While the essays on this web site, taken together, explain most of the essentials of my metaphysical system, some material is not covered, and the different essays take quite different approaches. The essays were mostly written for undergraduate and graduate courses in philosophy at the University of Toronto and York University. Thus, each essay is slanted to the issues that were addressed in whatever course it was written for. However, I hope soon to pull all this material together into a cohesive, single work that will explain my system more fully and with more focus, which will serve as my Ph.D. dissertation. In the meantime this brief overview gives the broad picture of what my philosophical system is, and how the various essays on these pages are inter-related. For those who do not wish to read through this entire page, the Quantum Phenomenology essay is probably the one you should read if you only have time to read one, as it is the closest to being comprehensive.

The basic approach I call "computational metaphysics", although this is a broad term that should be taken to represent not just my own system, but any metaphysics that takes the concepts of theoretical computer science as its first and most basic ontological principles. The idea behind computational metaphysics can be neatly summed up by the following slogan: "To exist is to be computable".

My philosophy is primarily rationalist, in the good-old-fashioned sense of Descartes: accept only what can be clearly and distinctly perceived, building everything up from immediate conscious experience. This principle is captured in Descartes' Cogito: "I think, therefore I am". This is the appropriate foundation on which to base all science. In particular, the apparent mysteries of quantum mechanics can be seen as really quite inevitable and not mysterious at all, if viewed from a resolute and uncompromising rationalist perspective. But most twentieth century scientists have, unfortunately, been poisoned by logical positivism into placing little faith in rationality. It is generally believed (with what is to me a truly befuddling stubbornness) that we are living in the One True World. Yet quantum mechanics, if interpreted literally, clearly requires a whole ensemble of worlds in order to work. This is the "many-worlds interpretation" of quantum mechanics due to Everett, and it is really the only true interpretation there is, as all the others postulate something inexplicable and mysterious beyond the mathematics of the theory. Yet not only does modern scientific experiment drive us to the conclusion that there exists more than a single universe, but the very principles of rationality do so also. The ancient Greeks, who founded rational enquiry, started out with the idea of many-worlds, in the theories of Anaximander and Parmenides. The issue continued to re-surface in modern philosophy long before there was any systematic empirical evidence for it. Leibniz was so perplexed as to how to deal with these other worlds that he decided that they did indeed exist, but only in the mind of God, who chose the best one to be the really existing One True World (the best of all possible worlds). F.H. Bradley, shortly before quantum theory came on the scene, developed his entire metaphysics on the notion of other worlds. Yet when evidence was discovered that the universe really does have this multi-world structure, the idea was ignored for years in favour of the invocation of all sorts of mystical and unknowable what-nots, only marginally more sophisticated than Leibniz's God (chief examples are the interpretations of Bohr and Bohm).

Once we get over our prejudice against many-worlds, much of what was perplexing about modern physics suddenly seems only natural. If we accept as a basic rationalist premise that only that which can in principle be mathematically formalized should be accepted as real, then not only do all possible worlds in some sense "exist", but they exist on equal footing with all mathematical structures, most of which are not anything we would call "worlds" at all. Only a small subset of such structures contain conscious life. It is a simple truism that we, as conscious creatures, can only exist within this subset. The attempt to understand the general features of the universe as a random selection out of the set of all possible consciousness-containing mathematical structures is called the "Many-Worlds Anthropic Principle".

A note on "isms": While I consider myself a rationalist, I also consider myself to be a sceptic. The sceptical rationalism that I adhere to does not presume that the world is necessarily a rationally conceivable structure (that would be irrational), but simply recognizes that rationality is currently my only tool with which to investigate the matter, and so sees the rational assumption of the ultimate formalizability of the universe as the only reasonable working hypothesis from which to proceed. My philosophy could perhaps be called "idealist", in that what is real is what can be thought of. However, idealism is sometimes defined as the belief that objective reality is mental, which I definitely do not hold. However, I do believe that physical objects, as physical, are mental. But this is not because in themselves they are somehow embued with life or consciousness, but rather that to speak of them as physical things apart from our consciousness is mistaken, and assumes that somehow the physical world exists apart from us. Their ultimate reality is simply mathematical, which is not at all mental, but neither is it "physical". To talk of the physical is to take a subjective stance. So my philosophy, while in some sense idealist, is also in some sense realist, since there is an objective reality. But that objective reality is mathematical, not physical, so it is a Platonic realism, not a materialist realism. So while I do not object to being called either an "idealist" or a "realist", it is less ambiguous to call me an "anti-materialist", a "formalist", a "mechanist" or a "computationalist".

