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The following is my interpretation of the philosophy of Parmenides of Elea , the Greek father of metaphysics. His only work, On Nature , is written in rather obscure verse, and so his thesis can be viewed from a variety of perspectives, of which mine is only one (although a fairly standard one). Parmenides' most important principle, hereafter called "Parmenides' Principle", was that anything rationally conceivable must exist. Nonbeing is not a thing and can neither be thought of nor spoken about in any meaningful or coherent way. Parmenides forbade talking as if there are possible things that nonetheless do not exist. He illustrated this principle by showing us three possible methods of inquiry, of which only one is valid. The following chart summarizes them.

The Parmenides is, quite possibly, the most enigmatic of Plato's dialogues. The dialogue recounts an almost certainly fictitious conversation between a venerable Parmenides (the Eleatic Monist) and a youthful Socrates, followed by a dizzying array of interconnected arguments presented by Parmenides to a young and compliant interlocutor named “Aristotle” (not the philosopher, but rather a man who became one of the Thirty Tyrants after Athens' surrender to Sparta at the conclusion of the Peloponnesian War). Most commentators agree that Socrates articulates a version of the theory of forms defended by his much older namesake in the dialogues of Plato's middle period, that Parmenides mounts a number of potentially devastating challenges to this theory, and that these challenges are followed by a piece of intellectual “gymnastics” consisting of eight strings of arguments (Deductions) that are in some way designed to help us see how to protect the theory of forms against the challenges. Beyond this, there is precious little scholarly consensus. Commentators disagree about the proper way to reconstruct Parmenides' challenges, about the overall logical structure of the Deductions, about the main subject of the Deductions, about the function of the Deductions in relation to the challenges, and about the final philosophical moral of the dialogue as a whole.

In his great poem, Parmenides uses an argument by elimination to select the correct "way of inquiry" from a pool of two, the ways of is and of is not , joined later by a third, "mixed" way of is and is not . Parmenides' first two ways are soon given modal upgrades - is becomes cannot not be , and is not becomes necessarily is not (B2, 3-6) - and these are no longer contradictories of one another. And is the common view right, that Parmenides rejects the "mixed" way because it is a contradiction? I argue that the modal upgrades are the product of an illicit modal shift. This same shift, built into two Exclusion Arguments, gives Parmenides a novel argument to show that the "mixed" way fails. Given the independent failure of the way of is not , Parmenides' argument by elimination is complete.

I argue for two claims. First I argue against the consensus view that accurate behavioral prediction based on accurate representation of cognitive states, i.e. mind reading , is the sustaining function of propositional attitude ascription. This practice cannot have been selected in evolution and cannot persist, in virtue of its predictive utility, because there are principled reasons why it is inadequate as a tool for behavioral prediction. Second I give reasons that favor an alternative account of the sustaining function of propositional attitude ascription. I argue that it serves a mind-shaping function. Roughly, propositional attitude ascription enables human beings to set up regulative ideals that function to mold behavior so as to make it easier to coordinate with.

John Palmer develops and defends a modal interpretation of Parmenides, according to which he was the first philosopher to distinguish in a rigorous manner the fundamental modalities of necessary being, necessary non-being or impossibility, and non-necessary or contingent being. This book accordingly reconsiders his place in the historical development of Presocratic philosophy in light of this new interpretation. Careful treatment of Parmenides' specification of the ways of inquiry that define his metaphysical and epistemological outlook paves the way for detailed analyses of his arguments demonstrating the temporal and spatial attributes of what is and cannot not be. Since the existence of this necessary being does not preclude the existence of other entities that are but need not be, Parmenides' cosmology can straightforwardly be taken as his account of the origin and operation of the world's mutable entities. Later chapters reassess the major Presocratics' relation to Parmenides in light of the modal interpretation, focusing particularly on Zeno, Melissus, Anaxagoras, and Empedocles. In the end, Parmenides' distinction among the principal modes of being, and his arguments regarding what what must be must be like, simply in virtue of its mode of being, entitle him to be seen as the founder of metaphysics or ontology as a domain of inquiry distinct from natural philosophy and theology. An appendix presents a Greek text of the fragments of Parmenides' poem with English translation and textual notes.

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would be lost.

Peter Geach has said that Russell's use of ‘propositional function’ is ‘hopelessly confused and inconsistent’. Geach is right, and attempts to say what exactly a Russellian propositional function is, or is supposed to be, are bound to end in frustration. Nevertheless, it may be worthwhile to pursue an account of propositional functions that accommodates a good deal of what Russell says about them and that can provide some of what he expected of them.

§1. Introduction. Although Whitehead and Russell’s Principia Mathematica (hereafter, PM ), published almost precisely a century ago, is widely heralded as a watershed moment in the history of mathematical logic, in many ways it is still not well understood. Complaints abound to the effect that the presentation is imprecise and obscure, especially with regard to the precise details of the ramified theory of types, and the philosophical explanation and motivation underlying it, all of which was primarily Russell’s responsibility. This has had a large negative impact in particular on the assessment of the socalled “no class” theory of classes endorsed in PM. According to that theory, apparent reference to classes is to be eliminated, contextually, by means of higher-order “propositional function”—variables and quantifiers. This could only be seen as a move in the right direction if “propositional functions,” and/or higher-order quantification generally, were less metaphysically problematic or obscure than classes themselves. But this is not the case—or so goes the usual criticism. Years ago, Geach (1972, p. 272) called Russell’s notion of a propositional function “hopelessly confused and inconsistent.” Cartwright (2005, p. 915) has recently agreed, adding “attempts to say what exactly a Russellian propositional function is, or is supposed to be, are bound to end in frustration.” Soames (2008) claims that “propositional functions . . . are more taken for granted by Russell than seriously investigated” (p. 217), and uses the obscurity surrounding them as partial justification for ignoring the no class theory in a popular treatment of Russell’s work (Soames, 2003).1 A large part of the usual critique involves charging Russell with confusion, or at least obscurity, with regard to what a propositional function is supposed to be. Often the worry has to do with the use/mention distinction: is a propositional function, or even a proposition.