This is actually a copy of a post from early on in my blog's life - back in April. However it was from before each post had its own page. Since I've been linking to it and referring to it a lot, I'd like to have it have a unique page. The discussion is from Smyth's book
Reading Peirce Reading. It's a fantastic book on how Peirce reads figures like Mill, Kant, and others. But its most interesting feature is an extended discussion of Peirce's view of "knowledge" in terms of neoPlatonism. Now Peirce as a neoPlatonist is a somewhat odd link to make. However he was very well read in ancient and medieval philosophers. (Somewhat of a rarity in that) Further he was very influenced by the medieval realists who in turn had a lot of neoPlatonic tendencies. An other good but quite different approach to Peirce as a neoPlatonist is Kelly Parker's paper of the same name. Parker largely considers the issue from the point of view of Peirce's notion of evolution. I should add that Parker has probably the best introduction to Peirce in his book The Continuity of Peirce's Thought. That book also focuses a lot on the role of the infinite in Peirce.
At first glance Peirce does not seem like your stereotypical neoPlatonist. He is completely focused in on logic, tends to be critical of mysticism and fuzzy thinking, typically doesn't have kind words for the transcendentalists like Emerson, and is primarily a scientist. Yet a lot of this is simply due to misunderstandings of neoPlatonism. I don't want to get drawn into a discussion of neoPlatonism proper, misreadings of Plotinus, nor my own general change of view from being very anti-neoPlatonic to seeing a lot of value in it. (Indeed I've come to see that a lot of what I see in Levinas, Heidegger, and Derrida can be seen among the neoPlatonists) Instead I want to quote from Smyth's book on Peirce's ontology of knowledge which is actually a neoPlatonic ontology of knowledge. These are excerpted from various places, primarily starting around page 58. To begin though, allow me a quote from Plotinus to set the stage.
If we have failed to understand, it is that we have thought of knowledge as a mass of theorems and an accumulation of propositions, though that is false even for our sciences of the sense realm. (Enneads V.8.4)
Note, I'm quoting the basic sections from Smyth -- I've left some out so the numbering will not be comprehensive
Conjecture 1 The class of items that constitute scientific knowledge at any given time is neither finite nor even denumberably infinite, and might exceed every number, finite and transfinite.
Smyth brings up relative to this an interesting paper from Langendoen and Postal in The Vastness of Natural Language wherein they "prove" that the number of sentences in natural languages is larger than the set of real numbers. (i.e. larger than aleph0, in terms of Cantor's notation) In philosophy of language the position is termed "extreme platonism." (I should note that it appears the proof is for certain formal languages and ignores the fact that not all sentences in a natural language are meaningful) The point is though that the idea that knowledge is finite is wrong, and that knowledge is actually even larger than the kinds of infinities we generally are able to think about. I should add, given recent discussions on LDS-Phil, that Platonism proper is typically taken to only assert a finite number of statements - although potentially a very large finite set. Also note that this is a real infinite and not a potential infinite ala Aristotle. A potential infinity is merely the potential to always continue. At best this is akin to counting the set of integers. Further at any point the set one has counted is always finite.
Conjecture 2 The subject to whom an item of scientific knowledge belongs is not always distinctly conscious of itself as subject, and it can think or speak unconsciously (that is, without having any distinct consciousness of the thoughts or speech that communicates the item of knowledge)
Definition 2 Something is an occult or theoretical object just in case it is (i) hidden from immediate inspection-or not directly observable, but (ii) its existence and properties can be made known to us through processes of reasoning that are experimental, provisional, and public.
I should hasten to add here that while the term occult has come to have an exteremly negative connotation, a lot of this is due to shoddy thinking among Renaissance neoPlatonists. If we think of it not as something "magical" but simply as a theoretical entity, like gravity, then it hopefully loses a lot of its mystique. The term occult simply means not detectable. So when a doctor speaks of occult blood in a specimen it just means blood you can't see without a microscope. Smyth uses the term due to its use among neoPlatonists, but one really must be careful in not reading too much into the term.
Conjecture 3 The 'I' as the owner of knowledge is an occult or theoretical object, which is known to us by reasoning from signs.
This is a very important point. I believe that a lot of what Paul Ricouer has written about the past decades is simply to establish this point. We assume in various guises, that we have priviledged unfettered acess to the "I" who thinks. I think therefore I am. However this "I" is a theoretical entity and not an immediate one.
Conjecture 4 The identity and continuity of a human life can be explained on the model of the identity and continuity of a science or a rational system of knowledge, but, in order for this to give us a coherent account, the logical operations involved in science must themselves have been conceived on the model of what is living, rather than of mere mechanisms. Mere mechanisms produce wholes by operations that only assemble or aggregate a pre-existing stock of parts by a fixed and unchanging set of rules; what is living cannot be defined by an enumeration of parts.