The following three essays attempt to develop these ideas on their own merits, as opposed to the rest of the essays, which are more historical. Each of these three attempts are quite different, having been written at different times in my own development, and thus they may even contradict each other in places. They are listed in reverse chronological order, so the first essay is probably the one that will most directly contribute to future work. If you can only read one essay, read that one.

Quantum Phenomenology

Starting with the Cogito, I attempt to derive the basic principles of recursive function theory (the backbone of all mathematics), and from that the principles of feedback control theory (the backbone of all biology), leading to the basic ideas of quantum mechanics (the backbone of all physics). Currently missing is any explicit discussion of the Anthropic Principle (for that, see the next essay on modality).

Here the ideas are developed within the framework of modal logic, and the Anthropic Principle is explicity discussed. While this may still be a promising approach, I have for now decided to step back from it, since too much of what I am given in modal logic textbooks assumes first order predicate logic as its foundation. I would like to start with the lambda-calculus, which I think is a far superior foundation for logic (and mathematics as well). Traditional first-order logic is not really "first-order" at all, but has layers of assumed and unjustified interpretation underneath it. I may come back to looking at what modal logic has to say at a future date when I can clearly see it as flowing out of more fundamental principles.

This paper concentrates on defending the rationalist principles behind many-worlds. It thus discusses some of the historical background of rationalism (Parmenides, Leibniz, and so on). The actual defence of the quantum mechanical world-splitting is probably less rigorous than the above two essays, and needs to be updated in light of them.

The rest of the essays are more historical, relating how these ideas played out in the minds of various philosophers that have had an influence on me.

On Nature by Parmenides of Elea

It all starts with Parmenides, the father of rationalism and of metaphysics. He was about as uncompromising in his rationalism as you can get, insisting that only that which can be spoken of or thought of should be accepted as existing. I have not been satisfied with the existing translations of Parmenides, and so have patched together a "translation" of sorts that picks and chooses from existing translations, and even resorts to mild paraphrase in spots in order to make the whole thing readable. It is not meant to be a rigorous and scholarly translation, although I am currently working with a Greek translator at producing a more scholarly version. In the meantime, it provides, I think, an approachable, readable introduction to Parmenides' work, and one that is consistent with my own interpretation of his thinking. I have also written a companion commentary that explains my interpretation more fully: Parmenides' Principle.

A look at why Kant thought geometry (and arithmetic) were synthetic a priori and not analytic. I agree with his thesis, but only if predicate logic is placed in the same category. This essay is important background for following the next Kant essay on transcendental idealism.

A reconstruction of Kant's transcendental deduction of the categories (logical functions), expressed in terms compatible with related modern ideas like recursion theory and the anthropic principle. Kant's notion of the synthetic a priori is essentially an early version of the modern anthropic principle. (The early Kant even speculated on the probable actual existence of many worlds, provided spaces higher than 3-D were possible.)

A description of Bradley's philosophy, which had much of the basic structure of quantum mechanics, but was all but ignored in the years following the formal quantum theories discovered by Heisenberg and Schrödinger.

This is a defence of my rationalist adherence to recursive function theory as the foundation for metaphysics, from the point of view of Platonic philosophy. The lambda-calculus is explained from scratch, so this essay could serve as a reasonable introduction to the subject (these sections are also reproduced in the Quantum Phenomenology paper). The notion of many worlds is only indirectly addressed in a footnote.

The role that recursive function theory plays in my philosophy owes much to Wittgenstein, who nonetheless was too stuck in the One True World dogma to develop it from a rationalist perspective. Instead, he resorted to mysticism, which he eventually rejected in favour of throwing out metaphysics altogether. Rationalism never seems to have seriously occurred to him. My own philosophy can be viewed as a kind of hybrid of Wittgenstein and F.H. Bradley.

Finally, there are two essays on the notion of substance in British empiricism. Both were written around the same time, and so take similar perspectives.  The first is The Inconsistency of Substance in the Metaphysics of John Locke, which discusses how Lock dealt with the problem of defending the nonsensical notion that there is something called "substance" that is unthinkable, but that somehow provides the bedrock for our One True World. The second essay discusses Berkeley's failed but interesting attempt to solve the same problem: The Rejection of Abstract Ideas in the Metaphysics of George Berkeley. Berkeley assumed something that I think is very dangerous, and which my defence of the lambda-calculus in other essays is meant to refute: that "real" things are passive and static, while anything that moves or has process is mental (or "semantical", or "interpretational").