Relevance and rationality by NICHOLAS ALLOTT

5.2 Optimization under constraints
We have established that no realistic model of reasoning, including therefore the
relevance theoretic comprehension procedure, can be an example of unbounded
rationality. Next I will consider optimization under constraints. This vision of
rationality ‘holds that the mind should calculate the benefits and costs of searching
for each further piece of information and stop search as soon as the costs outweigh
the benefits.’ (Gigerenzer and Todd, 1999, section 2.2)
Therefore a solution is reached without consulting all of the evidence, in contrast
to the way models of unbounded rationality work, using all possible information.
However the requirement that at each stage the costs and benefits of containing the
search be calculated leads to a computational explosion: ‘the paradoxical approach
is to model “limited” search by assuming that the mind has essentially unlimited
time and knowledge with which to evaluate the costs and benefits of future
information search.’ (Gigerenzer and Todd, 1999, section 2.2) This means that
‘optimization under constraints can require even more knowledge and computation
than unbounded rationality.’ (op cit, section 2.2, referring to work by Vriend,
1996; Winter 1975)
As a realistic model of cognition, then, relevance theory cannot rely on
optimization under constraints; indeed it does not, but there are two reasons why
someone might suppose that it does. First, according to the communicative
principle of relevance, ‘Every ostensive stimulus conveys a presumption of its own
optimal relevance’ (Sperber and Wilson 1986/95, p 158). This means that the
hearer is licensed to search for an optimally relevant interpretation: ‘An ostensive
stimulus is optimally relevant to an audience [if] it is the most relevant one
compatible with the communicator’s abilities and preference.’ (Wilson and
Sperber, 2002, section 3) So the relevance theoretic comprehension procedure
looks for the optimal solution, given a particular stimulus in a particular context.
Thus it appears to be an optimizing procedure, but as I shall argue, it is not a kind
of optimization under constraints.
Secondly, as previously noted, relevance is a matter of effort and effects, so the
generalization ‘stop when your expectations of [optimal] relevance are satisfied’
(Wilson and Sperber, 2002, section 3) may seem to be an injunction to calculate at
each stage the costs and benefits of continuing with the search and to stop when
the projected costs in effort outweigh the prospective benefits in cognitive effects.
This is a misinterpretation, however, for two reasons. First, the hearer is licensed
to ‘stop at the first interpretation that satisfies his expectations of relevance,
because there should never be more then one.’ (Wilson and Sperber, 2002, section
3) This follows from the special nature of ostensive-inferential communication: the
speaker ‘wants her utterance to be as easy as possible to understand so that the first
interpretation to satisfy the hearer’s expectations of relevance is the one she
intended to convey.’ (op cit. , section 3) This means that there is no need to
calculate the costs and benefits of continuing the search: what is at issue is rather
whether the cognitive effects are (more than) enough at some time, t, to justify the
processing effort incurred from the beginning of the search to that time.
The second reason why the relevance theoretic comprehension procedure could
not be a species of optimization under constraints is that from the beginning
Sperber and Wilson have been clear that ‘contextual effects and processing effort
are non-representational dimensions of mental processes’ (1986/95, pp 131). We
may sometimes have intuitions about degrees of effort and effect but efforts and
effects – and therefore relevance – are not generally mentally represented and
therefore cannot be used in computations. Thus there is no possibility that future
effort and effects could in general be summed and weighed up against each other
as optimization under constraints requires. p. 77-78

The argument that the relevance theoretic comprehension procedure is a type of
satisficing procedure comes from comparing Gigerenzer’s definition, ‘satisficing
(sets) an aspiration level and ends the search for alternatives as soon as one is
found that exceeds the aspiration level’ (Gigerenzer and Todd, 1999, section 2.3,
referring to work by Simon, 1956, 1990) with the specification of the relevance
theory comprehension procedure:
(a) Follow a path of least effort…(and)
(b) Stop when your expectations of relevance are satisfied. (Wilson and
Sperber, 2002 section 3)

In the case of ostensive-inferential communication,
‘relevance theory claims that use of an ostensive stimulus may create precise and
predictable expectations of relevance not raised by other stimuli.’ (Wilson and
Sperber, 2002, section 3) This is because ‘an ostensive stimulus is designed to
attract the audience’s attention. Given the universal tendency to maximise
relevance an audience will only pay attention to a stimulus that seems relevant
enough.p. 78-79

