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My objective in this article is to question whether the problem of free will can, within our current conceptual system, be framed coherently. It is already widely recognized that a mental faculty, the will, needed to initiate action, no longer fits with current thought. However, we can still ask whether human decisions and actions are determined by something other than the agent. So the important question is whether we still have a cogent concept of determinism . The two prevalent alternatives are a closed set of deterministic laws of nature, and a simple distillation of the principle of sufficient reason: all events must have a cause. I first provide examples showing that philosophical concepts come and go as categorial frameworks change. The modern concept of deterministic laws of nature was developed during the latter half of the modern period and is now being called seriously into question. G. W. Leibniz’s principle of sufficient reason could only be justified in theological terms, which most contemporary Western scholars reject. I end with an inadequate account of a dawning worldview based on complex adaptive systems theory, in which most human actions are best described in terms of non-necessitating propensities .

The principle of alternate possibilities ( PAP ) says that you are morally praiseworthy or blameworthy for something you do only if you could have done otherwise. Frankfurt examples are putative counterexamples to PAP. These examples feature a failsafe mechanism that ensures that some agent cannot refrain from doing what she does without intervening in how she conducts herself, thereby supposedly sustaining the upshot that she is responsible for her behavior despite not being able to do otherwise. I introduce a Frankfurt example in which the agent who could not have done otherwise is God. Paying attention to the freedom requirements of moral obligation, the example is commissioned, first, to assess whether various states of affairs that are unavoidable for God can be obligatory for God and for which God can be praiseworthy. The example is, next, used to unearth problems with conventional Frankfurt examples that feature human agents. I argue that conceptual connections between responsibility and obligation cast suspicion on these examples. Pertinent lessons that the divine Frankfurt example helps to reveal motivate the view that divine foreknowledge and determinism, assuming that both preclude freedom to do otherwise, may well imperil obligation and responsibility.

Divine freedom is reviewed with respect to three important themes: fate, revisions in divine decisions, and divine obligations. A study of the first theme yields the conclusion that God is free because He has absolute power and authority. In addition, God is free in relation to human beings in the sense that He can do what they do not expect. This theme is found under the heading of decree and measure, qaḍāʾ and qadar. Theologians have also grappled with the problem that the divine decrees appear to change, and on the tablet containing the divine decrees, there can be changes and erasures. This leads to the second topic, badāʾ, the apparent revision of divine decisions, which the theologians treat as abrogations of commands. God can be understood to foster a relationship with us in which He will appear to us as free to respond to our changing conditions, especially prayer and repentance. Finally, the obligations God sets for Himself and reveals to us through scripture are considered. This indicates a kind of divine freedom that only has meaning in the loving relationship between God and His servants that is cultivated through divine revelation. It is then suggested that these various dimensions of divine freedom can best be understood through complementing philosophical and scriptural approaches to the issues and that the understanding of this kind of synthetic hermeneutics can be deepened through comparative theology.

When it comes to the relation of modern mathematics and philosophy, most people tend to think of the three major schools of thought—i.e. logicism, formalism, and intuitionism—that emerged as profound researches on the foundations and nature of mathematics in the beginning of the 20th century and have shaped the dominant discourse of an autonomous discipline of analytic philosophy, generally known under the rubric of “philosophy of mathematics” since then. What has been completely disregarded by these philosophical attitudes, these foundational researches which seek to provide pure mathematics with a philosophically plausible justification by founding it on firm logico-philosophical bases, is that the genuine self-foundation of pure mathematics had been done before, namely during the 19th century, when it was developing into an entirely new and independent discipline as a concomitant of the continuous dissociation of mathematics from the physical world. This self-foundation of the 19th-century pure mathematics, however, was more akin to the German-idealist interpretations of Kant’s transcendental philosophy, than the post-factum, retrospective 20th-century researches on the foundations of mathematics. This article aims to demonstrate this neglected historical fact via delving into the philosophical inclinations of the three major founders of the 19th-century pure mathematics, Riemann, Dedekind and Cantor. Consequently, pure mathematics, with respect to its idealist origins, proves to be a formalization and idealization of certain activities specific to a self-conscious transcendental subjectivity.