After graduating from high school, Craig attendedWheaton College, majoring in communications.[21][6] He graduated in 1971 and married his wife, Jan, whom he met on the staff ofCampus Crusade for Christ, the next year.[21][22] They have two grown children and reside in suburban Atlanta, Georgia.[22]
In 1973, Craig entered the program inphilosophy of religion atTrinity Evangelical Divinity School north ofChicago, where he studied underNorman Geisler.[23][24][6] In 1975, Craig began doctoral studies in philosophy at theUniversity of Birmingham in England,[25] writing on the cosmological argument under the direction ofJohn Hick.[26][6] He was awarded a doctorate in 1977.[27] Out of this study came his first book,The Kalam Cosmological Argument (1979), a defense of the argument he first encountered in theologian Stuart Hackett's work on the same topic.[6]
Craig has written and spoken in defense of a version of thecosmological argument called theKalam cosmological argument.[a][57][58] While the Kalam originated inmedievalIslamic philosophy, Craig added appeals to scientific and philosophical ideas in the argument's defense.[6] Craig's work has resulted in contemporary interest in the argument, and in cosmological arguments in general.[59][60][61]
Craig formulates his version of the argument as follows:
Everything that begins to exist has a cause of its existence.
The universe began to exist.
Therefore, the universe has a cause of its existence.[56][59]
Craig's defense of the argument mainly focuses on the second premise,[62][63] which he offers several arguments for. For example, Craig appeals toHilbert's example of an infinite hotel to argue thatactually infinite collections are impossible, and thus the past is finite and has a beginning.[64][65][66] In another argument, Craig says that the series of events in time is formed by a process in which each moment is added to history in succession. According to Craig, this process can never produce an actually infinite collection of events, but at best a potentially infinite one. On this basis, he argues that the past is finite and has a beginning.[59][67][68]
The Kalam argument concludes that the universe had a cause, but Craig further argues that the cause must be a person.[56] First, Craig argues that the best way to explain the origin of a temporal effect with a beginning from an eternally existing cause is if that cause is a personal agent endowed with free will. Second, the only candidates for a timeless, spaceless, immaterial being are abstract objects like numbers or unembodied minds; but abstract objects are causally effete. Third, Craig usesRichard Swinburne's separation of causal explanation; causal explanation can be given in terms either of initial conditions and laws of nature or of a personal agent and its volitions; but a first physical state of the universe cannot be explained in terms of initial conditions and natural laws.[69]
Craig's arguments to support the Kalam argument have been discussed and debated by a variety of commentators,[70][71] includingAdolf Grünbaum,[72]Quentin Smith,[73] Wes Morriston,[74][75]Graham Oppy,[76]Andrew Loke,[77]Robert C. Koons,[78] andAlexander Pruss.[79] Many of these papers are contained in the two-volume anthologyThe Kalām Cosmological Argument (2017), volume 1 covering philosophical arguments for the finitude of the past and volume 2 the scientific evidence for the beginning of the universe.[80][81]
Craig is a proponent ofMolinism, an idea first formulated by theJesuit theologianLuis de Molina according to which God possesses foreknowledge of which free actions each person would perform under every possible circumstance, a kind of knowledge that is sometimes termed "middle knowledge".[82] Protestant-Molinism, such as Craig's, first entered Protestant theology through two anti-Calvinist thinkers:Jacobus Arminius andConrad Vorstius.[83] Molinists such as Craig appeal to this idea to reconcile the perceived conflict between God's providence and foreknowledge with human free will. The idea is that, by relying on middle knowledge, God does not interfere with anyone's free will, instead choosing which circumstances to actualize given a complete understanding of how people would freely choose to act in response.[84] Craig also appeals to Molinism in his discussions of theinspiration of scripture,Christian exclusivism, theperseverance of the Saints, and missionaryevangelism.[85]
Craig has written two volumes arguing for the historicity of theresurrection of Jesus,The Historical Argument for the Resurrection of Jesus (1985)[11][86] andAssessing the New Testament Evidence for the Historicity of the Resurrection of Jesus (3rd ed., 2002).[87][88] In the former volume, Craig describes thehistory of the discussion, includingDavid Hume's arguments against the identification ofmiracles. The latter volume is anexegetical study of theNew Testament material pertinent to theresurrection.
