(Abstract for Keynote Address appears at bottom of page)

### 'Intrinsic Properties of Properties' - Sam Cowling

Do properties have intrinsic properties of their own? If so, which second-order properties are intrinsic? In this paper, two competing views about second-order intrinsicality are outlined: generalism, according to which the intrinsic-extrinsic distinction cuts across all orders of properties and applies to the properties of properties as well as the properties of objects, and objectualism, according to which intrinsicality is a feature exclusive to the properties of objects. I then examine the case for generalism and consider some proposals for distinguishing intrinsic second-order properties from extrinsic ones. After addressing these broad questions about the nature of second-order intrinsicality, I introduce the Problem of Accidental Intrinsic Properties of Properties and use it as a case study for the significance of second-order intrinsicality. I conclude by briefly examining the interaction between the metaphysics of quantitative properties and second-order intrinsicality.

### 'Are Quantities Quantitative?' - Cian Dorr

(abstract)

### 'Quantum Metaphysical Indeterminacy' - Jessica Wilson

Can philosophical accounts of metaphysical indeterminacy (MI) shed light on quantum indeterminacy? Here we need to distinguish between ‘meta-level’ accounts of MI (e.g., the metaphysical supervaluationist accounts endorsed in Akiba 2004 and Barnes and Williams 2011), on which MI involves its being indeterminate which determinate state of affairs obtains, and ‘object-level’ accounts of MI (e.g., the determinable-based account endorsed in Wilson 2013), on which MI involves its being determinate (or just plain true) that an indeterminate state of affairs obtains (further cashed in terms of an object or system’s having of a determinable property, but no unique determinate of that determinable). Darby (2010) and Skow (2010) argue that meta-level approaches fail to capture quantum indeterminacy; Wolff (2015) argues that a determinable-based object-level account—implemented, in particular, as involving a system’s having a determinable spin property, but no determinate of that property—is the most promising of the available approaches, but mentions certain residual worries. In this talk, I summarize the present state of debate, and address Wolff’s residual worries.

## Saturday

### 'The Metaphysics of Dimensional Analysis' - Brad Skow

Velocity has dimensions (length)/(time). Force has dimensions (mass)(length)/(time*time). When looking for physical laws it helps to keep dimensions in mind, for typically laws can be written as dimensionally consistent equations, equations with the same dimensions on each side. But what are dimensions? What is it for a quantity to have a certain dimension? There have been those who have claimed that the dimension of a quantity has something to do with its essence, or nature, or definition. Others have said that the dimension of a quantity says something about how it is built up from basic quantities, the way the chemical formula for a substance says something about how it is built up from the elements. But the dominant view now seems to be that these people are wrong. The dominant view is that facts about a quantity’s dimension are (from a philosophical point of view) relatively boring facts about how the numbers we use to measure that quantity change when we change our scales of measurement. While some of the exciting claims about dimensions are false, at least one of them is, I think, true; I will defend it.

### 'Additivity and Dynamics' - Zee Perry

(abstract)

### 'Intrinsic Explanations and Numerical Representations' - Maya Eddon

In Science Without Numbers (1980), Hartry Field defends a theory of quantity that, he claims, is able to provide both i) an intrinsic explanation of the structure of space, spacetime, and other quantitative properties, and ii) an intrinsic explanation of why certain numerical representations of quantities (distances, lengths, mass, temperature, etc.) are appropriate or acceptable while others are not. But several philosophers have argued otherwise. In this paper I focus on arguments from Ellis and Milne to the effect that one cannot provide an account of quantity in “purely intrinsic” terms. I show, first, that these arguments are confused. Second, I show that Field’s treatment of quantity can provide an intrinsic explanation of the structure of quantitative properties; what it cannot do is provide an intrinsic explanation of why certain numerical representations are more appropriate than others. Third, I show that one could provide an intrinsic explanation of this sort if one modified Field’s account in certain ways.

(Abstract for Keynote Address appears at bottom of page)

## Sunday

### 'Reductionism about Physical Magnitudes' - Marco Dees

Elephants are more massive than mice. Are facts like these fundamental or can they be explained in other terms? I argue that the structure of physical quantities like mass reduces to facts about the dynamical role magnitudes of mass play in the laws of nature. On this view elephants are more massive than mice partly in virtue of the fact that elephants are harder to throw around. I argue for this view on the grounds that fundamental physical magnitude comparisons are explanatorily redundant.

