NOTES
Chapter 1.Ultimate Questions
1.William L. Rowe, âTwo Criticisms of the Cosmological Argument,â The Monist54 (1970); reprinted in Philosophy of Religion: Selective Readings, 2nd ed., ed. W. L. Rowe and W. Wainwright (New York: Harcourt Brace Jovanovich, 1989), 142â56 (see 153). On this principle in its relation to the cosmological ar- gument for the existence of God, see William L. Rowe, The Cosmological Argument(Princeton: Princeton University Press, 1975). See also Richard M. Gale, On the Nature and Existence of God(Cambridge: Cambridge University Press, 1991), and Alexander R. Pruss, âThe Hume-Edwards Principle and the Cosmological Argu- ment,â International Journal for Philosophy of Religion434 (1988): 149â65.
2.Note that neither of these is the same as (âp)( p@ (âx)E!x), which obtains trivially given the symbolic conventions adopted here.
3.G. W. Leibniz, Philosophical Papers and Letters, trans. and ed. L. E. Loem- ker (Dordrecht: Reidel, 1969), 487.
4.Ibid., 488.
5.See Arthur Conan Doyleâs story âThe Adventures of the Beryl Coronet,â originally published in Strand Magazine, 1892.
6.After all, there is no reason of the nature of a logico-theoretical principle why propositions cannot be self-certifying. Nothing vicious need be involved in self-substantiation. Think of âSome statements are trueâ or âThis statement stakes a particular rather than universal claim.â
7.Optimalism is closely related to optimism. The optimist holds that âWhatever exists is for the best,â whereas the optimalist maintains the converse, âWhatever is for the best exists.â However, when we are dealing with exclusive and exhaustive alternatives, the two theses come to the same thing. If one of the alternatives A, A1, . . . A n must be the case, then if what is realized is for the best, it follows automatically that the best is realized (and conversely).
Chapter 2. World Views
1.Wilhelm Dilthey, Weltanschauungslehre, vol. 8 of Gesammelte Schriften(Stuttgart: Teubner; Göttingen: Vandenhoeck & Ruprecht, 1961), 86â87. My translation.
2.See Stephen C. Pepper, World Hypotheses: A Study in Evidence(Berkeley and Los Angeles: University of California Press, 1942).
3.For example, Friedrich Paulsen, Richard MĂŒller-Freienfels, and Karl Jaspers.
Chapter 3. Terminological Contextuality
1.Bertrand Russell, Our Knowledge of the External World(London: Allen & Unwin, 1922), 107â8.
2.Arthur Eddington, The Nature of the Physical World(New York: Macmil- lan; Cambridge: Cambridge University Press, 1929), 126. Wilfrid Sellarsâ oft-cited distinction between âthe scientific imageâ and âthe manifest imageâ of things comes straight out of Russell via Eddington.
Chapter 5. Randomness and Reason
This chapter draws upon a paper of the same title published in Symposion: Journal of the Romanian Academy of Science2 (2015): 11â18.
1.See Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Gödel(New York: W. W. Norton, 2005). This was a favorite saying of Einsteinâs. In Ronald W. Clarkâs Einstein: The Life and Times(New York: World Publishing Company, 1971), it is quoted four times (pp. 19, 69, 113, and 340).
2.Letter to David Bohm of 24 November 1954. See Jeroen van Dongen, Einsteinâs Unification(Cambridge: Cambridge University Press, 2010), 181.
3.Actually, a way of developing relativity theory within the framework of ra- tional mechanics can be found in Arnold Sommerfeldâs Electrodynamics: Lectures in Theoretical Physics, vol. 3, trans. E. G. Ramberg (New York: Academic Press, 1964); German original, Vorlesungen ĂŒber theoretische Physik(Wiesbaden: Klemm Verlag, 1945). I owe this reference to my colleague Kenneth Schaffner.
