The motto of the information philosopher is "beyond logic and language." Specifically, we must show that logical positivism and logical empiricism, whose attack on metaphysics began as early as Auguste Compte in the early nineteenth century, have done nothing to solve any of the deep problems about the fundamental nature of reality.

Positivism is the claim that the only valid source of knowledge is sensory experience, reinforced by logic and mathematics. Together these provide the empirical evidence for science. Some see this as the "naturalizing" of epistemology.

Ernst Mach's positivism claimed that science consists entirely of "economic summaries" of the facts (the results of experiments). He rejected theories about unobservable things like Ludwig Boltzmann's atoms, just a few years before Albert Einstein used Boltzmann's work to prove that atoms exist.

The idea that all knowledge can be described by true statements began with Leibniz's vision of a universal ambiguity-free language based on a new symbol set, a characterica universalis, and a machine-like calculus ratiocinator that would automatically prove all necessary truths, true in "all possible worlds."

Gottlob Frege called Leibniz's idea "a system of notation directly appropriate to objects." In the three hundred years since Leibniz had this vision, logical philosophers and linguistic analysts have sought those truths in the form of "truth-functional" propositions and statements formulated in words, but they have failed to find any necessarily "true" connection between words and objects.

Frege had an enormous influence on Bertrand Russell, who shared Frege's dream of reducing mathematics, or at least arithmetic, to logic. The great Principia Mathematica of Russell and Alfred North Whitehead was the epitome of that attempt. It failed with the discovery of Russell's Paradox and later Gödel's incompleteness proof.

Russell hoped to work with the young Ludwig Wittgenstein to develop the "logical atoms," the simplest propositions, like "red, here, now," upon which more complex statements could be built. He saw the major problems of philosophy as problems of language and logic, that complete understanding of the natural world could be obtained through a complete set of logical propositions.

Wittgenstein's Tractatus Logico-Philosophicus was the height of logical positivism - the idea that all knowledge, including all science, can be represented in logically true statements or propositions - and the first hint of its failure, with its dark comments about how little can be said.

4.11 The totality of true propositions is the total natural science (or the totality of the natural sciences).

(Tractatus Logico-Philosophicus)

Logical positivists and the logical empiricists of the Vienna Circle not only asserted that all knowledge is scientific knowledge derived from experience, i.e., from verifiable observations, they also added the logical analysis of language as the principal tool for solving philosophical problems. They divided statements into those that are reducible to simpler statements about experience and those with no empirical basis. These latter they called "metaphysics" and "meaningless." While language is too slippery and ambiguous to serve as a reliable tool for philosophical analysis, quantitative information, which underlies all language use, is such a tool.

Logical positivists and empiricists mistakenly claim that physical theories can be logically deduced (or derived) from the results of experiments. A second flaw in all empiricist thinking since Locke et al. is the mistaken idea that all knowledge is derived from experience, written on the blank slate of our minds, etc. In science, this is the flawed idea that all knowledge is ultimately experimental. To paraphrase Kant and Charles Sanders Peirce, theories without experiments may be empty, but experiments without theories are blind.

By contrast, the modern hypothetical-deductive method of science maintains that theories are not the logical (or inductive) consequences of experiments. As Einstein put it, after shaking off his early enthusiasm for Mach's positivistic ideas, theories are "free inventions of the human mind." Theories begin with hypotheses, mere guesses, "fictions" whose value is shown only when they can be confirmed by the results of experiments. Again and again, theories have predicted behaviors in as yet untested physical conditions that have surprised scientists, often suggesting new experiments that have extended the confirmation of theories, which again surprise us. As pure information, scientific knowledge is far beyond the results of experiments alone.