Craig structures his arguments for the historicity of the resurrection under 3 headings:[89]
Various individuals and groups experienced appearances of Jesus alive after his death.
The earliestdisciples came to believe that God had raisedJesus from the dead despite strong predispositions to the contrary.
Craig argues that the best explanation of these three events is a literal resurrection.[91] He applies an evaluative framework developed by philosopher of history C. Behan McCullagh[92] to examine various theoretical explanations proposed for these events. From that framework, he rejects alternative theories such asGerd Lüdemann's hallucination hypothesis, the conspiracy hypothesis, andHeinrich Paulus orFriedrich Schleiermacher's apparent death hypothesis as lacking explanatory scope, explanatory power, and sufficient historical plausibility.[93][94] In 1996 Craig participated in theResurrection Summit, a meeting held atSt. Joseph's Seminary, New York, in order to discuss the resurrection of Jesus. Papers from the summit were later compiled and published in the bookThe Resurrection. An Interdisciplinary Symposium on the Resurrection of Jesus, edited by S.T Davis, D. Kendall and G. O'Collins.[95]
Craig defends apresentist version of theA-theory of time. According to this theory, the present exists, but the past and future do not. Additionally, he holds that there are tensed facts, such asit is now lunchtime, which cannot be reduced to or identified with tenseless facts of the formit is lunchtime at noon on February 10, 2020. According to this theory, presentness is a real aspect of time, and not merely a projection of our thought and talk about time. He raises several defenses of this theory, two of which are especially notable. First, he criticizesJ. M. E. McTaggart's argument that the A-theory is incoherent, suggesting that McTaggart's argument begs the question by covertly presupposing theB-theory. Second, he defends the A-theory from empirical challenges arising from the standard interpretation of Einstein'sSpecial Theory of Relativity (SR). He responds to this challenge by advocating a neo-Lorentzian interpretation of SR which is empirically equivalent to the standard interpretation, and which is consistent with the A-theory and with absolute simultaneity. Craig criticizes the standard interpretation of SR on the grounds that it is based on a discredited positivist epistemology. Moreover, he claims that the assumption of positivism invalidates the appeal to SR made by opponents of the A-theory.[96][97][98]
Craig argues that God existed in a timeless state causally prior to creation,[98] but has existed in a temporal state beginning with creation, by virtue of his knowledge of tensed facts and his interactions with events.[99] He gives two arguments in support of that view. First, he says that, given his tensed view of time, God cannot be timeless once he has created a temporal universe, since, after that point, he is related to time through his interactions and through causing events in time.[99] Second, Craig says that as a feature of his omniscience, God must know the truth related to tensed facts about the world, such as whether the statement "Today is January 15th" is true or not or what is happeningright now.[97][100][101][102][b]
Craig has published on the challenge posed byplatonism todivine aseity or self-existence.[104][12][105] Craig rejects both the view that God createsabstract objects and that they exist independently of God.[106] Rather, he defends anominalistic perspective that abstract objects are not ontologically real objects.[107] Stating that theQuine–Putnam indispensability argument is the chief support of platonism,[108] Craig criticizes the neo-Quinean criterion of ontological commitment, according to which the existential quantifier of first order logic and singular terms are devices of ontological commitment.[109][110]
Craig favors a neutral interpretation of the quantifiers offirst-order logic, so that a statement can be true, even if there is not an object being quantified over. Moreover, he defends a deflationary theory of reference based on the intentionality of agents, so that a person can successfully refer to something even in the absence of some extra-mental thing. Craig gives the example of the statement "the price of the ticket is ten dollars" which he argues can still be a true statement even if there is not an actual object called a "price".[111] He defines these references as aspeech act rather than a word-world relation, so that singular terms may be used in true sentences without commitment to corresponding objects in the world.[112] Craig has additionally argued that even if one were to grant that these references were being used as in a word-world relation, thatfictionalism is a viable explanation of their use; in particular pretense theory, according to which statements about abstract objects are expressions of make-believe, imagined to be true, even if literally false.[113]