4.Alice Calaprice, ed., The Expanded Quotable Einstein(Princeton: Prince- ton University Press, 2000), 260.
5.John Norton has reminded me that search problems such as that of the traveling salesman will often be solved most efficiently by probabilistically geared algorithms.
6.David Bodanis, Einsteinâs Greatest Mistake(Boston: Little, Brown and Co., 2016), 206.
7.I revert here to the title of John Rawlsâ classic paper âJustice as Fairness.â Is it fair that in American presidential elections the candidate who carries a state by .01 percent of the vote should get 100 percent of that stateâs representation in the Electoral College? The answer is an emphatic yesâexactly because the claims at issue are legal claims, and just this is what the law provides for. But the question âIs it just?â is something else again.
Chapter 6. Issues of Self-Reference and Paradox
1.See Aristotle, Soph. Elen. 180a35 and Nicomachaean Ethics1146a71. See also Carl Prantl, Geschichte der Logik im Abendlande, 4 vols. (Graz: Akademische Druck- und Verlagsanstalt, 1955), 1:50â51. According to Cicero, âSi dicis te men- tiri verumque dicis, mentirisâ (Academica priora, II, 30.95â96; and compare De divinatione, II, 11).
2.Eubulidesâ riddle was discussed not only by Aristotle and Cicero (see the preceding note) but by the Stoics (Prantl, Geschichte, 1:490). In medieval times it was a staple in the extensive discussions of insolubilia. See Prantl, Geschichte, 4:19, 41.
3.Several Greek philosophers, preeminently the Aristotelian Theophrastus and the Stoic Chrysippus, wrote treatises about the Liar Paradox. See Diogenes Laertius, Lives of Eminent Philosophers, V.49 and VII.196. The poet Phietas of Cos is said to have worried himself into an early grave by fretting over it, and its noto- riety was such that even St. Paul adverted to it in Titus1:12â13. The history of the Liar Paradox is discussed in substantial detail in Alexander RĂŒstowâs Der LĂŒgner: Theorie, Geschichte und Auflösung(Leipzig: B. G. Treubner, 1910; reprinted, New York & London: Garland Publishing Co., 1987).
4.Paul of Venice, in Prantl, Geschichte, 4:139 n. 569.
5.Prantl, Geschichte, 4:37 n. 146.
6.âSocrates dicens, se ipsum dicere falsum, nihil dicitâ (Prantl, Geschichte, 4:139 n. 569). A doctrine commonly endorsed in late medieval times was that paradoxical statements are not propositions and for this reason cannot be classified as true or false but must be deemed meaningless. See J. E. Ashworth, Language and Logic in the Post-Medieval Period(Boston: Reidel, 1974), 115, for later endorse- ments of this approach. Thus later writers dismissed insolubilia as not propositions at all but rather âimperfect assertionsâ (orationes imperfectae). See again Ashworth, Language and Logic, 116.
7.Paul of Venice, in Prantl, Geschichte, 4:138â39.
8.Ibid., 4:139 n. 539.
Chapter 7. Explanation and the Principle of Sufficient Reason
1.On the principle of sufficient reason, see the book of this title by Alexan- der R. Pruss (New York: Cambridge University Press, 2006), whose bibliography gives ample references.
Chapter 8.Intelligent Design Revisited in the Light of Evolutionary Neoplatonism
1.St. Thomas Aquinas characterized this hypostasis as âquod sumatur pro individuo rationalis naturae, ratione suae excellentiaeâ (Summa Theologiae, I, q. 29, art. 2, ad 1).
2.The literature on intelligent design theory is vast. Some representative works include Robert Dawkins, The Blind Watchmaker: Why the Evidence of Evo- lution Reveals a Universe without Design(New York: Norton Publishing Co., 1986); William A. Dembski, Mere Creation: Science, Faith, and Intelligent Design(Down- ers Grove, IL: InterVarsity Press, 1998); William A. Dembski, The Design Inference: Eliminating Cha...