morriston(2010) in 2010, and Morriston has responded to Craig(2010) in 2012. This will be a response to Morriston(2010) utilizing many of the main points of Craig(2010). In the next blog, I want to briefly unpack Craig(2010). Then I will contend that Morriston(2012)'s reply missed much of what Craig(2010) was trying to say. After this, I will touch on Morriston(2002) to see if there is anything new I can note on the symmetry issues between me and Alex. 

Series: Part 6 of 11: A response to Dr. Alex Malpass (tentative)

This is a tentative response to a blog by Alex Malpass entitled: Loke’s Singing Angels: the Kalam and abstract entities. Again, the blog is numerically ordered IAW with the Alex ordered his blog. 

1. Introduction - Alex reiterates his desire for a symmetry breaker between beginninglessness and endlessness. Craig wants to make the beginningless past an actual infinite and the endless future a potential infinite. Craig argues (and Alex agrees) that the number of events that 'have been' will always be finite. But Alex argues that Craig has missed Morriston's point, which is that the number of yet-to-be events that will eventually be is 'not growing', 'doesn't satisfy Craig's definition of a potential infinite', and hence is an actually infinite transfinite number. 

Series: Part 5 of 11: A response to Dr. Alex Malpass (tentative)

This is a response to Successive Addition by Alex Malpass. 

Alex proposes to discuss the following argument from Craig:

1. A collection formed by successive addition cannot be actually infinite.
2. The temporal series of past events is a collection formed by successive addition.

3. Therefore, the temporal series of past events cannot be actually infinite.

Alex will dispute 1. For Alex, 1 is true if you assume 3. Before I get to the body of the blog entry, I don't see how this follows. If the argument transitioned from 1 to 3 without the assistance of 2, I can see why someone might infer this. But with the inclusion of 2, it's not the case that 1 is true only if you assume 3. But perhaps I'm missing something and Alex perhaps answers this later. 

Series: Part 4 of 11: A response to Dr. Alex Malpass (tentative)

This is in response to Alex Malpass's blog entry entitled Infinity, Hume, and Euclid. Again, sections are organized topically in accordance with the way Malpass topically organized his blog entry. 

Introduction - Alex will argue against the absurdity that one can perform inverse operations in transfinite arithmetic. I'm not sure this is possible because subtraction/division is prohibited (and/or meaningless) in transfinite arithmetic. 

Series: Part 3 of 11: A response to Dr. Alex Malpass

This is a response to "More on the potential/actual infinite part 1.2" by Alex Malpass. 

1. I think Alex makes an inaccurate point here. From what I can tell, Craig mentions that Hart disagrees with Cantor's Intuition in footnote 33 of his Kalam Cosmological Argument (1979). 

But why must we say that every class has a number? If the class of natural numbers is a potential infinite, increasing just as Thomson describes, then it is indefinite and cannot be said to possess an actually infinite number elements. See Hermann Weyl, 'Mathematics and Logic', American Mathematical Monthly 53 (1946): 2-13. That a potential infinite need not imply an actual infinite, as Cantor contended, is argued by Hart, 'Potential Infinite', pp. 254-64. 

Alex claims that Craig argues that Cantor's Thesis is refuted in W.D. Hart's ‘The Potential Infinite‘ (Proceedings of the Aristotelian Society, New Series, Vol. 76 (1975 – 1976), pp. 247-264). To say that Craig affirms simple refutation doesn't seem to be reflected in the footnote. I stand corrected if I missed another part of the book. But it seems to me that all Craig is saying is that Hart argues that the potential infinite 'need not imply' an actual infinite. That seems to be a lot different than claiming that Hart demonstrates the falsity that 'all' potential infinities imply actual infinities. 

Series: Part 2 of 11: A response to Dr. Alex Malpass (Edit: 2/25/19)

This is a response to More on the actual/potential infinite by Dr. Alex Malpass. 

In this blog, Alex helpfully explores Cantor's Thesis (CT): 'the potential infinite entails an actual infinite'. As I did before, I'll correlate my sections topically with how Alex divided his blog topically. 

Series: Part 1 of 11: A response to Dr. Alex Malpass

This will be a response to a blog post entitled: Craig’s List – Omniscience and actually existing infinities. 

To read Malpass' blog entries in their entirety, I encourage you to visit the link. I'll be touching on the entries topically and voicing inchoate criticisms as they come. I'll also organize the topics numerically for clarity.