Only Friends, Despite the Rumors: Philosophy of Mind's Consciousness and Intentionality

Being evasive as it is, philosophers have often tried to do without consciousness. Despite this, it has played a key role in the endeavours of philosophy of mind, as witnessed by its reputation as a "mark of the mental" and works of philosophers like John Searle and Daniel Dennett. Intentionality has shared a similar role, such that one and the other have often been brought together in a symbiotic relationship (Searle 1990) or deemed coextensive (Crane 1998).\ud Such promiscuity is not necessary. The revolution brought about by embodied and situated approaches seem to leave little place for such an association. Intentionality is seldom studied in the new paradigm, and when it is, new models of it are applicable to biological and robotic structures which, by most accounts, probably have no consciousness (Millikan 1984, Menary 2006). Menary (2009) also notes that the same could be said of scholastic accounts of intentionality. On the other hand, consciousness is being studied and various ways which do not involve intentionality or anything similar.\ud I suggest that the association between these two notions has to do with the particular intellectual environment that prevailed in traditional philosophy of mind. Considerations about access and the good fortune of cognitivism, among other factors, made for a culture that emphasized the gap between behaviour on one hand and the the mental states that characterize us when we are in a disposition to cause behaviour on the other. In such conditions, concepts like intentionality and consciousness acted as bridge and allowed for a language which enabled accounts of the mind that remained somewhat comprehensive and unified, while leaving the gap unfilled. As they were covering the most problematic and elusive parts of our understanding of the mind, there was both enough similarity in the ways we used those concepts, and enough vagueness in how we accounted for their realization in physical systems, to make a rapprochement inevitable.\ud When a new paradigm swept away the cognitivist conception of representation, some philosophers and cognitive scientists turned to more embodied and situated models of cognition. Representations in this paradigm (such as Millikan’s (1995) and Clark’s (1997)) are “action-oriented”, thus leaving no gap between action and representation – getting an account of the complex representations that we communicate in propositions is thus seen as a matter of empirical investigation. If there is no gap, concepts like intentionality and consciousness are called to play different roles in accounts of the mind – roles which do not permit any confusion.\ud The poster will highlight relevant differences in the philosophical climate as they project themselves in accounts of representation (following Gallagher 2008), and make salient the link between this climate and the role of cognition in philosophy of mind

On hamiltonian colorings of block graphs

A hamiltonian coloring c of a graph G of order p is an assignment of colors to the vertices of G such that $D(u,v)+|c(u)-c(v)|\geq p-1$ for every two distinct vertices u and v of G, where D(u,v) denoted the detour distance between u and v. The value hc(c) of a hamiltonian coloring c is the maximum color assigned to a vertex of G. The hamiltonian chromatic number, denoted by hc(G), is the min{hc(c)} taken over all hamiltonian coloring c of G. In this paper, we present a lower bound for the hamiltonian chromatic number of block graphs and give a sufficient condition to achieve the lower bound. We characterize symmetric block graphs achieving this lower bound. We present two algorithms for optimal hamiltonian coloring of symmetric block graphs.Comment: 12 pages, 1 figure. A conference version appeared in the proceedings of WALCOM 201

Loyalist Lieutenant Jeremiah French and His Uniform

There are many unique and remarkable uniforms in the collections of the Canadian War Museum, some of which go back quite far into our history. One of these, probably the oldest presently known uniform that can be assigned to a unit raised in Canada, is that of Lieutenant Jeremiah French of the King’s Royal Regiment of New York

Rainbow Connection Number and Connected Dominating Sets

Rainbow connection number rc(G) of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we show that for every connected graph G, with minimum degree at least 2, the rainbow connection number is upper bounded by {\gamma}_c(G) + 2, where {\gamma}_c(G) is the connected domination number of G. Bounds of the form diameter(G) \leq rc(G) \leq diameter(G) + c, 1 \leq c \leq 4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, AT-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G) \leq 3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds. An extension of this idea to two-step dominating sets is used to show that for every connected graph on n vertices with minimum degree {\delta}, the rainbow connection number is upper bounded by 3n/({\delta} + 1) + 3. This solves an open problem of Schiermeyer (2009), improving the previously best known bound of 20n/{\delta} by Krivelevich and Yuster (2010). Moreover, this bound is seen to be tight up to additive factors by a construction of Caro et al. (2008).Comment: 14 page

On the metric dimension of corona product graphs

Given a set of vertices $S=\{v_1,v_2,...,v_k\}$ of a connected graph $G$, the metric representation of a vertex $v$ of $G$ with respect to $S$ is the vector $r(v|S)=(d(v,v_1),d(v,v_2),...,d(v,v_k))$, where $d(v,v_i)$, $i\in \{1,...,k\}$ denotes the distance between $v$ and $v_i$. $S$ is a resolving set for $G$ if for every pair of vertices $u,v$ of $G$, $r(u|S)\ne r(v|S)$. The metric dimension of $G$, $dim(G)$, is the minimum cardinality of any resolving set for $G$. Let $G$ and $H$ be two graphs of order $n_1$ and $n_2$, respectively. The corona product $G\odot H$ is defined as the graph obtained from $G$ and $H$ by taking one copy of $G$ and $n_1$ copies of $H$ and joining by an edge each vertex from the $i^{th}$-copy of $H$ with the $i^{th}$-vertex of $G$. For any integer $k\ge 2$, we define the graph $G\odot^k H$ recursively from $G\odot H$ as $G\odot^k H=(G\odot^{k-1} H)\odot H$. We give several results on the metric dimension of $G\odot^k H$. For instance, we show that given two connected graphs $G$ and $H$ of order $n_1\ge 2$ and $n_2\ge 2$, respectively, if the diameter of $H$ is at most two, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(H)$. Moreover, if $n_2\ge 7$ and the diameter of $H$ is greater than five or $H$ is a cycle graph, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(K_1\odot H).

Synchronization of electrically coupled resonate-and-fire neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs