As a second cousin to Gödel’s theorem, I propose that:

All attempted truth statements include at least one term that is insufficiently defined.

Feeding the preceding statement to itself, a candidate term would be insufficiently: another entire statement (or set of statements) would be required to propose criteria for ‘sufficiency’, and that statement (or set) would also be a candidate for application of the original Principle.

[original insight on 16-Feb-2004; typed up the following day]

I propose to assess the integrity of entities by a recursive test:

• An entity is well-defined when construction of its immediate ‘meta-entity’ is awkward to nonsensical (example: practise makes meta-practise, but the latter is scarcely meaningful).

• An entity is weakly defined—hence open to decomposition into a collection of entities—when construction of multiple meta-entities is easy and the results are meaningful (example: from theory to meta-theory to meta-meta-theory continues to give meaningful results, though one more recursion seems to break the chain).

[original insight ca. 15-Jan-2002]

The usual structure of scientific inquiry involves proposing a process to explain some puzzling object or event (hypothesis), followed by carefully replicated and observed models (experiments) based on the hypothesized explanation; these either do or don’t end with the results predicted by the explanation that they supposedly model. Most such experiments fail, entirely or in part, to lead to the expected outcomes; the process thus becomes iterative rather than terminal. A corollary is that ‘failure’ is generally more informative than immediate and total success. A second corollary is that the process is a blend of induction and deduction, and that neither of these has priority, nor does either give useful outcomes when applied alone.

This sort of ‘normal science’ is, incidentally, at risk of predicting outcomes that are inherently impossible to test by experiment for any of several compelling reasons, as listed by Alvin Weinberg in “Science and trans-science”.

In addition, ‘normal science’ obscures the extent to which its underlying process is a nearly universal feature of human mental activity, and a possible pivot for codification of large parts of philosophy. This position seems to me to be foreshadowed in Hooker’s work, but not taken by him as far (or argued as clearly) as it might be.

The term I favour over hypothesis is assertion: nearly all human statements or actions may be viewed as hypotheses of a sort, with consequences contingent on the congruence (or lack of same) between each statement or action and the context into which each is launched. But where a ‘normal science’ hypothesis is usually assumed to be a self-contained entity, however long the chain of iterations it may start or be embedded in, my intended meaning for assertion is that it be understood to include any alteration in context provoked by its own launching: thus it necessarily labels a constellation of entities. Moreover, assertion is open to evaluation in terms of complete but also partial success/congruence, as well as partial or complete negation/incongruence. At the extreme, an exceedingly well confirmed (or totally negated) assertion becomes a ‘self-fulfilling (or self-negating) prophecy’.

[initial ms. Version of 11-Sept-2004]

From time spent trying to sort out why the history of academic geography is so full of embarrassing slips into philosophic pitfalls, I conclude that the core errors mostly come from sloppy ontology. I would say that branch of philosophy accounts for a large part of all confusion in reasoning, and so deserves a lot more attention than it ever has had in pretty well all academic disciplines, from humanities through social sciences and not excluding ‘hard’ sciences.

Ontology I take to be the processes aimed at picking apart the wholeness of the universe: i.e., the condition in which everything is to some degree connected to everything else. Its goal is to establish as entities those collections of phenomena which are least entangled with adjacent collections (or distant ones, though I can’t think of any cases), usually marked by a label in plain language—a name—or a symbol to be used in mathematical formulae. That goal is compromised by constraints on human thought in a brain that did not evolved to work comfortably or rapidly with ill-defined entities, and so is all too easily applied to absurd, contradictory, and invalid entities. Oh, for a mind that checked for, and spat out, wrong-headed entities before allowing thought to begin!

[original typed version of 2-JAN-2008]

In a small (100<n<10,000) organization with voluntary membership there is a built-in, systemic ‘path of least resistance’ that is deadly to the medium-term (5-15 years) survival of such organizations. It follows from the way leadership goes to those individuals who want it, have the energy to exercise it, and have goals they believe in. This hazard may have parallels in businesses and bureaucracies, but my experience is insufficient to argue the case.

The hazard is greatest when several individuals who share a goal (or a set of goals) occupy most or all leadership offices, and give their ‘pet aim’ priority over the success, survival and growth of the organization. Examples of such ‘ideologically driven takeovers’ abound: committed Anti-Semites, Communists, Fascists, Anti-abortionists, Teetotalers, etc., have driven any number of well-intentioned voluntary organizations into dissolution. A striking Canadian example is the checkered leadership history of the Alliance, Progressive Conservative, and eventual ‘merged’ Conservative Party of Canada.

Organizations with voluntary membership depend on the attractive force of shared belief that an organization of like-minded people offers: support, satisfaction and success in outcomes that solitary individuals cannot hope to match. A prime hazard to such a sharing of belief is a divergence between the defining goals of the organization as viewed by membership and leadership.

People who are willing to take on the extra effort that leadership roles demand are also—quite often, though not invariably—people with ‘pet notions’, ‘monomanias’, or other idées fixes. Ordinary members, too, can have such divergent priorities; but in that case they usually will find a reason to abandon membership in the organization in question.

When a ‘leadership clique’ of the sort described above emerges, and when it fails to make persuasion of the general membership to its point of view a priority (and especially when it refuses to accept “no” as an answer!), the organization is doomed. As soon as the membership comes to understand their leaders’ indulgence in divergent priorities, they have only two paths open: turf the rascals, or abandon a membership that no longer offers sufficient attractions. The former path may salvage the situation or bring down the structure, depending on details in a particular case. The latter path may dissolve the organization or lead it to transmute into an organization with altered aims, depending on the proportion of the membership that is persuaded to the leadership’s set of goals and the intensity of their loyalty to the organization and esteem for individual leaders and other continuing members.

[first typed version: 29-Mar-2005]