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Sun argues that mechanisms and representations (and thus computational models) are an important and necessary part of scientific theories and that that is true especially in cognitive science.

Sun argues that computational cognitive models describe mechanisms and representations in cognitive science well.

Sun argues that computational cognitive models provide productive rather than just descriptive accounts of cognitive phenomenology and therefore have more explanatory value.

I would argue that algorithms are more accessible than $\mu$-recursive functions as a way to explain certain things.

Some things are just easier thought of in terms of manipulations than of equations. But this does not say anything about the expressiveness of either tool.

Also, algorithms are already 'runnable' and need to translation into computer programs to be studied by computational methods.

Sun argues that a computational model for a verbal-conceptual theory in cognitive science is a theory in itself because it is more specific.

Strictly speaking, every parameterization of an algorithm realizing a computational model distinct from every other parameterization, following Sun's argument.

Sun argues that the failure of one computational model which is a more specific version of a verbal-conceptual theory does not invalidate the theory, especially if a different computational model specifying that theory produces phenomenology consistent with empirical data.

The way to describe human cognition is by describing how its state changes from one moment to another, given input.

The idea of embodied cognition is not just that cognitive processes are influenced by bodily states.

The idea of embodied cognition is not just that cognitive processes are influenced by bodily states.

Wilson and Golonka argue that early research in cognitive science operated under the assumption that our sensory organs aren't very good and the brain needs to make up for that.

Newer results show, according to the authors, that our perceptual world does give us many resources (in brain, body, and environment) to respond to our environment without the need for creating detailed mental representation and operating on them.

The replacement hypothesis of embodiment (not the one in anthropology) states that a description of the dynamics of body, brain, and environment can replace a description of human cognition in terms of representations and computational processes.

Clark called evidence for the ideas that non-classical tools are necessary to understand cognition are necessary and that representations and computation are bad categories for thinking about cognition weak (in 1999).

He conjectured that there is a middle ground between embodied and disembodied cognition.

Jones and Love propose three ways of Bayesian Enlightenment'.

Bayesian theory can be used to describe hypotheses and prior beliefs. These two can then be tested against actual behavior.

In contrast with Bayesian Fundamentalism', this approach views prior and hypotheses as the scientific theory to be tested as opposed to the only (if handcrafted) way to describe the situation, which is used to see whether once again optimality can be demonstrated.

Statistical decision theory and Bayesian estimation are used in the cognitive sciences to describe performance in natural perception.