On interpreting Gödel's Second Theorem

Summary In this paper I have considered various attempts to attribute significance to G2.²⁵ Two of these attempts (Beth-Cohen and the position maintaining that G2 shows the failure of Hilbert's Program), I have argued, are literally false. Two others (BCR and Resnik's Interpretation), I have argued, are groundless.I would like to thank Dale Gottlieb, Stephen Barker, Tim McCarthy, Philip Kitcher, Michael Resnik and Richmond Thomason for extensive and helpful discussion of this work.     

The simple substitution property of Gödel's intermediate propositional logics S n 's

The simple substitution property provides a systematic and easy method for proving a theorem from the additional axioms of intermediate prepositional logics. There have been known only four intermediate logics that have the additional axioms with the property. In this paper, we reformulate the many valued logics S' _n defined in Gödel [3] and prove the simple substitution property for them. In our former paper [9], we proved that the sets of axioms composed of one prepositional variable do not have the property except two of them. Here we provide another proof for this theorem.     

Gödel,Carnap and the Fregean Heritage

Synthese - Thorough a detailed analysis of version III of Gödel's Is mathematics syntax of language?, we propose a new interpretation of Gödel's criticism against the...     

Gödel,Kant, and the Path of a Science

Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz and Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallels between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “secure path of a science” for both mathematics and philosophy. Gödel's temporal subjectivism and metaphysical conceptual objectivism are presented as positively or negatively motivated by Kant's viewpoints. A remark on Gödel's collapse of modalities (in accordance with the collapse of objective time) is added.     

Jonathan Edwards, God, and “particular minds”

Although philosophical theologians have sometimes claimed that human beings are necessarily dependent on God, few have developed the idea with any precision. Jonathan Edwards is a notable exception, providing a detailed and often novel account of humanity’s essential ontological, moral, and soteriological dependence on God.     

God, Time and the Kalām Cosmological Argument

The Kalām cosmological argument deploys the following causal principle: whatever begins to exist has a cause. Yet, under what conditions does something ‘begin to exist’? What does it mean to say that ‘X begins to exist at t’? William Lane Craig has offered and defended various accounts that seek to establish the necessary and sufficient conditions for when something ‘begins to exist.’ I argue that all of the accounts that William Lane Craig has offered fail on the following grounds: either they entail that God has a cause or they render the Kalām argument unsound. Part of the problem is due to Craig’s view of God’s relationship to time: that God exists timelessly without creation and temporarily with creation. The conclusion is that Craig must abandon either the Kalām argument or his view of God’s relationship to time; he cannot consistently hold both.     

Incommensurability,incomparability, and God’s choice of a world

Anselmian theism holds that there necessarily exists a being, God, who is essentially unsurpassable in power, knowledge, goodness, and wisdom. This being is also understood to be the creator and sustainer of all that is. In contemporary analytic philosophy of religion, this role is generally understood as follows: God surveys the array of possible worlds, and in his wisdom selects exactly one for actualization, based on its axiological properties. In this paper, I discuss an under-appreciated challenge for this account of the Anselmian God’s selection of a world. In particular, I urge that there are failures of comparability between various possible worlds, and I argue that, given certain assumptions, these failures threaten the rationality of God’s choice of a world. To the extent that rationality is deemed necessary for unsurpassability, this result also challenges the core Anselmian notion that God is an unsurpassable being.