In preparation for writing a systematic philosophical theology, Craig undertook a study of the doctrine of the atonement which resulted in two books,The Atonement (2019) andAtonement and the Death of Christ (2020).[114]
Also as a preliminary study for his systematic philosophical theology Craig explored the biblical commitment to and scientific credibility of an original human pair who were the universal progenitors of mankind.[115] Following the Assyriologist Thorkild Jacobsen, Craig argues on the basis of various family resemblances that Genesis 1-11 plausibly belongs to the genre of mytho-history, which aims to recount historical persons and events in the figurative and often fantastic language of myth. Most recently Craig has begun writing a projected multi-volume systematic philosophical theology.[116]
As a non-voluntaristicdivine command theorist, Craig believes God had the moral right to command thekilling of the Canaanites if they refused to leave their land, as depicted in theBook of Deuteronomy.[127][128][129] This has led to some controversy, as seen in a critique by Wes Morriston.[130][131] Craig has also proposed aneo-Apollinarian Christology in which the divine logos stands in for the human soul of Christ and completes his human nature.[132]
According toNathan Schneider, "[many] professional philosophers know about him only vaguely, but in the field of philosophy of religion, [Craig's] books and articles are among the most cited".[6] Fellow philosopherQuentin Smith writes that "William Lane Craig is one [of] the leading philosophers of religion and one of the leading philosophers of time."[133]
In 2021, Academic Influence ranked Craig the nineteenth most influential philosopher in the world over the previous three decades (1990–2020) and the world's fourth most influential theologian over the same period.[134][135]
In 2009,New AtheistChristopher Hitchens had an interview before his debate with Craig in that same year. During that interview, Hitchens said: "I can tell you that my brothers and sisters and co-thinkers in the unbelieving community take [Craig] very seriously. He's thought of as a very tough guy. Very rigorous, very scholarly, very formidable. [...] I say that without reserve. I don't say it because I'm here. Normally, I don't get people saying: 'Good luck tonight' and 'don't let us down', you know. But with him, I do."[136]
In 2011, with respect and compliment to his debating skills,New AtheistSam Harris once described Craig as "the one Christian apologist who seems to have put the fear of God into many of my fellow atheists".[6][137]
Following a 2011 debate with Craig,Lawrence Krauss stated that Craig had a "simplistic view of the world" and that in the debate, Craig had said "disingenuous distortions, simplifications, and outright lies".[138]
In 2014, he was named alumnus of the year by Wheaton College.[21]
After his debate with Craig in 2014,Sean Carroll expressed frustration: "the following pattern repeated multiple times: Craig would make an argument, I would reply, and Craig would just repeat the original argument".[139][non-primary source needed]
The Only Wise God: The Compatibility of Divine Foreknowledge and Human Freedom. Grand Rapids: Baker Bookhouse. 1987.ISBN1-57910-316-2,978-1-57910-316-3
———; Copan, Paul (2004).Creation out of Nothing: A Biblical, Philosophical, and Scientific Exploration. Grand Rapids: Baker Bookhouse.ISBN0-8010-2733-0.
——— (2008). Smith, Quentin (ed.).Einstein, relativity and absolute simultaneity. London; New York: Routledge.ISBN978-0415591669.
A Reasonable Response: Answers to Tough Questions on God, Christianity, and the Bible (with Joseph E. Gorra). Chicago: Moody Publishers. 2014.ISBN0802405991 /ISBN978-0802405999
On Guard for Students: A Thinker's Guide to the Christian Faith. Colorado Springs: David C. Cook. 2015.ISBN0781412994 /ISBN978-0781412995
——— (2016).God Over All: Divine Aseity and the Challenge of Platonism. New York, NY: Oxford University Press.ISBN978-0-19-878688-7.
——— (2017).God and Abstract Objects: The Coherence of Theism III: Aseity. Berlin: Springer.ISBN978-3-319-55383-2.
——— (2020).Atonement and the Death of Christ: An Exegetical, Historical, and Philosophical Exploration. Waco, TX: Baylor University Press.ISBN978-1-4813-1204-2.
——— (2021).In Quest of the Historical Adam: A Biblical and Scientific Exploration. Grand Rapids, MI: Eerdmans.ISBN978-0-8028-7911-0.