### 'Comparativism about Mass and the Initial Variable Problem' - Niels Martens

Absolutism about mass, as it features in Newtonian Gravity, is the view that the most fundamental facts about material bodies vis-à-vis their masses are facts about which intrinsic mass they possess. Mass relations hold in virtue of these intrinsic facts. Comparativism about mass is the view that the most fundamental facts about material bodies vis-à-vis their masses just concern how they are related in mass. Dagupta (2013) argues that, since 1) comparativism is empirically adequate, and 2) comparativism is ontologically more parsimonious, we should favour comparativism. I will explore whether each of these premises indeed holds. In this paper I cash out the empirical adequacy of a theory in terms of its ability to correctly generate the set of empirically possible models. This leads me to formulate the Initial Variable Problem for the comparativist: proving the empirical adequacy of comparativism means finding a set of comparativist initial variables that solves the Initial Variable Problem. I will discuss several such attempts, that is several choices of initial variables. Finally, I will raise some question marks as to the alleged ontological parsimony of comparativism.

### 'Determinism and Theories of Quantity' - David Baker

(abstract)

## Keynote Address:

(All references in this abstract are from Professor Mundy’s final paper, ‘Quantity, Representation and Geometry’, P.Humphreys (ed.), Patrick Suppes: Scientific Philosopher, Kluwer 1994, Vol. 2, 59-102. Available **HERE**.)

### 'Looking Back a Little and Forward a Lot' - Brent Mundy

Philosophy talks (Loewer, David Lewis). Good and bad metaphysics (Sider 4-dimensionalism, “the talk”, Compton scattering); urelements, quantifier-free physics (1990). Metaphysics

*is*proto-science, not merely

*like*science. Kuhnian transition from

**projective**(evidential-conjectural-speculative) metaphysics to normal science. Scientists understand that projective metaphysics not forced by a normal-science crisis is “philosophical” but philosophers don’t. Pathologies of professionalization. “Read metaphysics from your best current theory” – far too conservative. Both historical and theoretical support for this viewpoint.

**Kuhnian framing relation [[**. Qualitative metaphysics [[ qualitative theory [[ normal science including quantitative theory and observation. Historical cases, with qualitative data (Franklin, Black-Fourier, Faraday, Carnot, de Broglie, Mach). Normal science *can’t* give it’s own foundations, just as deduction can’t determine the rules of proof, and the equations of Maxwell or GTR can’t tell you what the e-m field or the s-t manifold are.

How philosophers should approach projective metaphysics: **safe but shallow** vs **deep but risky** (both professionally and cognitively). Initial problem-framing: Tractatus logical metaphysics → what quantitative metaphysics or quantitative logic? (1987b) “Logic is ultra-physics”. In what formal language is fundamental theory expressed, for a logical realist? Form of a law, modal logic. Properties vs relations (Aristotle-Leibniz-Russell), hiding relations in the geometry, Euclid and the syllogism, multigrade relations (1989a), evidence for first-order atomic facts.

**Safe-historical:** 18th-century transition from synthetic-geometrical to coordinate-analytical representation. Newton and Faraday already did “science without numbers”, with scientific not philosophical motivations and benefits. Mathematics as credential: “Parisian holy writ” (Grattan-Guinness, Fresnel, Marat). Newton’s proof of Kepler’s second law, versus mass-shell diagrams in Minkowski space. Synthetic differential geometry, moving and infinitesimal diagrams, neusis proofs. Metaphysics of analytical mechanics (Lagrange vs Hamilton, 3rd law), geometry of phase space. Newtonian QM? Virtual processes in classical statics, BKS, Feynman path-integral. E-M: Wheeler-Feynman, pre-acceleration.

**Safe-reformulative:** Analyze whole theories not just theories of quantity. (“what if all the masses doubled?”) Use scientific criteria (me vs. Field). Physical interpretation of logical constructions. Quantifier-free classical mechanics (1990). Why are equations so important? Why so many linear laws? Algebra of quantities. *Intrinsic* means wholly coordinate-free, not just *invariant* under coordinate changes; may still be *qualitative* (synthetic) or *intrinsic-quantitative*, and on different type-theoretic levels (1994). Inner-product geometry → intrinsic-quantitative relationist theory of curved spacetime using integral theorems (1983, 1989b). Synthetic space-time geometry vs “hole argument” (1992).

**Speculative:** Dynamics more basic than geometry, microstructure prior to both. Mach’s principle. Anti-[set theory, spacetime, classical analysis] → discrete microreduction of continuous quantities, for classical physics also. Linearity from counting. Quantization from discretization. Relationism and QM (non-locality, QFT) Quantum phase and gauge theories. Is QM two theories? Tegmark “mathematical universe hypothesis”. Fundamental theory is no longer Baconian-beneficial; has it become dangerous? Doomsday scenarios. Should we stop? Can we stop? Magic glasses.