Comments I’ve written, ever meaning to extend …
Peter Cameron’s Blog
Re: Hadamard Revisited
Comment 1
In a line of thinking that goes back through Peirce to Aristotle, intellectual creation and discovery are treated under the heading of apagoge (abductive or retroductive reasoning). Here is a memorable passage from Peirce’s essay titled “The Neglected Argument for the Reality of God”.
The whole series of mental performances between the notice of the wonderful phenomenon and the acceptance of the hypothesis, during which the usually docile understanding seems to hold the bit between its teeth and to have us at its mercy,—the search for pertinent circumstances and the laying hold of them, sometimes without our cognizance, the scrutiny of them, the dark laboring, the bursting out of the startling conjecture, the remarking of its smooth fitting to the anomaly, as it is turned back and forth like a key in a lock, and the final estimation of its Plausibility,—I reckon as composing the First Stage of Inquiry. Its characteristic formula of reasoning I term Retroduction, i.e. reasoning from consequent to antecedent. In one respect the designation seems inappropriate; for in most instances where conjecture mounts the high peaks of Plausibility,—and is really most worthy of confidence,—the inquirer is unable definitely to formulate just what the explained wonder is; or can only do so in the light of the hypothesis. In short, it is a form of Argument rather than of Argumentation.
Retroduction does not afford security. The hypothesis must be tested. This testing, to be logically valid, must honestly start, not as Retroduction starts, with scrutiny of the phenomena, but with examination of the hypothesis, and a muster of all sorts of conditional experiential consequences which would follow from its truth. This constitutes the Second Stage of Inquiry. For its characteristic form of reasoning our language has, for two centuries, been happily provided with the name Deduction.
Re: Information, Postmodernism, and Time Signatures
Comment 1
Bit strings do not information make,
Nor ironic bards John Cage.
All you need is AURORAS —
Average Uncertainty Reduction
On Receiving A Sign.
Comment 2
C.S. Peirce proposed a logical framework for information theory as far back as 1865, suggesting that the “laws of information” were key to unlocking the puzzle of how scientific inquiry works. He later formulated a logarithmic measure for information content and pursued his ideas about information in parallel with his attempts to articulate modal logics in the diagrammatic syntax of logical graphs.
You may find it worth your while to look into some of this work. The following web page contains a very rough set of notes that will serve to provide further links:
Comment 3
Like many before him, Peirce is seeking to understand the workings of scientific inquiry — all in the light of its evolution from the simplest forms of adaptation, learning, and reasoning, through the routine procedures of everyday explanation and problem-solving, to the most developed forms we see in living communities of inquiry. He inclines toward the hypothesis that science does work somehow or other and seeks to articulate in logical terms how that might be. This is a question about the “logic of science”, and the provisional answers he develops, if springing from Aristotle’s analytics of abductive, deductive, and inductive reasoning, introduce a wealth of novel turns to the quest.
Re: Culture, Tribes, or Just an Illusion
Paradisaical Logic
Negative operations (NOs), if not more important than positive operations (POs), are at least more powerful or generative, because the right NOs can generate all POs, but the reverse is not so.
Which brings us to Peirce’s amphecks, NAND and NNOR, either of which is a sole sufficient operator for all boolean operations.
In one of his developments of a graphical syntax for logic, that described in passing an application of the Neither-Nor operator, Peirce referred to the stage of reasoning before the encounter with falsehood as “paradisaical logic, because it represents the state of Man’s cognition before the Fall.”
Here’s a bit of what he wrote there —
Inquiry Into Inquiry 
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