^Craig's own version of the Kalām argument is succinct: 1. 'Everything that begins to exist has a cause of its existence.' 2. 'The universe began to exist,' i.e., the temporal regress of events is finite. 3. 'Therefore the universe has a cause of its existence' Following Ghazali, Craig argues that this cause must be a personal will. Nothing but the arbitrary choice of a free agent could explain why the world was created at one time rather than another, or (if time comes into being with the first event) why the first event did not have a predecessor.[56]
^When Craig says that God is timeless "prior to" the creation of time, the relevant notion of priority is not supposed to be temporal, as there is no time temporally prior to the first moment of time. Rather, Craig means to suggest that God is prior to time in some non-temporal sense that is difficult to specify, and which involves the idea that God was the cause of the universe. Several philosophers have argued that Craig's notion of non-temporal priority is not clear.[100][96][102] Craig has attempted to clarify his view in response.[103]
^Reichenbach (2017). "In his widely discussed writings William Lane Craig marshals multidisciplinary evidence for the truth of the premises found in the kalām argument.... [much more discussion follows]"
^Sun, Eryn (September 30, 2011)."Dawkins defends decision not to debate apologist William Lane Craig".Christianity Today. Retrieved2019-06-12....[Craig is] the leading Christian apologist, famous for his revival of the Kalam cosmological argument which asserts that God caused the universe to first exist.
^Horn, Trent (July 17, 2013)."New Support for the Cosmological Argument".catholic.com. Retrieved2019-06-12.Although the argument fell into relatively obscurity after it was promoted in the Middle Ages, it received new life through William Lane Craig's 1979 book The Kalam Cosmological Argument. Craig has become the argument's leading proponent, and thanks to his famous debates with atheists that end up on YouTube, the kalam argument has become well-known and is vigorously dissected by critics.
^Craig, William Lane (February 5, 2018)."Questions on Certainty and Debate". Retrieved2019-07-22.But that doesn't undermine my knowledge that I was born in Peoria, Illinois and raised in Keokuk, Iowa.
^Craig, William Lane."Debating".Reasonable Faith. Archived fromthe original on 2014-05-12. Retrieved2014-05-08.
^Craig, William Lane (November 5, 2007)."Faith and Doubt". Retrieved2019-07-10.To speak personally, I myself was not raised in an evangelical home, but I became a Christian my third year of high school.
^Cramer, David C."John Hick (1922—2012)".Internet Encyclopedia of Philosophy.ISSN2161-0002. Retrieved2019-06-12.Many of [Hick's] former students are now established Christian philosophers in their own right, including ... William Lane Craig...
^"The Cadbury Lectures 2015: God Over All Back to 'The Cadbury lectures' 16 March - 20 March 2015".University of Birmingham. Retrieved2019-07-22.Hosted by the John Hick Centre for Philosophy of Religion. Our theme for 2015 is 'God Over All', and will consist of a series of lectures given by Professor William Lane Craig (Talbot School of Theology and Houston Baptist University; PhD University of Birmingham 1977).
^ab"Humboldt Network: Prof. Dr. William L. Craig".Alexander von Humboldt Foundation. Alexander von Humboldt-Stiftung/Foundation. Archived fromthe original on 2019-07-16. Retrieved2019-07-16.Host(s) and host institute(s) during Humboldt sponsorship: Prof. Dr. Wolfhart Pannenberg, Ludwig-Maximilians-Universität München, München; Start of first sponsorship: 01.01.1978
^Pearson, Samuel C. (October 1988). "Book Review: The Historical Argument for the Resurrection of Jesus during the Deist Controversy. William L. Craig".The Journal of Religion.68 (4). The University of Chicago Press: 595.doi:10.1086/487941.In this large study, which apparently grew out of a dissertation prepared under the supervision of Wolfhart Pannenberg...
^"William Lane Craig Named TEDS Alumnus of the Year".Trinity International University. Archived fromthe original on 2016-08-28. Retrieved2019-06-12.Craig earned master's degrees from TEDS in philosophy of religion, as well as in church history and the history of Christian thought. He taught philosophy of religion at TEDS from 1980–1986.
^abCraig, William Lane (2000). "Author Bio".The Only Wise God: The Compatibility of Divine Foreknowledge & Human Freedom (Reprint edition (January 2000) ed.). Wipf and Stock.ISBN978-1579103163.From 1980 to 1986 he taught philosophy of religion at Trinity, during which time he and Jan started their family. In 1987 they moved to Brussels, Belgium, where Dr. Craig pursued research at the University of Louvain until 1994.
