A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

Transport of patterns by Burge transpose

We take the first steps in developing a theory of transport of patterns from Fishburn permutations to (modified) ascent sequences. Given a set of pattern avoiding Fishburn permutations, we provide an explicit construction for the basis of the corresponding set of modified ascent sequences. Our approach is in fact more general and can transport patterns between permutations and equivalence classes of so called Cayley permutations. This transport of patterns relies on a simple operation we call the Burge transpose. It operates on certain biwords called Burge words. Moreover, using mesh patterns on Cayley permutations, we present an alternative view of the transport of patterns as a Wilf-equivalence between subsets of Cayley permutations. We also highlight a connection with primitive ascent sequences.Comment: 24 pages, 4 figure

Understanding Evans

This paper is largely exegetical/interpretive. My goal is to demonstrate that some criticisms that have been leveled against the program Gareth Evans constructs in The Varieties of Reference (Evans 1980, henceforth VR) misfire because they are based on misunderstandings of Evans’ position. First I will be discussing three criticisms raised by Tyler Burge (Burge, 2010). The first has to do with Evans’ arguments to the effect that a causal connection between a belief and an object is insufficient for that belief to be about that object. A key part of Evans’ argument is to carefully distinguish considerations relevant to the semantics of language from considerations relevant to the semantics (so to speak) of thought or belief (to make the subsequent discussion easier, I will henceforth use ‘thought’ as a blanket term for the relevant mental states, including belief). I will argue that Burge’s criticisms depend on largely not taking account of Evans’ distinctions. Second, Burge criticizes Evans’ account of ‘informational content’ taking it to be inconsistent. I will show that the inconsistency Burge finds depends entirely on a misreading of the doctrine. Finally, Burge takes Evans to task for a perceived over-intellectualization in a key aspect of his doctrine. Burge incorrectly reads Evans as requiring that the subject holding a belief be engaged in certain overly intellectual endeavors, when in fact Evans is only attributing these endeavors to theorists of such a subject. Next, I turn to two criticisms leveled by John Campbell (Campbell, 1999). I will argue that Campbell’s criticisms are based on misunderstandings – though they do hit at deeper elements of Evans’ doctrine. First, Campbell reads Evans’ account of demonstrative thought as requiring that the subject’s information link to an object allows her to directly locate that object in space. Campbell constructs a case in which one tomato (a) is, because of an angled mirror, incorrectly seen as being at a location that happens to be occupied by an identical tomato (b). Campbell claims that Evans’ doctrines require us to conclude that the subject cannot have a demonstrative thought about the seen tomato (a), though it seems intuitively that such a subject would be able to have a demonstrative thought about that tomato, despite its location is inaccurately seen. I show that Evans’ position in fact allows that the subject can have a demonstrative thought about the causal-source tomato in this case because his account does not require that the location of demonstratively identified objects be immediately accurately assessed. What is crucial is that the subject have the ability to accurately discover the location. Second, Campbell criticizes Evans’ notion of a fundamental level of thought. I show that this criticism hinges on view of the nature and role of the fundamental level of thought that mischaracterizes Evans’ treatment of the notion

Constancy Mechanisms and the Normativity of Perception

In this essay, we draw on John Haugeland’s work in order to argue that Burge is wrong to think that exercises of perceptual constancy mechanisms suffice for perceptual representation. Although Haugeland did not live to read or respond to Burge’s Origins of Objectivity, we think that his work contains resources that can be developed into a critique of the very foundation of Burge’s approach. Specifically, we identify two related problems for Burge. First, if (what Burge calls) mere sensory responses are not representational, then neither are exercises of constancy mechanisms, since the differences between them do not suffice to imply that one is representational and the other is not. Second, taken by themselves, exercises of constancy mechanisms are only derivatively representational, so merely understanding how they work is not sufficient for understanding what is required for something, in itself, to be representational (and thereby provide a full solution to the problem of perceptual representation)

Adaptationism, Deflationism, and Anti-Individualism

An examination of the externalist theories of Tyler Burge, Daniel Dennett and Ruth Millikan

Un perfil con historia. El edificio AT&T de Johnson/Burgee

Un perfil con historia. El edificio AT&T de Johnson/Burge

Cruise Report 73-KB-20: Abalone

(2pp.

Cruise Report 73-KB-15: Abalone investigations

(4pp.