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.
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.
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.
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.
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.
Brakel begins straightaway defining his terms: intellect, will, and judgment. Intellect involves judgment, along with conscience and comprehension. Judgment involves determining whether some proposition is true/false, some argument is valid/invalid/sound/unsound, some term clear/unclear, or some person/place/thing is [fill in your desired predication]. Judgment is involved with seeing whether or not something is to loved or hated. The Will is connected to ability. I agree. But Brakel connects it with the ability to love/hate. This is a sneaky move. Brakel seems to just make it an analytical truth that abilities are necessarily tied to affections. It will be a short, expected move if Brakel now wants to enslave the will to the affections. If he does, this will have to be demonstrated before I assent. He mentions that these terms are discussed more in chapter 10, so we'll have to hold off for more detail until we get there. Until then, any conclusions deduced, akin to Euclid and his axioms, are only as good as the axioms themselves.
I've begun reading The World of the Imagination: Sum and Substance by Eva T. H. Brann. I'm very excited to read it and I'll be reading this over the coming weeks. I want to tie some of the insights in the book to a possible Ph.D. thesis I want to do on C.S. Lewis' Argument from Desire for God's existence. I believe that imagination is the cornerstone of the argument. Unfortunately, Brann is focusing on Imagination being primarily an image-making faculty or the power or faculty of presenting to the 'mind's eye' the forms of things without their matter, the abstraction of which involves the idea of pulling from Memory an object and presenting the object while the object is physically absent. I can imagine a red ball without there being any red balls around me. I say 'unfortunately' because this is an understanding of Imagination that Lewis veers away from in his essay The Language of Religion (it's an essay found here). There, Lewis distinguishes the image-making faculty from whatever it is that is responsible for why the image arises in the mind's eye in the first place. It is the difference between an indention in the sand on the beach and the wave that caused the indention. If anyone is familiar with Lewis' Great War with Owen Barfield, you know that such thoughts were already being wrestled with. There seems to be a debt to Coleridge from both authors, though Lewis seems to blend Coleridge with Hegel a lot more than Barfield did. In fact, Barfield's corpus seems to be footnotes to, and commentary on, Coleridge. Brann, however, thinks Coleridge is mistaken in the way he understood Imagination. I'm not sure why, apart from etymological or philological considerations.
Some critics of the Resurrection of Christ suggest that the Empty Tomb isn't historical because empty tombs were literary devices. That is, many ancient authors mention empty tombs as literary devices. Or, so argues this anonymous author on Reddit (s/he quotes from the book on the left to substantiate his/her claims: let's just call this author Reddit, for convenience - there are 24 authors, I think, mentioned in the quotation). If the empty tomb is a literary device, then it's not meant to be taken historically. (Also mentioned is the 'Post-Mortem Appearance' Motif, but I think what I say below applies to this sufficiently.)
Dutch Reformed Theologian Wilhelmus à Brakel (1635-1711) wrote a chapter called Man’s Free Will or Impotency and the Punishment Due Upon Sin in his four-volume work The Christian's Reasonable Service (published in 1700) The title in Dutch is De Redelijke Godsdienst (which translates to 'Reasonable Religion'). It's in the first volume, second section (Anthropology: Doctrine of Man), 15th chapter. I'm very interested in the Free Will debate and I've been recommended this chapter as a Biblical perspective on the issue. From what I can tell, it is a defense of compatibilism from a Biblical perspective. The following series will consist of my thoughts on the chapter.