^"Contributors".International Philosophical Quarterly.33. Fordham University Press: 142. 1993.William Lane Craig is a visiting scholar at the Inst. Supérieur de Philosophie at the Catholic Univ. of Louvain (B-3000 Leuven, Belgium), PhD from Univ. of Birmingham (Eng.) and DTh from the Univ. of Munich, he taught at Westmont College and is a Fellow of the Alexander von Humboldt Siftung. Interested in Philosophy of Religion and of Space and Time, he includes in his publications the books The Kalam Cosmological Argument and Divine Foreknowledge and Human Freedom.
^abKristof, Nicholas (December 21, 2018)."Professor, Was Jesus Really Born to a Virgin?".The New York Times. p. SR23. Retrieved2019-06-12.Here's my interview of William Lane Craig, professor of philosophy at Talbot School of Theology and Houston Baptist University.
^Craig, William Lane; Harris, Kevin (March 3, 2019)."Dr Craig's Interview in the New York Times".Reasonable Faith. Retrieved2019-08-05.That's one of the reasons we founded Reasonable Faith over ten years ago
^Craig, William Lane (1988). "Tachyons, Time Travel, and Divine Omniscience".The Journal of Philosophy.85 (3):135–150.doi:10.2307/2027068.JSTOR2027068.
^Craig, William Lane (1994). "Robert Adams's New Anti-Molinist Argument".Philosophy and Phenomenological Research.54 (4):857–861.doi:10.2307/2108416.ISSN0031-8205.JSTOR2108416.
^Craig, William L. (June 1, 1979). "Wallace Matson and the crude cosmological argument".Australasian Journal of Philosophy.57 (2):163–170.doi:10.1080/00048407912341171.ISSN0004-8402.
^Quinn, Philip I. (2003). "God, Existence Of". In van Huyssteen, J Wentzel Vrede (ed.).Encyclopedia of Science and Religion. Thomson-Gale. pp. 381–382.ISBN9780028657042.
^McGrath, Alister E. (2009).Science and Religion: A New Introduction. John Wiley & Sons.ISBN9781405187909.This form of the kalam argument has been widely debated in recent years. One of its most significant defenders has been William Lane Craig...
^David S. Sytsma; Jordan Joseph Ballor; Matthew T. Gaetano, eds. (2019).Beyond Dordt and 'De Auxiliis' : the dynamics of Protestant and Catholic soteriology in the sixteenth and seventeenth centuries. Leiden: Brill. pp. 103–26,148–68.ISBN978-90-04-37711-0.OCLC1107692846.
^Davis, Stephen T., Kendall, Daniel and O'Collins, Gerald (1998) The Resurrection: An Interdisciplinary Symposium on the Resurrection of Jesus. Oxford: Oxford University Press
^abQuarum, Merrit (2003). "Review: Time and Eternity: Exploring God's Relationship to Time".Journal of the Evangelical Theological Society.46 (4):746–749.
^abHelm, Paul (Spring 2014). Zalta, Edward N. (ed.)."Eternity".The Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information (CSLI), Stanford University.ISSN1095-5054. Retrieved2019-06-15.
^abDeng, Natalja (March 22, 2018)."Eternity in Christian Thought".The Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information (CSLI), Stanford University. Retrieved2024-04-22.
^“No Trouble: A Reply to Wielenberg.” Theologica 5/1 (2021). doi.org/10.14428/thl.v4i3.58143; “A Reply to Wielenberg on a Timeless First Cause.”
^The Atonement. Elements in the Philosophy of Religion. Cambridge: Cambridge University Press, 2018; Atonement and the Death of Christ: An Exegetical, Historical, and Philosophical Exploration. Waco, Tex.: Baylor University Press, 2020.
^In Quest of the Historical Adam: A Biblical and Scientific Investigation. Grand Rapids, Mich.: Wm. B. Eerdmans, 2021.
^For a preview see his “On Systematic Philosophical Theology.” Philosophia Christi 23/1 (2021): 11-25.
Copan, Paul; Craig, William Lane, eds. (2009).Contending with Christianity's Critics: Answering New Atheists & Other Objectors. Nashville, Tennessee: B&H Academic.ISBN978-0-8054-4936-5.
