3: Hands & Machines. Descartes and Spinoza: Craft and Reason and The Hand of De Beaune [The Kvond Spinoza’s Foci Summary Series]

Summary of kvond’s ideas, by Corry Shores
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The Kvond Spinoza’s Foci Summary Series

[Kvond’s original work with Spinoza’s optics and lens craftsmanship has led me to see Spinoza’s ideas in a whole new way. If you have the chance, check out his blog, especially his work with Spinoza. He’s a world class Spinoza scholar.]

Kvond of Frames /sing

Spinoza’s Foci

Part I: The concept of the Philosopher as Lens Grinder

Descartes and Spinoza: Craft and Reason and The Hand of De Beaune

In La Dioptrique, Descartes designs an automated machine for grinding hyperbolic lenses.

[Image obtained gratefully from this same Frames /sing entry]

He charged Florimond De Beaune to build it. But the craftsman wounded his hand so much in that effort, that he would have to abandon the project altogether. Kvond writes:

Descartes’ craftsmanless, all-turning machine could not be achieved. It is as if its “reason” had chewed up even the best of earth’s craftsman. (kvond)

Descartes assesses the failure to Constantijn Huygens Sr., father of Christiaan Huygens:

“Do you think I am sad? I swear to you that on the contrary, I discern, in the very failure of the hands of the best workers, just how far my reasoning has reached” (Descartes and the Hyperbolic Quest, 70).

Spinoza expresses a different attitude about such matters of safety, in the letter 32 to Oldenberg, when discussing Christiaan Huygens' lens grinding.

Experience has sufficiently taught me, that the free hand is better and more sure than any machine for polishing spherical moulds. (R. H. M. Elwes, Transl.)

Huygens it seems shares this appreciation for working class craftsmanship. He considered Rembrandt’s skills to be a product of his working class family background.

Descartes, however, thought that his feats of reason could lift him into a higher class. His machine would allow him to manufacture lenses without the use of his hands. And he seemed to even enjoy the idea that a technically-adept craftsman cut his hands trying to build the machine, as if proving Descartes’ higher social place. Spinoza, however, did not wish for “a rationality so clear that it would distance itself from the hands that were to manifest it.” Kvond continues, “Perhaps Spinoza keeps in his mind the hand of De Beaune.”

Spinoza. The Letters. from the R. H. M. Elwes translation, available online at:

http://www.sacred-texts.com/phi/spinoza/corr/corr12.htm

Argument from Noise, 3. Beyond Traditional Computation, in Schonbein, "Cognition and the Power of Continuous Dynamical Systems"

by Corry Shores
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[Nick Bostrom & Anders Sandberg argue for digital computation instead of analog for simulating human cognition. They base their contention in part on the "argument from noise." The entries in this series summarize Schonbein's defense of that argument.]

Whit Schonbein

Cognition and the Power

of Continuous Dynamical Systems

3. Beyond Traditional Computation

Jerry Fodor is an example of a classicist who argues that Turing machines suffice to model cognition. Others, for example, Van Gelder, contest that we need a more computationally powerful model for human cognition. For, cognitive behavior might be "much more subtle and complex than the standard concept of representation [and therefore computation] can handle." (qt. 60b)

Horgan explains that the alternative dynamical systems approach "'involves a potentially more powerful kind of mathematics' that can deal with a cognition system that realizes 'a function so complex and subtle that it is not tractably computable.'" (qt60bc)

It is not entirely clear what "more powerful" means in these claims. We could use Schonbein's "computational hierarchy." We list which computers are capable of computing which functions. The more powerful ones are those that can compute more functions than the others. This is probably because they have greater resources to do so.

Those who argue for non-classical models also advocate continuous rather than discrete values for defining cognitive models. Van Gelder, for example, notes that "differential equations utilize continuous values." (60c) And Horgan explains that "the mathematics of dynamical systems is fundamentally continuous mathematics rather than discrete mathematics." (60c)

Turing required that computational states be discrete. But the values in continuous systems make use of "infinitely precise values" that can "differ by an arbitrarily small degree." Hence analog systems differ fundamentally from traditional digital automata. (60d)

Continuous systems, then, are "non-computational" in the sense that they can compute functions that are not Turing-computable. Furthermore, Horgan believes that "suitably modified neural networks are the sorts of things that could realize such 'non-computational' systems." (60d)

He writes,

dynamical systems whose transitions are computable are actually a relative rarity, and it is certainly possible for noncomputable dynamical systems to be subserved by neural networks – at least if the networks are made more analog in nature by letting the nodes take on a continuous range of activation values, and/or letting them update themselves instantaneously rather than by discrete time steps. (qt61a, emphasis mine)

In fact, it has already been shown that analog artificial neural networks (AANNs) are more computationally powerful than Turing machines. They are super-Turing-computable.

these networks are relatively simple: They are first-order, recurrent, and synchronously updated; they use saturated-linear activation functions; and have a finite number of nodes. (61b)

If such a system used just numerical quantities that were rational numbers (and hence are specifiable as ratios between integers), then they would be Turing equivalent. "However, if one allows for continuous weights and activations, AANNs are capable of computing functions not computable by TMs" (61c)

Dynamicists claim that we need computational models more powerful than Turing machines in order to model cognition. "Part of this claim revolves around the use of formalizations that make use of continuous values, which implies that these systems cannot be understood in terms of classical computation." (61c) Because certain neural networks can handle continuous variables, it is "at least logically possible" to produce super-Turing-equivalent systems.

