25/03 - Lucas Rosenblatt (Colloquium Logicae)

Capturing Naive Validity in the Strict-Tolerant Approach

Rejecting the structural rule of Cut has been recently proposed as a strategy to avoid both the usual semantic paradoxes and the so-called Validity Paradox. In this paper we consider if a theory that rejects Cut is capable of accurately representing its own notion of validity. We claim that the standard rules governing a naive validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious problem: an internalized version of Cut can be proved. We also evaluate a number of possible ways of escaping this difficulty.


11/03 - Emiliano Boccardi

If it ain’t Moving it shall not be Moved: real passage for A-theorists

Imagine two friends sitting on a beach, looking at a ship far away. Because of the distance, they cannot just tell by looking at it whether the ship is moving or not. “I bet it’s moving” says one. “No it’s not!”, says the other. Do they disagree about something? And if yes, what is the disagreement exactly about?

After some time the two friends look again and the ship has obviously moved, although it looks to them just as still as it looked before: its position (relative to them) has changed. “Aha!”, says the first, “I told you it was moving!” “You were right, it was moving. I lost the bet!”, says the other. What was this bet about?

Physics and mathematics  textbooks  follow  Bertrand  Russell  in accounting  for  a  body‘s instantaneous velocity not merely as equal to, but moreover as identical to the time-derivative of its trajectory. On this view, a body’s instantaneous velocity is ontologically parasitic on its trajectory. This deflationist understanding of change was heavily inspired by Weierstrass’ and Cantor’s understanding of limit and infinity. According to Weierstrass’ conception of limits and infinitesimals (now the received view), variables are just denotational schemas: they contribute to the sole purpose of denoting large numbers of (unchanging) facts about their values. The values of the variables do not themselves vary: they do not “approach”, let alone “reach” their limits, or change in any sense, contrary to what they were ambiguously alleged to be doing in prior formulations (since Newton’s and Leibniz’s). Of course, according to this conception, neither do variables themselves vary or change, in spite of their evocative name. It was this reconceptualization of the notion of limit that inspired Russell’s treatment of the antinomies involved in the notion of indefinitely growing series of things (such as those involved in Zeno’s paradoxes): “Weierstrass”, he says, “by strictly banishing all infinitesimals has at last shown that we live in an unchanging world, and that [Zeno’s] arrow, at every moment of its flight, is truly at rest” (POM, p. 347).

Likewise, many philosophers of time argue that the passage of time is identical with the fact that different times subsequently instantiate presentness.

However, I shall argue in the first part of this talk, it is tempting to think that the initial disagreement between the two friends is about a property instantiated by the ship at (and only at) the time of the bet (t1). What they observe at the time of the assessment of the bet (t2), according to this intuitive view, is the comparative fact that the ship’s location at t1 is different from its location at t2. They agree that this provides indirect evidence for the further (non-comparative) fact that the ship was moving at t1. If the ship is found at different positions at times right after t1, this must be because at t1 it possessed an intrinsic kinematic quantity in addition to its position.

If this explanatory pattern is sound, then the comparative fact that (a) the location of the ship at t1 is different from its location at t2, must be ontologically distinct from the (non-comparative) fact that (b) the object has been in motion for enough times between t1 and t2. In short, according to this view, the displacement of the ship is a posthumous consequence of its state of motion (velocity) throughout the time interval considered, hence fact b (the explanans) cannot be identical to fact a (the explanandum). Analogously, I shall defend the thesis that yesterday became past because time passes. The passage of time ought to explain the ensuing comparative fact that Today’s presentness followed Yesterday’s presentness, so it cannot be thought of as identical with it. The ensuing view construes passage as an intrinsic, non-comparative feature of time instants.

In the second, more tentative part of the talk, I shall bring this issue to bear on the formal semantics of axiomatic treatments of aspect. In particular, I shall consider different solutions to the so called Imperfective Paradox, and test them against the desiderata put forward in the first part of the talk.


Arntzenius, F. (2000) Are there really instantaneous velocities? Monist 83:187–208

Bach, E. (1986) The algebra of events, Linguistics and Philosophy, 9(1):5–16

Bigelow, J. (1991) Worlds enough for time. Nouˆs 25:1–19
. Bigelow J, Pargetter R (1990) Science and necessity. Cambridge University Press, Cambridge

Boccardi, E. (2015) If it ain't Moving it shall not be Moved, Topoi, 34(1): 171-185

Dowty, D. (1979) Word Meaning and Montague Grammar, Dordrecht: Reidel

Hall, N. (2004) Two concepts of causation. In: Collins, Hall N, Paul, LA (eds)

Causation and counterfactuals. The MIT Press, Cambridge, pp 225–276

James, W. (1987) Writings 1902–1910. Literary Classics of the United States inc., New York

Lange, M. (2005) How can instantaneous velocity fulfill its causal role? Philos Rev 114(4): 433–468

Le Poidevin, R. (2002) Zeno’s arrow and the significance of the present. In: Callender

Craig, University Cambridge (eds) Time, reality and experience. Press, Cambridge

Parsons, T., 1989, “The progressive in English: Events, states and processes”, Linguistics and Philosophy, 12(2): 213–241

–––, 1990, Events in the Semantics of English, Cambridge MA: MIT Press.

Prior, A., 1967, Past, Present, and Future, Oxford: Oxford University Press.

Russell, B. (1938) Principles of mathematics. W.W. Norton & Company, inc, New York

Tooley, M. (1988) In defense of the existence of states of motion. Philos Top 16:225–254