Deep truths and trivialities

Collected trivialities on algebra derivations

1. Derivations in general 1 1.1. Definitions and conventions . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. The module of derivations . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4. The k-algebra RA (M) . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5. Compositions and tensor products . ....

The Problem of Deep Competitors and the Pursuit of Epistemically Utopian Truths

According to standard scientific realism, science seeks truth and we can justifiably believe that our successful theories achieve, or at least approximate, that goal. In this paper, I discuss the implications of the following competitor thesis: Any theory we may favor has competitors such that we cannot justifiably deny that they are approximately true. After defending that thesis, I articulate...

Natural Principles and Fundamental Truths

REVIEW Microarray truths and consequences

For many, analysis of a microarray experiment starts with a spreadsheet of expression levels. While great attention is duly paid to RNA extraction, preparation and hybridization, relatively little care is devoted to extraction of expression levels from the fluorescent image. By delegating this step to a click of the mouse the exact extraction process is masked and researchers may be unwittingly...

Inaccessible truths and infinite coincidences

It is one of the salient features of an intuitionistic philosophy of mathematics that it denies the possibility that there may be infinite coincidences in mathematics: if a sentence is true, it can only be because there is a finitely expressible reason for it. The same view was expressed from a different standpoint by Hilbert in 1924 when he asserted that in mathematics there is ignorabimus. It...