Categorical Perception as an Analogy

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Categorical Perception as an Analogy

model 1 = correct attributions + noise

One thought would be: start from the true attributions and understand variations as errors.

This idea would mean that there is explanatory asymmetry between correct attributions and errors.

This seems like it might be the right model for studying, say, physical cognition (see Sanborn, Mansinghka, & Griffiths, 2013’s ‘noisy Newton framework’, for example) or numerical cognition.

... but expert disagreement!

But when we look at philosophical sources, we find that there is little prospect of obtaining the truth ...

insert-transcript#92931867-c0ff-45d3-8e9a-2380c8310f7a-here

Which things manifest agency?

‘The paramecium’s swimming through the beating of its cilia, in a coordinated way, and perhaps its initial reversal of direction, count as agency.’

(Burge, 2009, p. 259)

∞todo: needs updating (have additional sources, more quotes; also needs small fixes for nuance) See `projects/talk-mindreading-unkowns` repo.

INTENTION	yes	no
Is it a mental state?	Davidson (1978)	Thompson (2008)
Is it a belief?	Velleman (1989)	Bratman (1987)
Entails belief?	Harman (1976)	Levy (2018)
Linked to planning?	(Bratman, 1985)
Incompatible with habitual?		Kalis & Ometto (2021)
Entails non-observational knowledge	Anscombe (1957)
Comes in two kinds?	Searle (1983)	Brozzo (2021)

The disagreements concern basic questions about intention.

∞todo: needs updating (have additional sources, more quotes; also needs small fixes for nuance, e.g. Hyman’s position isn’t strictly incompatible with knowledge being a mental state (especially if you add a funny Hyman-inspired notion of what it is to be a mental state).)

distinctive = has value distinct from true belief

KNOWLEDGE	yes	no
Is it a mental state?	Williamson (2000)	Hyman (1999)
Knowing entails believing?	Rose & Schaffer (2013)	Radford (1966)
Is it a form of belief?	Sosa (2007)	Williamson (2000)
Valuable for action?	Plato’s Meno	Kaplan (1985)
Is humanly attainable?	[lots]	Unger (1975)
Depends on context?	Lewis (1996)	[lots]

How about just picking a theory? Or perhaps even taking several and considering, for each, the hypothesis that this is how the folk understand knowledge.

Actually this is sometimes the right thing to do. But there are some obstacles.

obstacles

- many incompatible theories, each only slightly different from nearby alterantives

- differences hard to operationalize

- unclear when conflicting theories vs compatible theories of different things

this is why I do not think we can explain agreement and variation by appeal to correct attributions.

no?

model 1 = correct attributions + noise

I haven't offered a decisive objection, of course. But for me it’s time to explore other models.

model 2 ≈ categorical perception

Catgeorical perception of colour is a case where there is confident local agreement and variation between groups.

Perhaps we can use this as a rough, partial model for mindreading?

∞todo: categorical colours as a model

individual differences Witzel & Gegenfurtner (2018)

Berinmo vs Himba

there are constraints, but they are abstract (yes: categories probably mostly contiguous in similarity spaces; not: determined by unique hues (although unique hues play some role))

colour case has two uses:

1. we approach it without knowing what the true categories are, or even whether there are any (and I think we need the same for mindreading)

2. [use later, after MAC—supress for now] shows that we need standards (analogy: categories); does not show that any kind of norm is involved

see fT8Qa5Mn2Vx7Lp4Rs9KcHw.md

Look, you can get monolingual German speakers to categorize colours and they will produce quite uniform boundaries.

Witzel & Gegenfurtner, 2013 figure 6

These are mononlingual German speakers (∞check)

Individuals are fairly consistent over time. (‘Variation across was higher than within observers.’)

There are some individual differences, even in number of catgeories, but you can see that they are broadly aligned.

So I take this to be a model for local agreement.

By contrast if we look across cultures ...

caption: ‘Figure 6. Color naming. The colors in the graphic refer to the color names used for a particular test color in a particular session by a particular observer. The x-axis refers to the variation in hue as in Figure 3. Each column refers to a particular stimulus color at isoluminance. The horizontal black lines separate layers that correspond to the data for each participant. Within each layer, the rows represent repeated measurements of color naming in different experimental sessions. Vertical black lines correspond to the category boundaries calculated through the modes of the single measurements. Supplementary Figure S6 provides the graphic for dark and light. Variation across was higher than within observers.’

Here is the counterpart of variation between groups

Indeed, the extensions of colour terms vary quite radically between languages.

(Ongoing research concerns whether there is any kind of universal prinicple behind the pattern.)

English

Roberson & Hanley (2010, p. Figure 1c)

Berinmo

Roberson & Hanley (2010, p. Figure 1b)

So here’s the parallel I see: in both mindreading attributions and categorical colour perception, we have confident local agreement and variation between groups.

Of course there are points of disanalogy, and I'll come to one of those later. But for now I want to consider the positives.

confident local agreement

variation between groups

In colour (as in mindreading), there is confident local agreement and variation between groups.

How do we explain both local agreement and variation in the colour case?

Here we already have quite a lot of evidence

local agreement we get through training!

nice demonstration: training novel categorical colour effects (see `m8Qv2Lt5Rx7Kn3Hs9Pc4Aw.md`) USE THIS AS A MODEL FOR MAC idea

In the mindreading case, Earlier I observed that mindreading needs background assumptions. We were then asking where these background assumptions come from.

How to explain both agreement and variation?

- need to ask where background assumptions come from

background assumptions ≈ category boundaries

Zhou et al. (2010, p. Figure 1)

Adults can learn novel hue divisions inside an existing basic colour category, and this learning can alter later discrimination and visual-search performance (Ozgen & Davies, 2002; Martinovic, 2024; Zhou et al., 2010).

Relevance for this talk: suggests that categorical colours are acquired through a process of training.

NB: Zhou et al. (2010) isn’t strictly about boundary-learning as I think they just have Pp label specific shades (∞check); but Ozgen & Davies (2002) and Martinovic (2024) are more direct. (I mention Zhou et al. (2010) just because it’s a nice figure and a very neat paradigm)

Zhou et al. (2010, p. Figure 1): ‘Experimental materials. (A) Printed-rendered versions of the four colors used with their ordinary names. (B) Printed-rendered versions of the four colors used with their new names to be acquired by the subjects. (C) Sample display for the visual search task. The target occupied any of the four positions (position 1, 2, 3, or 4). This example shows a between-category LVF pair.’

source in notes: `iouasod1vb6.md`

4-6 months : ~5 categories

Skelton, Catchpole, Abbott, Bosten, & Franklin (2017)

~1-3 years : ‘slow mapping’ of colour words

Wagner, Dobkins, & Barner (2013)

Children know that a colour word refers to a category, but not which one. (Before this they tend not to treat colour words as colour relevant at all.)

adult categories acquired over years,
influenced by language and culture,
differ from infant categories

Maule, Skelton, & Franklin (2023)

I think this is maybe a good model for mindreading standars.

There is minimal theory of mind early in infancy.

That probably influences the development of mindreading standards in some unknown way, without fixing them.

The ‘slow mapping’ stage corresponds to the developmental trajectory noted by Wellman et al in the scaling theory of mind research. But in mindreading it is even more protracted.

Language and culture surely also plays a role. Today there is likely less diversity in the past just because we are all more culturally connected.

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Categorical Perception as an Analogy

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