Logic and Theism: Arguments For and Against Beliefs in God
Sobel (Jordan)
Source: Sobel (Jordan) - Logic and Theism: Arguments For and Against Beliefs in God
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Preface (Full Text)

  1. This book is about beliefs in the existence of God in two senses. It is about beliefs in God in the sense of their objects, the propositions believed. And it is about beliefs in God in the sense of states of minds. Classical arguments and evidence for and against propositions affirming God's existence are studied, as well as Pascalian practical arguments for and against cultivating states of belief in God.
  2. Questions of truth, and of belief, concerning God's existence come after questions regarding what would be God's nature. Discussions of arguments in this book are predicated on several conceptions often combined, and sometimes moderated, of what God would be like. Chapter I, "’GOD' and ‘god', and God," goes into these conceptions. Its business is to establish the broad perspective from which issues concerning God's existence, and what would be This One's nature, are taken.
  3. Then come chapters about theoretical arguments for beliefs in God. Chapters II through IV are about demonstrative arguments that would establish God's existence without the aid of contingent assumptions or premises:-
    • The classical ontological arguments of Rene Descartes, St. Anselm, and Baruch Spinoza (Chapter II);
    • The modal1 ontological argument of Charles Hartshorne and Alvin Plantinga (Chapter III); and
    • Kurt Godel's ontological proof (Chapter IV).
  4. Chapters V and VI examine connected ordinary deductive arguments that make use of contingent premises:
    • Thomas Aquinas' argument for a first use,
    • An argument of David Hume's character Demea,
    • Samuel Clarke, and especially Gottfried Leibniz for ultimate reasons.
  5. Chapter VII reviews and extends David Hume's masterful study of arguments from design, which arguments purport not to deduce God's existence, but only to make a case for it, that is, to marshal evidence that, while not strictly entailing the hypothesis of a designing God's existence, make it probable. Chapter VIII interprets and discusses Hume's critique of testimonial evidence for miracles, and through them for particular gods.
  6. Next come chapters on what would be salient parts of God's nature.
    • Chapter IX attends to challenges to omnipotence considered alone and in combination with other possible divine attributes.
    • Chapter X takes up challenges to omniscience considered alone.
    • Going with these chapters is a substantial appendix to Chapter XII that studies the issue of divine omniscience and freedom of choice.
  7. There are then chapters on theoretical arguments against the existence of God.
    • Chapter XI attends briefly to demonstrative arguments that would, if successful, establish that neither God nor ‘anything very like him' could exist. It attends at greater length to ‘the empirical problem of evil' and to arguments that would establish that ‘on the evidence of evil' there is probably no god.
    • Chapter XII is about the problem of evil in its classical form: Examined are deductive arguments in a series that starts with ‘Epicurus' old problem,' arguments that would if successful establish that the existence of a perfect god is logically incompatible with the existence of evil, or, if not with that, then with this world's not being a best possible world, or, if not with that, then with this world's not being a best possible world that a perfect god could have actualized for sure, or, if not that...
  8. Chapter XIII is about beliefs in God as states of mind. It studies practical arguments for cultivating beliefs in God, arguments that work with values for and probabilities of possible consequences of theistic beliefs, and of steps taken to acquire them. (Not conjured for comment are 'anti-Pascalian' practical arguments for avoiding theistic beliefs and eliminating them, because of consequences of having, and of acquiring, them.)
  9. The logic and mathematics used are explained as required.
    • Notations of elementary predicate logic come into discussions of Rene Descartes's ontological argument, as well as of St. Anselm's, and of Thomas Aquinas's first cause argument (Chapters II and V). It helps to bring out certain amphibolies or structural ambiguities of English sentences that feature words of quantity such as ‘a' and ‘something.'
    • Russell's theory of descriptions is used to sort out more elusive amphibolies of relevance to Spinoza's ontological argument (Chapter II).
    • Modal logic2 figures in discussions of Hartshorne's and Plantinga's and Godel's ontological arguments (Chapters III and IV), of cosmological arguments (Chapter VI), of omnipotence (Chapter IX), of arguments for evil and objections to them (Chapter XII), and of omniscience and freedom (Chapter XII, Appendix). A natural deduction system for first-order quantified modal logic3 is explained in an appendix for Chapter III and used to confirm several informal arguments of that chapter. That system is extended in an appendix for Chapter IV to accommodate articulations of Godel's reasoning in his ontological proof, and to confirm other informal arguments of the chapter.
    • Bayesian confirmation theory is explained for discussions of the evidence of design for a designer, of the evidence for miracles of testimony to miracles, and of the evidence of evil against a perfect god (Chapters VII, VIII, and XI). Chapter XIII includes a series of exercises in Bayesian rational choice theory.
    • Particular attention is paid to the play in these Pascalian arguments of infinities, both standard Cantorian cardinal infinities and nonstandard Robinsonian hyperreal 'infinimals.'
    • Hyperreal infinitesimals enter explications floated of Hume's ideas of ‘degrees of proof' and of ‘highest certainties' (Chapter VIII).
    • [But… Footnote ] regarding technical material: formal derivations and models are relegated to appendices. Some technical material within chapters can be skipped over without loss of continuity.
  10. [Snip … remarks on the pre-publication & provenance of various passages; thanks to colleagues, etc.]

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