Peter Richard Forrest

Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper has done (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”.

I reply to seven objections to anthropomorphic theism: (1) That anthropomorphic theism is idolatrous. In reply I rely on the concept/conception distinction. (2) That faith requires certainty. In reply I argue that full belief may be based on probable inference. (3) That the truly infinite is incomprehensible. In reply I distinguish two senses of knowing what you mean. (4) "You Kant say that!" In reply I distinguish shallow from deep Kantianism. (5) "Shall Old Aquinas be forgot?" In reply I discuss the simplicity of God. (6) What those garrulous mystics say about the ineffable. In reply I argue that mystics should be anthropomorphites. (7) Antitheodicy. In reply I distinguish the community of all agents from the community of finite frail agents

In this paper I compare two versions of non-eliminative physicalism (reductive physicalism and supervenience physicalism) with four of the five theses of classical theism: divine non-contingency, divine transcendence, divine simplicity, and the aseity thesis. I argue that:1. Both physicalism (either version) and classical theism require intuition-transcending identifications of some properties or possibilities.2. Among other identifications, both reductive physicalism and classical theism need to identify psychological with functional properties.3. Both reductive physicalism and classical theism have a problem with consciousness.4. Both reductive physicalists and classical theists should distinguish fine and coarse grained theories of properties.

William Rowe in his Can God be Free? argues that God, if there is a God, necessarily chooses the best. Combined with the premise that there is no best act of creation, this provides an a priori argument for atheism. Rowe assumes that necessarily God is a ‘morally unsurpassable’ being, and it is for that reason that God chooses the best. In this article I drop that assumption and I consider a successor to Rowe ’s argument, the Argument from Arbitrariness, based on the premise that God does not act arbitrarily. My chief conclusion will be that this argument fails because, for all we know, there can be non- arbitrary divine choices even if there is no best act of creation

In this paper I present the Discrete Space-Time Thesis, in a way which enables me to defend it against various well-known objections, and which extends to the discrete versions of Special and General Relativity with only minor difficulties. The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is. Having argued that it is an open question whether or not space-time is discrete, I then turn to some possible empirical evidence, which we do not yet have. This evidence is based on some slight differences between commonly occurring differential equations and their discrete analogs.

In this paper I have had two aims. One was to describe a number of pantheist or near pantheist religious attitudes, including the influence of many worlds theories. The other was to indicate some of the ways we might arrive at Pantheism.One final remark: when assessing religious positions the intellectual grounds for accepting or rejecting them should, I suggest, be whether they make sense of things, that is, enable us to understand. The ways to Pantheism, or to near Pantheism, should therefore be interpreted as part of a comparison between ways of understanding.

I consider three candidates for ultimate understanding: (1) ultimate agency, the familiar idea of understanding the existence and nature of the universe as created by God for good reasons; (2) axiarchism, the initially counter-intuitive idea that goodness is the first cause of contingent reality; and (3) plenitude, the thesis that all possible types of situation are real. After some initial clarification, I note the problems with axiarchism, and offer solutions. These solutions require the unification of space and time as space-time, and the consequent introduction of what might be called hypertime, but which I take to be true time—Time with an upper case “T”. I note how axiarchism and plenitude may be combined into the Plenum Bonum thesis that all and only good universes are real. Next, I note some problems with agency as an ultimate way of understanding. Finally, I solve these by means of a theory of agency as completing axiarchism, the Good versus Good theory.

Either from concrete examples such as tomatoes on a plate, an egg carton full of eggs and so on, or simply because of the braces notation, we come to have some intuitions about the sorts of things sets might be. (See Maddy 1990.) First we tend to think of a set of particulars as itself a particular thing.. Second, even after the distinction between settheory and mereology has been carefully explained we tend to think of the members of a set as in some sense parts. And third we tend to think that there is something represented by the braces. Now if there were experts who got their intuitions from elsewhere then we could discard these rather crude ideas about egg cartons and so on. But I suspect the intuitions of experts are, just like those of the rest of us, based on notation and simple examples.

That God is of great beauty is religiously significant as a component of the widespread hope of a blessed experience in this or the next life. This motivates the project of formulating the strongest coherent thesis of divine beauty. This chapter has two parts. In Section 9.1 I argue for the incoherence of Perfect Divine Beauty. The natural reaction to this incoherence is to replace the idea of perfection, but in a way that coheres with the theists’ religious tradition. I explore a range of such replacements, motivating the thesis of Pre-eminent Divine Beauty, that the actual divine beauty is infinitely greater than that of the physical universe. In Section 9.2 I examine various arguments against God’s great beauty. They are the Argument from Divine Simplicity (and the related the Argument from Divine Spirituality), the Argument from Divine Necessity, and the Argument from Moral Righteousness.