History and Intentions in the Experience of Artworks by Alessandro Pignocchi

This paper sketches a model of the
14 experience of artworks based on the mechanisms of
15 intention attribution, and shows how this model makes it
16 possible to address the issue of personal background
17 knowledge empirically. I claim that the role of intention
18 attribution in art experience has been incorrectly accounted
19 in the literature because of an overly narrow definition of
20 ‘‘intention.’’ I suggest that the observer can recover not
21 only the artist’s abstract projects, but any kind of mental
22 states that have played a causal role during the production
23 of the work. In addition, I suggest that this recovery occurs
24 in large part unconsciously and/or implicitly. p. 1

researchers in the 54
humanities doubt the existence of artistic universals, 55
arguing that the way we evaluate an artwork always 56
depends on what we know about its context of production 57
(Danto 1981). For instance, we will not attribute the same 58
value to an impressionist painting if we believe that it was 59
painted in 1872 or last year (Genette 1997). p. 1

106 Although some authors have denied any role for intention
107 attribution in the experience of artworks (Wimsatt and
108 Beardsley 1954), nowadays the majority recognizes that
109 intention attribution must play some role (Danto 1981;
110 Iseminger 1992; Levinson 1979; Walton 1970). However,
111 this role may have been incorrectly described, or, at the
112 least, some of its important components may have been
113 neglected (Pignocchi 2012). This is due, first, to an iden-
114 tification of the artist’s intention with her conscious and
115 abstract aims, as if a work of art could be produced on the
116 basis of a single intention or a small set of them. p. 2

Discussing Painting as an art,
179 (Carroll 2011) claimed that Wollheim position should be
180 called ‘‘mentalist’’ and not ‘‘intentionalist’’ since it con-
181 siders many kinds of mental states, including unconscious
182 one, that are not traditionally considered as intentions.
183 However, I want to try to subsume all of these mental states
184 under the common label ‘‘intention,’’ to insist on the notion
185 of causality. p. 3

The take-home message of this article is that the 874
intention attribution that determines part or all our expe- 875
rience of an artwork and of its properties can be implicit 876
and unconscious. Thus, we frequently do not notice their 877
influence. We have the impression of liking or disliking the 878
work or its properties per se. We say that we ‘‘like’’ this 879
artwork, without noticing that what we actually like is the 880
content of the intentions that we see behind it (we find them 881
sincere, sophisticated, original, coherent, audacious) and 882
their skilful realization in the work. p. 9

Linguistic anthropology: Language as a non-neutral medium by Alessandro Duranti

[To appear in The Cambridge Handbook of Sociolinguistics, Edited by Raj Mesthrie]

In this chapter I focus on
three essential properties of language that are usually assumed by linguistic
anthropologists: (1) language is a code for representing experience, (2) language
is a form of social organization, and (3) language is a system of differentiation. p. 4

The idea that in using a given language speakers are forced into
interpretations of the world that they cannot quite control dates at least as far
back as the writings of Johann Gottfried Herder and the diplomat and linguist
Wilhelm von Humboldt (see Bauman and Briggs 2003: Chapter 5). p. 5

Implicit in this line of work is that the notion of habitus has become
associated with a conceptualization of language as a practice that is quite
different from the ways in which language has been conceived of in the literature
on linguistic relativity as discussed above. In this new perspective, which
characterizes what I have elsewhere called the “third paradigm” in linguistic
anthropology, language is viewed as being composed of more than just lexicon
and grammar. It also includes communicative resources such as prosody, tempo,
volume, gestures, body posture, writing tools and conventions, and visualization
(see for example Goodwin 2000; Finnegan 2002). p. 13

After the publications of two
posthumous works of two philosophers – Ludwig Wittgenstein’s (1953)
unfinished Philosophical Investigations and J.L. Austin’s (1975) lectures How To Do
Things With Words –, an increasing number of scholars began to see language
predominantly as action rather than mostly (or exclusively) as a code to express
ideas or represent events. p. 16-7

Building on these insights and in interaction with a number of innovative
scholars (e.g. Kenneth Burke, Erving Goffman, John Gumperz, William Labov),
starting in the mid-1960s Dell Hymes began to alter the object of study of earlier
generations of linguistic anthropologists by shifting the attention from ‘language’
(a system, e.g. a grammar) to ‘speaking’ (an activity, e.g. telling a story). p. 18

In the 1960s no one could have agreed more with the idea that language is a
form of social organization than a group of sociologists who became known as
“conversation analysts.” This explains the inclusion of articles by Harvey Sacks
and Emanuel Schegloff in Gumperz and Hymes’ (1972) edited volume Directions
in Sociolinguistics: The Ethnography of Communication. Sacks and Schegloff were
arguing within sociology that one should study conversation as a prominent site
of social organization. p. 19

Research on language ideology is closely related to but still distinct from
Pierre Bourdieu’s (1991) concept of symbolic domination. In his view, the social
value of the language varieties that we speak (e.g. the dialect or dialects we are
comfortable with, the register range) is given by the place of such varieties within
a linguistic market that the individual cannot control. Therefore, for Bourdieu, as
users of particular linguistic language varieties we are the victims of a system of
social discrimination that has profound consequences for our chances to succeed
in society. p. 27

 

Mathematical Reasoning and External Symbolic Systems by Catarina Dutilh Novaes

This paper is nice in that it discusses several cultures and draws upon Stanislas Dehaene and similarly experiment-based data.

