While there has been much work on cosmological arguments, novel objections will be presented against the modern day rendition of the Kalām cosmological argument as standardly articulated by William Lane Craig. The conclusion is reached that this cosmological argument and several of its variants do not lead us to believe that there is inevitably a supernatural cause to the universe. Moreover, a conditional argument for atheism will be presented in light of the Big Bang (...) Theory. (shrink)

This paper is a reply to Professor William Lane Craig's “Graham Oppy On The kalām Cosmological Argument” Sophia 32.1, 1993, pp. 1–11. Further references to the literature are contained therein.

Part of the kalam cosmological argument draws upon the claim that an actual infinite cannot exist. Classical theists also maintain both that some individuals will earn eternal life and that God infallibly foreknows the future. The claim that these latter two theses do not require that an actual infinite exists because God possesses an intuitive, rather than propositional intellect, is examined and rejected. Although the future is potential, rather than actual, classical theism requires that the future be, (...) in a sense, actually infinite. (shrink)

ABSTRACTIn the late 1970s the big bang model of cosmology was widely accepted and interpreted as implying the universe had a beginning. At the end of that decade William Lane Craig revived an argument for God known as the Kalam Cosmological Argument based on this scientific consensus. Furthermore, he linked the big bang to the supposed biblical concept of creation ex nihilo found in Genesis. I shall critique Craig's position as expressed in a more recent update (...) and argue that contemporary cosmology no longer understands the big bang as the ultimate beginning, seriously undermining the KCA. I will further contend that book of Genesis should not be understood as describing creation ex nihilo anyway. (shrink)

This paper examines the Kalam Cosmological Argument, as expounded by,William Lane Craig, insofar as it pertains to the premise that it is metaphysically impossible for an infinite set of real entities to exist. Craig contends that this premise is justified because the application of the Cantorian theory to the real world generates counterintuitive absurdities. This paper shows that Craig’s contention fails because it is possible to apply Cantorian theory to the real world without thereby generating counterintuitive absurdities, (...) provided one avoids positing that an infinite set of real entities is technically a set within the meaning of such theory. Accordingly, this paper proposes an alternative version of the application of Cantorian theory to the real world thereby replacing the standard version of such application so thoroughly criticized by Craig. (shrink)

In ‘Professor Mackie and the Kalam Cosmological Argument’ , 367–75), Professor William Lane Craig undertakes to demonstrate that J. L. Mackie's analysis of the kalam cosmological argument in The Miracle of Theism is ‘superficial’, and that Mackie ‘has failed to provide any compelling or even intuitively appealing objection against the argument’ . I disagree with Craig's judgement; for it seems to me that the considerations which Mackie advances do serve to refute the (...) class='Hi'>kalam cosmological argument. Consequently, the purpose of this paper is to reply to Craig's criticisms on Mackie's behalf. (shrink)

Craig (1981) presents and defends several different kalam cosmological arguments. The core of each of these arguments is the following ur argument.

This paper begins with a fairly careful and detailed discussion of the conditions under which someone who presents an argument ought to be prepared to concede that the argument is unsuccessful. The conclusions reached in this discussion are then applied to William Lane Craig’s defense of what he calls “the kalam cosmological argument.” Perhaps unsurprisingly, the chief contention of the paper is that Craig ought to be prepared to concede that “the kalam cosmological (...) argument” is not a successful argument. The paper pays particular attention to Craig’s recent criticisms of Adolf Grünbaum’s contention that “the kalam cosmological argument” presupposes “the normalcy of nothingness”; and it also addresses some methodological issues raised by Craig’s response to my previous criticisms of his replies to critiques of “the kalam cosmological argument” provided by Grünbaum, Hawking, and Davies. (shrink)

William Lane Craig has revived interest in the medieval kalām argument to the point where it is now one of the most discussed arguments for God’s existence in the secondary literature. Still, the reception of Craig’s argument among philosophers of religion has been mostly critical. In the interest of developing an argument that more philosophers of religion would be inclined to support, I will lay the philosophical groundwork for a new kalām cosmological argument that, in (...) contrast with Craig’s argument, does not adopt such controversial positions as the dynamic theory of time and the metaphysical impossibility of an actual infinite. (shrink)

Wes Morriston contends that William Lane Craig's argument for the impossibility of a beginningless past results in an equally good argument for the impossibility of an endless future. Craig disagrees. I show that Craig's reply reveals a commitment to an unmotivated position concerning the relationship between actuality and the actual infinite. I then assess alternative routes to the impossibility of a beginningless past that have been offered in the literature, and show that, contrary to initial appearances, these routes (...) similarly seem to support the impossibility of an endless future. (shrink)