However, a number of arguments have been offered to the conclusion that AANNs (and other continuously valued automata) are nomologically impossible, i.e., not realizable by physical systems in our world. (61d)

Schonbein will now examine three such arguments.

Schonbein, Whit. "Cognition and the Power of Continuous Dynamical Systems." Mind and Machines, Springer, (2005) 15: pp. 57-71.

More information at:

http://www.springerlink.com/content/xtx321861761117r/?p=91ba33f01d0a4099b74dcad02b1a5860π=2

PDF might be available to you at:

http://www.springerlink.com/content/xtx321861761117r/fulltext.pdf

Logos in Martin Moors' Mythos and Logos course

summarization of Moors' ideas, by Corry Shores

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[Metaphysicians discuss and explain reality through linguistically-expressed conceptions. There is a certain logic to this explanatory discourse, namely, a discursive logic. For example, contradictions are not permitted (unless paradox is for some reason to be permitted.) This logic is used to describe reality according to various theoretical systems. Hence]

Logos is the power of redescribing reality in rational discourse.

[Also, metaphysicians are not just concerned with reality. They are also concerned with their means of discussing reality. In other words, metaphysicians are interesting in understanding that very logic they use when discussing reality. But what grounds this logic must be something higher than that logic. It must transcend it. So metaphysicians use their explanatory logic to understand that very same logic. In this way,]

Logos is the search for an understanding of understanding.

[This way, metaphysicians become aware of the way they think. That is to say, they develop a consciousness of the way they think. Thus logos is this sort of higher consciousness. Hence]

Logos is consciousness of consciousness. It seeks what is most logically prior, the 'a priority.'

[An element of the discursive logic that metaphysicians use is criticism, namely, self-criticism, which allows metaphysicians to see shortcomings in their methodological logic so to improve it. Hence,]

Logos is the internal criticism that establishes its own organic self-renewal.

In this way, Kant's Critique of Pure Reason is a rational critique on reason. [We may use our rational faculties to judge our manner of reasoning. And when we judge our rational faculties using our reason, we do not do so from an anti-rational perspective.] However, Dostoyevsky and Nietzsche, for example, give a genuine critique of pure reason, because they examine rationality critically from a non-rational point-of-view. [But when we use our rational faculties to criticize our manners of reasoning, we look at rationality from a rational critical standpoint.]

[Taken from the first lecture of Professor Martin Moors Philosophy of Being 2008 course: From Mythos to Logos - From Logos to Mythos," at the Katholieke Universiteit Leuven. Professor Moors is not just a remarkably gifted instructor, he is as well a renowned metaphysician and Kant scholar. His publication list is available here.

The ideas I here present are not my property, but belong to Prof. Moors. A suggested citation:

Moors, Martin. "From Mythos to Logos - From Logos to Mythos: Class 1." Katholieke Universiteit Leuven, Belgium. 25-Sept-2008.

]

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Plato's Epistemic Rationality and Irrationality (A-Rationality), and Hetero-Rationality, in Martin Moors Mythos and Logos course

summarization of Moors' ideas, by Corry Shores
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The gods on high bear the highest knowledge.

This highest knowledge is intuitive, noetic knowledge. Below it is discursive or dianoetic knowledge. The lowest forms of knowledge are belief and sensible representation.

Corresponding to epistemic rationality is epistemic a-rationality or irrationality. Not anti-rationality. What is anti-logical comes out of the logical. But the a-rational or a-logical is hetero-logical.

There are three levels of heterology (a-logic). That is to say, logic has three others: the hyper-rational, the para-rational, and the hypo-rational.

The heterologies correspond with the levels of rationality:

Myth is hyper-rational, because it is higher than rational discourse.

Science is para-rational. Even though it is a rational discourse on being, it is not metaphysics.

Sensible representation (aesthesis) has not yet been made rational, and hence is hypo-rational.

Knowledge moves upwards from sensibility to divine intuitive knowledge, namely, to myth and religion.

Metaphysicians inquire into metaphysical matters. But how are metaphysicians to understand their own field of inquiry? By comparison with other fields inquiry. So, by coming into contact with other manners of inquiry, metaphysical inquiry develops dialectically. Hence, when metaphysicians compare their field with science, for example, they further define and distinguish -- and thereby further develop -- metaphysical inquiry's methods and theories.

This schema will be useful when discussing the relationship between mythology and metaphysics.

[Taken from the first lecture of Professor Martin Moors Philosophy of Being 2008 course: From Mythos to Logos - From Logos to Mythos," at the Katholieke Universiteit Leuven. Professor Moors is not just a remarkably gifted instructor, he is as well a renowned metaphysician and Kant scholar. His publication list is available here.

The ideas I here present are not my property, but belong to Prof. Moors. A suggested citation:

Moors, Martin. "From Mythos to Logos - From Logos to Mythos: Class 1." Katholieke Universiteit Leuven, Belgium. 25-Sept-2008.

]

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