It is an almost trivial observation that the practice of mathematics typically
involves a lot of ‘scribbling and fiddling’ with symbols, diagrams and special
notations. Taking as a starting point the idea that both the written and the
oral languages used by mathematicians are philosophically relevant aspects
of their practices, the aim of this paper is to discuss in more detail the exact
status of external symbolic systems, systems of writing in particular, for
mathematical reasoning and mathematical practice. Are they merely convenient
devices? Are they essentially heuristic components? Can mathematics
be practiced without recourse to symbolic systems? In what sense, if any,
can different forms of writing be said to be constitutive of doing mathematics? …

Indeed, the investigation takes
into account three different levels: the synchronic level of a person ‘doing
math’ at a given point in time; the diachronic, developmental level of how an
individual learns mathematics; and the diachronic, historical level of the development
of mathematics as a discipline through time. It will be argued that
the use of external symbolic systems is constitutive of mathematical reasoning
and mathematical practice in a fairly strong sense of ‘constitutive’, but
not in the sense that manipulating notations is the only route to mathematical
insight. p. 45

b. Mathematical reasoning is conducted in vernacular languages; notations
are merely convenient short-hands
This position, as described by Macbeth, views mathematical reasoning as
constitutively independent of special systems of notation, but as inherently
tied to vernacular languages. p. 47

c. Mathematical reasoning is not language-dependent
On this view, to ‘do’ mathematics would be a purely private, inner process,
which can then be expressed and communicated a posteriori in some public
medium such as systems of notations or spoken languages.

Thus, positions b. and c. both reject the notion that mathematical (written)
notations are constitutive of mathematical practice. Positions a. and b. have
in common the idea that mathematical reasoning requires some sort of external,
linguistic medium to come about (as opposed to thoroughly internalist
position c.), yet disagreeing on the exact nature of this medium. p. 48

I here argue that, based on empirical data drawn from different
fields, a strong case can be made for the claim that external media are
constitutive of mathematical knowledge and mathematical reasoning in the
stronger sense that, even when a given person is apparently not manipulating
symbols, such as a mental calculator, she in fact typically relies extensively
on internalized versions of external devices (at least in most cases). p. 51-2

It is known for
example that the fastest and least error-prone mental calculations are those
consisting in adding a given number smaller than 10 to a multiple of 10 (10,
20, 30 etc.); this is arguably because the reasoner mentally ‘replaces’ the 0
on the right-side of one of the numerals with the other numeral.9 So it seems
that, while not using ‘paper and pencil’ at that particular moment, the operation
being implemented relies significantly on the mode of presentation of
the Hindu-Arabic numeral system as a place-value system, and thus on an
internalization of external symbols. p. 52

Going back to the three positions presented above, it seems clear that, even
if at specific occasions (i.e. the synchronic level), ‘doing math’ does not require
the act of manipulating external symbols (as the defender of position
c., the ‘documentist’, would have it), from a diachronic, developmental point
of view, external symbols appear to be a necessary condition for the emergence
of mathematical concepts and mathematical reasoning. Moreover, I
have argued that many of the processes which appear to take place exclusively
‘in the head’ are in fact internal simulations of external processes; in
such cases, there is a clear sense in which external representations are constitutive
of mathematical reasoning, even if they are simulated and manipulated
mentally. p. 55

She takes two interesting cases, that of a savant and a blind mathematician, as interesting exceptions to prove the rule

Many mathematicians see numbers as digits, and while they can do
amazing things when it comes to understanding the very root of an
equation, only when you ‘see’ it and do the mathematics together
can you really understand where it comes from.
Padgett’s claim that many (most?) mathematicians ‘see numbers as digits’
is indeed very much in the spirit of the views defended here. But his final
observation is what is most revealing: he refers to a form of ‘seeing’
the root of an equation that is independent of seeing numbers as digits, and
thus a form of mathematical insight which is presumably not inherently tied
to external representations (crucially, the fractals he draws are renditions of
what he ‘sees’ prior to making the drawings themselves). Notice however
Padgett’s suggestion that both this ‘seeing’ ability and ‘doing the mathematics’
(presumably, operating with symbols) are required to understand where
the root of an equation ‘comes from’. p. 59

But rather than disproving the claim that mathematical
practice is fundamentally tied to forms of writing, at least some blind
mathematicians seem in fact to confirm it in that the ways in which they produce
mathematical knowledge are often significantly different from those of
sighted mathematicians. To use Jason Padgett’s terminology, we might say
that, unlike most mathematicians, blind mathematicians arguably do not predominantly
see ‘numbers as digits’, and at times this seems to provide them
with privileged insight with respect to some specific problems. p. 61