Kalam cosmological arguments have recently been the subject of criticisms, at least inter alia, by physicists---Paul Davies, Stephen Hawking---and philosophers of science---Adolf Grunbaum. In a series of recent articles, William Craig has attempted to show that these criticisms are “superficial, iII-conceived, and based on misunderstanding.” I argue that, while some of the discussion of Davies and Hawking is not philosophically sophisticated, the points raised by Davies, Hawking and Grunbaum do suffice to undermine the dialectical efficacy of kalam (...) cosmological arguments. (shrink)

William Lane Craig has argued that there cannot be actual infinities because inverse operations are not well-defined for infinities. I point out that, in fact, there are mathematical systems in which inverse operations for infinities are well-defined. In particular, the theory introduced in John Conway's *On Numbers and Games* yields a well-defined field that includes all of Cantor's transfinite numbers.

A simple solution to the problem of time is proposed by postulating that if the Universe is time-like, stationary, and bounded then it could be divided into static temporal gradations or contours. Hence, an energy diffusion flux (EDF) equation was established from which the Planck and the Hubble times have been derived. It is then found that time is unimportant after applying Gauss's Law on EDF when looking for a characteristic length of the Universe א. An uncertainty rule was also (...) found that may limit our simultaneous information between the scope of looking into space and the masses that it comprises. The paper concludes that if the Universe was in a stationary state and bounded, then, it did not begin to exist when compared to a vast and, probably, timeless Background. It appears to begin to exist because the information is largely mediated by optics. Thus, time is more epistemological in nature rather than ontological because of the limit that light imposes against instantaneous access to information. For this reason, the beginninglessness of the Universe should not preclude one from saying that the Universe does have a cause. (shrink)

This is a review of *The Kalām Cosmological Argument* (edited by Paul Copan and William Lane Craig). In this review, I focus primarily on the papers in the first volume by Waters, Loke, and Oderberg. (I have also written an independent review of the second volume.).

This is a commissioned review of Copan, P. and Craig, W. The Kalām Cosmological Argument Volume Two: Scientific Evidence for the Beginning of the Universe New York: Bloomsbury, US$172.50, ISBN 978-1-50-133587-7.

This paper provides a taxonomy of cosmological arguments and givesgeneral reasons for thinking that arguments that belong to a given category do not succeed.

The book discusses the structure, content, and evaluation of cosmological arguments. The introductory chapter investigates features essential to cosmological arguments. Traditionally, cosmological arguments are distinguished by their appeal to change, causation, contingency or objective becoming in the world. But none of these is in fact essential to the formulation of cosmological arguments. Chapters 1-3 present a critical discussion of traditional Thomistic, Kalam, and Leibnizian cosmological arguments, noting various advantages and disadvantages of these approaches. Chapter (...) 4 offers an entirely new approach to the cosmological argument - the approach of theistic modal realism. The proper explananda of cosmological arguments on this approach is not change, causation, contingency or objective becoming in the world. The proper explananda is the totality of metaphysical reality - all actualia and all possibilia. The result is the most compelling and least objectionable version of the cosmological argument. (shrink)

Hypotheses about the shape of causal reality admit of both theistic and non-theistic interpretations. I argue that, on the simplest hypotheses about the causal shape of reality—infinite regress, contingent initial boundary, necessary initial boundary—there is good reason to suppose that non-theism is always either preferable to, or at least the equal of, theism, at least insofar as we restrict our attention merely to the domain of explanation of existence. Moreover, I suggest that it is perfectly proper for naturalists to be (...) undecided between these simple hypotheses about the causal shape of reality: contrary to the proponents of cosmological arguments, there are no decisive objections to any of these simple hypotheses. (I argue this case in detail in connection with objections offered by William Lane Craig; however, I believe that the case holds quite generally.). (shrink)

We draw out significant consequences of a relatively popular theory of metaphysical modality—branching actualism—for cosmological arguments for God’s existence. According to branching actualism, every possible world shares an initial history with the actual world and diverges only because causal powers (or dispositions, or some such) are differentially exercised. We argue that branching actualism undergirds successful responses to two recent cosmological arguments: the Grim Reaper Kalam argument and a modal argument from contingency. We also argue that (...) branching actualism affords a response to one popular defense of the classic contingency argument. What results are new difficulties for several cosmological arguments arising from the metaphysics of modality. (shrink)