This is probably one of the key aspects of neoPlatonic thought, and gets back to that quote I started the discussion off. The point is that while we've often thought of life as simply an aggregate of parts, conceived of in a mechanistic way, that can't be true. In neoPlatonism this is often conceived of as considering humans as words. A word never has an exhaustive meaning. It always is open to a kind of linguistic play and connotative behavior. Further it comes to take a meaning by its place in a sentence and surrounding context. As one shifts the context the meaning of the word shifts and changes. Peirce has an ironic take on this notion, "you are only a word and not even a complete sentence." This notion of conceiving existence in terms of linguistic existence rather than substance is very important for many philosophers and probably explains a lot of what Heidegger, Derrida, and others do as well. Plotinus put it like this, "all lives are thoughts . . . every life is some form of thought." (Enneads, III.8.8). This is not to deny our identity as selves, merely clarify it as being more than simply a substance changing through time. In neoPlatonism anything which displays this sense of life is called soul.
Definition 3 Our theory of the mental should treat a human mind as a theoretical object introduced to explain signs or public and physical evidences of logical reasonings associated with human beings. A theory of logical forms as "living forms" explains these changes in the signs of thought by a teleology (rational purpose) governing possible changes in the laws of the changes in signs. But efficient causes or causes that commence or alter motions are always only physical causes and human minds are not efficient or moving causes.
This is an extension of the idea of man as a sign or a word as opposed to "stuff" in simple causal interactions.
Conjecture 5 Since the data for the reasonings in science must be public facts, and since, the logical standards or rules of the reasoning are communal, the results of scientific inquiry should also be regarded as belonging to a collective self or community, a kind of transcendental cosa nostra, rather than an individual ego or private mind. It is a higher standpoint, ethically and logically, than that of the ego.
This is very similar to what Searle calls corporate meaning. It is the fact that language must in some sense and to some degree be shared for the very possibility of language to take place. This transcendental subject is a kind of community which can know and can increase in knowledge. Of course in neoPlatonism there is a sense of a world-mind and a world-soul which is basically the unity of all soul and all mind. While once again misunderstandings tend to treat this as something magical, mystical, or in other negative senses, if we conceive of it simply as communal knowledge due to the inherent nature of language it loses a lot of those perjorative connotations. We speak a word in a kind of imitation of this corporate meaning that the word carries. This is very similar, if not identical to how within neoPlatonism a spoken word is in imitation of soul. (Soul, since words have a "living" nature to them due to the play within natural languages)
Conjecture 6 For a logician of science in the Neoplatonic tradition
science conveys an entirely objective and impersonal point of view, for
which:
(i) the relations that are established in valid reasonings are assumed to he
relations between public and objective facts, and within which
(ii) the hypothesis that there are private and personal reasoners will be
constructed so as to explain certain particular relationships between public,
objective facts that suggest the existence of bad reasonings, which, in turn,
means that
(iii) our knowledge of our own minds as distinct from the minds of others
presupposes a distinction between good and bad reasonings that must itself
be a distinction that can be drawn with reference only to public signs of the
reasonings and without reference to individual minds or their cognitive acts.
Conjecture 7 Neoplatonism in logic commits our logician as young Romantic to a fallibilist principle according to which 'to be human is to err'. The main function of the hypothesis that we each have our own mind is to account for objective evidence of bad reasonings that takes the form of demonstrably foolish public behavior.
All the previous conjectures really commit us to a notion of fallibilism that is quite extensive. It occurs both because man is a "word" and thus open to multiple interpretations and because of the very nature of infinite knowledge that can never be had by finite beings.
Conjecture 8 In the order of epistemological causation, the objects come first in this sense: any initiation of a movement or change in the concepts that result in knowledge has to be caused by the dynamic objects of the knowledge. So Neoplatonism in our logic of science means accepting a fundamental tenet of Aristotelian empiricism.
The exact meaning of this is a bit more complex, but might be termed "the argument of surprise." Nature acts upon us and our knowledge arises from this act from "without" that is never under our control. In a way, I think that neoPlatonism actually pushes this notion far farther than many traditional modern philosophies. As Peirce said, "the mind can only transform knowledge, but never originate it, unless it be fed with facts of observation." (5.392) Put simply, this is just the acceptance of traditional notions of Naturalism.
Definition 4 In Neoplatonic logic, something counts as inquiry just in case it is (i) a change of thoughts, caused by objects and terminated by a stability or fixity of thoughts, where (ii) the movements of thought are mediated by changes in public signs, and (iii) each alteration in the signs of thought can be reviewed, criticized and controlled by the standards of what is, or purports to be, an objective and impersonal logic.
Conjecture 9 The sign-theory of universals. Every act of
scientific understanding of objects consists of a sequence of reasonings in
which
(i) the reasonings are signs whose objects themselves are signs
that are caused by signs in a chain of signs that extends back to the ultimate
object of the understanding, where
(ii) these signs actually constitute
the properties and relationships of the object understood, in the sense that
(iii) what the object of knowledge really is, that is to say, any real
property or any real relationship of the object that initiated the inquiry, is
some predicate or other general sign of the object of inquiry that comes
itself to be designated as a possible object of inquiry. These signs
constituting the ultimate objects of knowledge are usually called
"experimental phenomena" or "reproducible effects."
Now all this is fairly long. But hopefully it clarifies for some, especially for those with some background in philosophy, where I am coming at these problems.
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