Online research in philosophy

LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and $\bigwedge, \bigvee$ (both of bounded arity). Then for every d ≥ 0 and n ≥ 2, there is a set Td n of depth d sequents of total size O(n3 + d) which are refutable in LK by depth d + 1 proof of size exp(O(log2 n)) but such that every depth d refutation must have the size at least exp(nΩ(1)). The sets Td n express a weaker form of the pigeonhole principle.

I discuss Fitch & Denenberg's argument that no correction for brain size is needed when assessing callosal size. Morphometric criteria may not be sufficient to determine whether corrections are needed. Functional studies of callosal transfer will ultimately specify whether corrections for size are necessary in each case.

I develop a Russellian representationalist account of size experience that draws importantly from contemporary vision science research on size perception. The core view is that size is experienced in ‘body-scaled’ units. So, an object might, say, be experienced as two eye-level units high. The view is sharpened in response to Thompson’s (forthcoming) Doubled Earth example. This example is presented by Thompson as part of an argument for a Fregean view of size experience. But I argue that the Russellian view I develop handles the Doubled Earth example in a natural and illuminating way, thereby avoiding the need to posit irreducible experiential ‘modes of presentation’. I also address a kind of neo-Fregean ‘reference-fixing’ view of size experience, that shares features with the Russellian view developed. I give reasons for favoring the latter. Finally, I argue that Peacocke’s claim that spatial experience is ‘unit free’ is not persuasive.

The usefulness of effect-size differs in utilitarian experiments from its use in theory corroborations. Chow introduces the question of the relationship of effect-size to practical validity and the role of the assessment of “importance” in this. This review develops this question and suggests the actuarial table as a replacement for effect-size in practical decision-making.

Environmental policy has a size bias. Small organisms, such as microorganisms, command less attention from environmentalists than larger organisms, such as birds and large mammals. A simple thought experiment involving microscopic polar bears and giant microorganisms illustrates the importance of size in environmental ethics. Given the positive correlation between body size and brain size, there is probably a basis for a size bias in environmental ethics using ethical frameworks based on conations. This paper examines the relevance of the size of organisms in environmental ethics. It emphasizes the need to understand the theoretical reasons for the importance of size, and not to base a size bias merely on a subjective anthropocentric prejudice favouring large organisms.

2. Invariant Sensorimotor Features ("Affordances"). To say this is not to declare oneself a Gibsonian, whatever that means. It is merely to point out that what a sensorimotor system can do is determined by what can be extracted from its motor interactions with its sensory input. If you lack sonar sensors, then your sensorimotor system cannot do what a bat's can do, at least not without the help of instruments. Light stimulation affords color vision for those of us with the right sensory apparatus, but not for those of us who are color-blind. The geometric fact that, when we move, the "shadows" cast on our retina by nearby objects move faster than the shadows of further objects means that, for those of us with normal vision, our visual input affords depth perception. From more complicated facts of projective and solid geometry it follows that a 3-dimensional shape, such as, say, a boomerang, can be recognized as being the same shape Ð and the same size Ð even though the size and shape of its shadow on our retinas changes as we move in relation to it or it moves in relation to us. Its shape is said to be invariant under these sensorimotor transformations, and our visual systems can detect and extract that invariance, and translate it into a visual constancy. So we keep seeing a boomerang of the same shape and size even though the shape and size of its retinal shadows keep changing.

Berkeley and Helmholtz proposed different indirect mechanisms for size perception: Berkeley, that size was conditioned to various cues, independently of perceived distance; Helmholtz, that it was unconsciously calculated from angular size and perceived distance. The geometrical approach cannot explain size-distance paradoxes (e.g., moon illusion). The dorsal/ventral solution is dubious for close displays and untestable for far displays.

Lehar argues that a simple Neuron Doctrine cannot explain perceptual phenomena such as size constancy but he fails to discuss existing, more complex neurological models. Size models that rely purely on scaling for distance are sparse, but several models are also concerned with other aspects of size perception such as geometrical illusions, relative size, adaptation, perceptual learning, and size discrimination.