Hypotheses about the shape of causal reality admit of both theistic and non-theistic interpretations. I argue that, on the simplest hypotheses about the causal shape of reality—infinite regress, contingent initial boundary, necessary initial boundary—there is good reason to suppose that non-theism is always either preferable to, or at least the equal of, theism, at least insofar as we restrict our attention merely to the domain of explanation of existence. Moreover, I suggest that it is perfectly proper for naturalists to be (...) undecided between these simple hypotheses about the causal shape of reality: contrary to the proponents of cosmological arguments, there are no decisive objections to any of these simple hypotheses. (I argue this case in detail in connection with objections offered by William Lane Craig; however, I believe that the case holds quite generally.). (shrink)

An application of some recent work on the science of generic thought.

This paper is a critical review of *Big Bang Cosmology* by Quentin Smith and William Lane Craig. (The book is a collection of previously published papers; most are concerned, in one way or another, with kalam cosmological arguments for the existence of God.).

In this article, I will discuss some of the arguments for and against the existence of God, in particular the monotheistic God believed in the Abramahamic religions (Judiasm, Islam, and Christianity) as well as Babism, the Bahai Faith, and Sikhism. Arguments for the existence of God try to argue that either God exists (based on other things people agree with) or that belief in God is reasonable. Arguments against the existence of God try to argue that the existence of God (...) leads to some contradiction or other absurdity. (shrink)

Causal finitism, the view that the causal history of any event must be finite, has garnered much philosophical interest recently—especially because of its applicability to the Kalām cosmological argument. The most prominent argument for causal finitism is the Grim Reaper argument, which attempts to show that, if infinite causal histories are possible, then other paradoxical states of affairs must also be possible. However, this style of argument has been criticized on the grounds of (i) relying (...) on controversial modal principles, and (ii) providing a false diagnosis of the paradoxes involved. In this paper, I develop a new kind of Grim Reaper argument immune to these criticisms. I show that, by using insights from the literature on time travel, causal finitists should instead argue that infinite causal histories are problematically inexplicable, as they entail the possibility of unexplained foiling mechanisms. The fruits of this paper are that (i) a novel supporting argument for the Kalām is developed, and (ii) along the way of building this argument, it is shown that the literatures on time travel and causal finitism are deeply and intimately connected. (shrink)

A key premise of the kalam cosmological argument is that the universe began to exist. However, while a number of philosophers have offered powerful criticisms of William Lane Craig’s defense of the premise, J.P. Moreland has also offered a number of unique arguments in support of it, and to date, little attention has been paid to these in the literature. In this paper, I attempt to go some way toward redressing this matter. In particular, I shall argue (...) that Moreland’s philosophical arguments against the possibility of traversing a beginningless past are unsuccessful. (shrink)

This chapter provides an overview and critical discussion of cosmological arguments for theism, with special focus on the Kalam argument and arguments from contingency.

I hold that the considerations adduced in kalam cosmological arguments do not embody reasons for reflective atheists and agnostics to embrace the conclusion of those arguments, viz. that the universe had a cause of its existence. I do not claim to be able to show that reflective theists could not reasonably believe that those arguments are sound; indeed, I am prepared to concede that it is epistemically possible that the arguments procede validly from true premises. However, I am (...) prepared to make the same concession about the following argument: Either 2+2=5 or God exists; 2+2?5; therefore God exists . But nobody could think that this argument deserves to be called a proof of its conclusion (even if it is sound). Of course, this latter argument is obviously circular: (almost) no one who was not antecedently persuaded of the truth of the conclusion would (have reason to) believe the first premise. But this fact does not entail that admittedly non circular arguments, such as the kalam cosmological arguments, cannot fail to be equally dialectically ineffective. And, indeed, that is the view which I wish to defend: there is not the slightest reason to think that kalam cosmological arguments should be dialectically effective against reasonable and reflective opponents. (shrink)

The cosmological argument, while considered to be deductive by some of its propounders, is not considered fool-proof by others. However, given the fact that causality is intrinsic to our thinking, reasoning towards ultimate causality remains significant. Andrew Loke capitalizes on this in his recent book.