Copan, Paul; Craig, William Lane, eds. (2017a).The Kalām Cosmological Argument: Philosophical Arguments for the Finitude of the Past. Bloomsbury Studies in Philosophy of Religion. London: Bloomsbury Press.ISBN978-1501352539.
Copan, Paul; Craig, William Lane, eds. (2017b).The Kalām Cosmological Argument: Scientific Evidence for the Beginning of the Universe. Bloomsbury Studies in Philosophy of Religion. London: Bloomsbury Press.ISBN978-1501352584.
Copan, Paul; Flannagan, Matthew (2014).Did God Really Command Genocide?: Coming to Terms with the Justice of God. Baker Books.ISBN978-0801016226.
Cowan, Steven B.; Spiegel, James S. (2009).The Love of Wisdom: A Christian Introduction to Philosophy. Nashville, Tennessee: B&H Academic.ISBN978-0-8054-4770-5.
Craig, William Lane (1979). "Wallace Matson and the Crude Cosmological Argument".Australasian Journal of Philosophy.57 (2):163–170.doi:10.1080/00048407912341171.ISSN1471-6828.
——— (1986). "The Problem of Miracles: A Historical and Philosophical Perspective". InWenham, David;Blomberg, Craig (eds.).Gospel Perspectives. Vol. 6. Sheffield, England: JSOT Press. pp. 9–40.
——— (1991). "'Lest Anyone Should Fall': A Middle Knowledge Perspective on Perseverance and Apostolic Warnings".International Journal for Philosophy of Religion.29 (2):65–74.doi:10.1007/bf00133805.ISSN1572-8684.S2CID159974214.
——— (2000b) [1987].The Only Wise God: The Compatibility of Divine Foreknowledge and Human Freedom. Eugene, Oregon: Wipf and Stock Publishers.ISBN978-1-57910-316-3.
——— (2012a). "God and Abstract Objects". In Stump, J. B.; Padgett, Alan G. (eds.).The Blackwell Companion to Science and Christianity. Malden, Massachusetts: Wiley-Blackwell. pp. 441–452.doi:10.1002/9781118241455.ch38.ISBN978-1-4443-3571-2.
——— (2014). "Anti-Platonism". In Gould, Paul M. (ed.).Beyond the Control of God? Six Views on the Problem of God and Abstract. New York: Bloomsbury Academic. pp. 113–126.ISBN978-1-62356-365-3.
——— (2016).God Over All: Divine Aseity and the Challenge of Platonism. New York: Oxford University Press.ISBN978-0-19-878688-7.
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Craig, William Lane (2020).Atonement and the Death of Christ: An Exegetical, Historical, and Philosophical Exploration. Waco, Texas: Baylor University Press.ISBN978-1-4813-1204-2.
Craig, William Lane (2021).In Quest of the Historical Adam: A Biblical and Scientific Investigation. Grand Rapids, Michigan: Wm. B. Eerdmans.ISBN978-0802879110.
Craig, William Lane;Moreland, J. P., eds. (2000).Naturalism: A Critical Analysis. Routledge Studies in Twentieth Century Philosophy. Vol. 6. London: Routledge.ISBN978-0-415-23524-2.
Creel, Richard E. (2014).Philosophy of Religion: The Basics. Chichester, England: Wiley-Blackwell.ISBN978-1-118-61945-2.
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Loke, Andrew Ter Ern (2017).God and Ultimate Origins: A Novel Cosmological Argument. Cham, Switz.: Springer.ISBN978-3319861890.
McGrew, Timothy; McGrew, Lydia (2009). "The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth". In Craig, William Lane;Moreland, J. P. (eds.).The Blackwell Companion to Natural Theology. Chichester, England: Wiley-Blackwell. pp. 593–662.doi:10.1002/9781444308334.ch11.ISBN978-1-4051-7657-6.
Moreland, J. P.; Craig, William Lane (2003).Philosophical Foundations for a Christian Worldview. Downers Grove, Illinois: InterVarsity Press.ISBN978-0-8308-2694-0.
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"William Lane Craig".Contemporary Authors Online. Detroit, Michigan: Gale. 2007.
Williams, Peter S. (2013).A Faithful Guide to Philosophy: A Christian Introduction to the Love of Wisdom. Milton Keynes, England: Paternoster.ISBN978-1-84227-811-6.