In ‘The Kalam Cosmological Argument Neither Bloodied nor Bowed’ , David Oderberg provides four main criticisms of the line of argument which I developed in ‘Time, Successive Addition, and Kalam Cosmological Arguments’ . I argue here that none of these lines of criticism succeeds. Further I re-emphasise the point that those who maintain that the temporal series of past events is formed by ‘successive addition’ are indeed thereby committed to a highly contentious strict finitist (...) metaphysics. (shrink)

This paper is a response to David Oderberg's discussion of the Tristram Shandy paradox. I defend the claim that the Tristram Shandy paradox does not support the claim that it is impossible that the past is infinite.

This paper discusses the treatment of "infinity" in philosophy of religion, including its use in discussions of divine attributes, and its use in various arguments about the existence of God (including the kalam cosmological argument and Pascal's wager). The aim of the paper is to set out -- and where possible, to resolve -- various foundational problems about infinity.

This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has (...) a cause for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist. -/- Friends of the KCA have sought to defend their view that physical reality began to exist in two distinct ways. As I discuss in chapter 2, the first way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a priori arguments meant to show that, as a matter of metaphysical necessity, the past must be finite. If the past is necessarily finite, then the past history of physical reality is necessarily finite. And if having a finite past suffices for having a beginning, then, since the past history of physical reality is necessarily finite, physical reality necessarily began to exist. I show that the arguments which have been offered thus far for the view that the past is necessarily finite do not succeed. Moreover, as I elaborate on in chapter 5, having a finite past does not suffice for having a beginning. -/- As I discuss in chapter 3, the second way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a posteriori arguments meant to show that we have empirical evidence that physical reality has a finite past history. For example, the big bang is sometimes claimed to have been the beginning of physical reality and, since we have excellent empirical evidence for the big bang, we have excellent empirical evidence for the beginning of physical reality. The big bang can be understood in two ways. On the one hand, the big bang can be understood as a theory about the history and development of the observable universe. Understood in that sense, then I agree that the big bang is supported by excellent empirical evidence and by a scientific consensus. On the other hand, some authors (particularly science popularizers, science journalists, and religious apologists) have wrongly interpreted big bang theory as a theory about the beginning of the whole of physical reality. As I argue, while a beginning of physical reality may be consistent with classical big bang theory, classical big bang theory does not provide good reason for thinking that physical reality began to exist. -/- In part II, I turn to discussing three necessary, but not necessarily sufficient, conditions for physical reality to have a beginning. Before discussing the three conditions, in chapter 4, I introduce three metaphysical accounts of the nature of time (A-theory, B-theory, and C-theory) as well as some formal machinery that will subsequently become useful in the dissertation. I introduce the first of the three conditions in chapter 5. According to the Modal Condition, physical reality began to exist only if, at the closest possible worlds without time, physical reality does not exist. I show that this condition helps us to make sense of various views in both theology and philosophy of physics. In chapter 6}, I introduce the second of my three conditions, the Direction Condition, according to which, roughly, physical reality began to exist only if all space-time points agree about the direction of time, so that all space-time points can agree that physical reality's putative beginning took place in their objective past. In chapter 7, I discuss the third condition, the Boundary Condition, according to which physical reality began to exist only if there is a past temporal boundary such that physical reality did not exist before the boundary. I show that there are two senses in which physical reality could be said to have had a past temporal boundary. Lastly, in chapter 8, I show that there is a relationship between my three conditions and classical big bang theory, even though the relationship is not the one usually identified in the literature. -/- In part III, I present four arguments for the view that, at the present stage of philosophical and scientific inquiry, we cannot know whether physical reality satisfies the three necessary conditions to have had a beginning and, consequently, we cannot know whether physical reality had a beginning. As I will prove in chapter 9, no set of observations that we currently have, when conjoined with General Relativity, entails that physical reality satisfies the Direction or Boundary Conditions. As I show in chapter 10, considerations in the philosophical foundations of statistical mechanics entail either that the Cosmos violates the Modal Condition or else that there is a transcendental condition on the possibility of our knowledge of the past that prevents our access to data we would need to gather to determine whether physical reality satisfies the Boundary Condition. In chapter 11, I show that there are a number of live cosmological models according to which physical reality does not satisfy the Boundary Condition. As long as we don't know whether any of those cosmological models are correct, we do not know whether physical reality satisfies the Boundary Condition. Lastly, I turn to confirmation theory and show that, at our present stage of inquiry, ampliative inferences for the conclusion that physical reality satisfies the Modal, Direction, and Boundary Conditions are not successful. (shrink)

Robert Koons has recently defended what he claims is a successful argument for the existence of a necessary first cause, and which he develops by taking “a new look” at traditional arguments from contingency. I argue that Koons’ argument is less than successful; in particular, I claim that his attempt to “shift the burden of proof” to non-theists amounts to nothing more than an ill-disguised begging of one of the central questions upon which theists and non-theists disagree. I (...) also argue that his interesting attempt to bridge (part of) the familiar gap between the claim that there is a necessary first cause and the claim that God exists is beset with numerous difficulties. (shrink)

We formulate a sort of "generic" cosmological argument, i.e., a cosmological argument that shares premises (e.g., "contingent, concretely existing entities have a cause") with numerous versions of the argument. We then defend each of the premises by offering pragmatic arguments for them. We show that an endorsement of each premise will lead to an increase in expected utility; so in the absence of strong evidence that the premises are false, it is rational to endorse them. (...) Therefore, it is rational to endorse the cosmological argument, and so rational to endorse theism. We then consider possible objections. (shrink)

Richard Gale and Alexander Pruss contend that their ‘new cosmological argument’ is an improvement over familiar cosmological arguments because it relies upon a weaker version of the Principle of Sufficient Reason than that used in those more familiar arguments. However, I note that their ‘weaker’ version of the Principle of Sufficient Reason entails the ‘stronger’ version of that principle which is used in more familiar arguments, so that the alleged advantage of their proof turns out to be (...) illusory. Moreover, I contend that, even if their argument did rely on a weaker version of the Principle of Sufficient reason, nontheists would still be perfectly within their rights to refuse to accept the conclusion of the argument. (shrink)

Explicit atheism is a philosophical position according to which belief in God is irrational, and thus it should be rejected. In this paper, I revisit, extend, and defend against the most telling counter arguments the Kalām Cosmological Argument in order to show that explicit atheism must be deemed as a positively irrational position.

In this paper I intend to identify some points of disagreement between theism and atheism. I will try to point out three epistemological clashes occurring in the controversial treatment of cosmological arguments. I am not assessing the arguments pro and contra, which have been thoroughly studied and discussed, but just trying to understand the misunderstanding.

Most of the historically salient versions of the Cosmological Argument rest on two assumptions. The first assumption is that some contingeney (i.e., contingent fact) is such that a necessity is required to explain it. Against that assumption we will argue that necessities alone cannot explain any contingency and, furthermore, that it is impossible to explain the totality of contingencies at all.The second assumption is the Principle of Sufficient Reason. Against the Principle of Sufficient Reason we will argue that (...) it is unreasonable to require, as the Principle of Sufficient Reason does, that any given whole of contingent facts has an explanation. Instead, it depends on the results of empirical investigation whether or not one should ask for an explanation of the given whole.We argue that if a cosmological argument invokes either of the two assumptions, then it fails to prove that a necessity is needed to explain the universe of contingent facts. (shrink)

Socratic dialogue written for use as an undergrad or highschool resource in the Philosophy of Religion. This dialogue covers the standard formulation and objections to Aquinas' Second Way. Unpublished at this time - to be updated and included in book (in progress).

This paper is a response to David Oderberg's criticisms of a previous paper of mine. (Bibliographical details are provided in the article.).

This paper criticises the cosmological argument that Tim O'Connor provides in his book *Theism and Ultimate Explanation*.

Many physicists have thought that absolute time became otiose with the introduction of Special Relativity. William Lane Craig disagrees. Craig argues that although relativity is empirically adequate within a domain of application, relativity is literally false and should be supplanted by a Neo-Lorentzian alternative that allows for absolute time. Meanwhile, Craig and co-author James Sinclair have argued that physical cosmology supports the conclusion that physical reality began to exist at a finite time in the past. However, on their view, the (...) beginning of physical reality requires the objective passage of absolute time, so that the beginning of physical reality stands or falls with Craig's Neo-Lorentzian metaphysics. Here, I raise doubts about whether, given Craig's NeoLorentzian metaphysics, physical cosmology could adequately support a beginning of physical reality within the finite past. Craig and Sinclair's conception of the beginning of the universe requires a past boundary to the universe. A past boundary to the universe cannot be directly observed and so must be inferred from the observed matter-energy distribution in conjunction with auxilary hypotheses drawn from a substantive physical theory. Craig's brand of Neo Lorentzianism has not been sufficiently well specified so as to infer either that there is a past boundary or that the boundary is located in the finite past. Consequently, Neo Lorentzianism implicitly introduces a form of skepticism that removes the ability that we might have otherwise had to infer a beginning of the universe. Furthermore, in analyzing traditional big bang models, I develop criteria that Neo-Lorentzians should deploy in thinking about the direction and duration of time in cosmological models generally. For my last task, I apply the same criteria to bounce cosmologies and show that Craig and Sinclair have been wrong to interpret bounce cosmologies as including a beginning of physical reality. (shrink)

This chapter is a critical discussion of the third chapter of Tim O'Connor's *Theism and Ultimate Explanation*. In this chapter, O'Connor advances the 'existence stage' of his cosmological argument from contingency. I argue that naturalists have good reason to think that on each of the live hypotheses -- infinite regress, brute contingency, brute necessity -- naturalism is preferable to theism.

Over the course of his work, Graham Oppy developed numerous important criticisms of versions of the cosmological argument. In this article I am not concerned with his specific criticisms of cosmological arguments but rather with his claim that the cosmological arguments per se are not good arguments, for they provide no persuasive or convincing reason for believing the conclusion that God exists and are embedded in theories that already affirm the conclusion. I want to explore what (...) he believes makes an argument good, contend that cosmological arguments can have functions within worldviews other than persuasion, and consider his recent modifications of the discussion that address competing worldviews. (shrink)

In the second chapter of her <i>Institutions de Physique</i> Emilie Du Chatelet gives two cosmological arguments for the existence of God. In this chapter I focus on the first of these arguments. I argue that, while it bears some significant similarities to arguments given by John Locke and Christian Wolff, it improves on these arguments in at least two ways. First, it avoids a potential equivocation in Locke's argument; and second, it avoids Wolff's mere stipulation that whoever claims (...) that there cannot be an infinite regress of contingent beings does not understand what a sufficient reason is. I finally argue that her argument avoids a related objection, considered by David Hume, on which to explain a causal chain is merely to explain each link in the chain. (shrink)

This article argues that not all arguments from parts to wholes commit the informal logical fallacy of composition,and especially not the cosmological argument for God which moves from the contingent existence of all the parts of the cosmos to the contingent existence of the whole.

Some people -- including the present author -- have proposed and defended alternative restricted causal principles that block Robert Koons’s ’new’ cosmological argument without undermining the intuition that causation is very close to ubiquitous. In "Epistemological Foundations for the Cosmological Argument", Koons argues that any restricted causal principles that are insufficient for the purposes of his cosmological argument cause epistemological collapse into general scepticism. In this paper I argue, against Koons, that there is no (...) reason to suppose that my favourite restricted causal principle precipitates epistemological collapse into general scepticism. If we impose the ’same kinds’ of restrictions on causal epistemological principles and on principles of general causation, then we cannot be vulnerable to the kind of argument that Koons develops. (shrink)

This chapter discusses methodology in feminist history of philosophy and shows that women philosophers made interesting and original contributions to the debates concerning the cosmological argument. I set forth and examine the arguments of Mary Astell, Damaris Masham, Catherine Trotter Cockburn, Emilie Du Châtelet, and Mary Shepherd, and discuss their involvement with philosophical issues and debates surrounding the cosmological argument. I argue that their contributions are original, philosophically interesting, and result from participation in the ongoing debates (...) and controversies about the cosmological argument, causal principles, and necessary existence. (shrink)

This work deals with problems involving infinities and infinitesimals. It explores the ideas behind zero, its relationship to ontological nothingness, finititude (such as finite numbers and quantities), and the infinite. The idea of infinity and zero are closely related, despite what many perceive as an intuitive inverse relationship. The symbol 0 generally refers to nothingness, whereas the symbol infinity refers to ``so much'' that it cannot be quantified or captured. The notion of finititude rests somewhere between complete nothingness and something (...) having no end. -/- My concern is that many of the philosophers arguing for or against the ontology (or possibility) of an actual infinite set are unaware or unfamiliar with the mathematical literature attempting to clearly and rigorously define these terms. I believe it is a mistake to leave mathematicians out of this conversation, as analysts in particular have defined (and used) infinity in a way that is relevant to the ongoing debate between philosophers. -/- For this paper, I have selected examples from Principles of Analysis by Walter Rudin, which has become a standard text for Real Analysis classes taken by pure mathematicians and engineers. I will also restrict the scope of examples to Euclidean spaces for simplicity. Finally, I will be using addition, + and multiplication * in their usual way. (shrink)