Jacques Dubucs

FEASIBILITY IN LOGIC

One of the most disputed issues in contemporary philosophy is the following: should we admit a vericonditional theory of meaning, which makes room for truth-conditions that possibly transcend our ability to know whether they are fulfilled or not, or rather, as the anti-realist suggests, should we replace these conditions by assertability-conditions whose fulfillment, when obtaining, cannot fail to be recognized? I will not declare myself in this debate, which is notoriously difficult to adjudicate and which tends to look like a dialogue of the deaf on the own confession of some of its protagonists (Wright 1986, 252). For a long time – and one is still in the habit of summing up the matter this way – the controversy has been taken as essentially dealing with the general possibility, for truth, to transcend the recognizability of truth: what the realist would admit, and what the anti-realist, for her part, would deny, is the possibility for a sentence to be true and yet generally not to be likely to be recognized as such. By now however, that demarcation is widely considered inadequate. As Dummett himself eventually recognized in his 1972 postscript to ‘Truth’ (1978, 23– 24), a realist could very well accept the principle of non-transcendence for truth by granting that any truth ought to be recognizable as such, if not by us, at least by some hypothetical being whose intellectual capacities and observing powers would exceed at will those with which we are endowed. As far as she professes a doctrine that significantly differs from realism, the anti-realist is therefore committed to a general definition of the conditions under which, contrary to creatures that could be more or less emancipated from our cognitive or physical limitations, we are ourselves, we human beings are able to recognize the truth of a sentence, that is to recognize the conditions under which a sentence is assertable by us in the first place. In the sequel I shall confine myself to that only question. In other words, I shall not examine whether it might be legitimate or necessary to wholly

Radical Anti-Realism and Substructural Logics

We first provide the outline of an argument in favour of a radical form of anti-realism premised on the need to comply with two principles, implicitness and immanence, when trying to frame assertability-conditions. It follows from the first principle that one ought to avoid explicit bounding of the length of computations, as is the case for some strict finitists, and look for structural weakening instead. In order to comply with the principle of immanence, one ought to take into account the difference between being able to recognize a proof when presented with one and being able to produce one and thus avoid the idealization of our cognitive capacities that arise within Hilbert-style calculi. We then explore the possibility of weakening structural rules in order to comply with radical anti-realist strictures.

Logique, effectivité et faisabilité

This paper can be read as an attempt at providing philosophical foundations to linear logic. The only plausible form of philosophical antirealism deals with practical feasibility rather than with effectivity in principle. The very notion of recognizability is ambiguous, audit has to be considered from a stricter perspective than currently done. The intuitionistic assertability conditions are to be reinforced. This change requires a move towards a frame in which the circumstances of the application of a logical rule can be specified. Gentzens sequential calculi provide such a frame, when some structural rules have been removed or limited.

Truth and experience of truth

Fifty years ago (Bourbaki 1960, p.46) wrote of intuitionism as ‘a school that will probably be remembered only as a historical blip’. Of course, this very prophecy looks today like an historical oddity because, as a matter of fact, intuitionism has survived. Nevertheless, the sense in which it has survived needs clarification. The most striking feature of the present situation of intuitionism is that some sort of peaceful coexistence with classicism has been eventually reached. Times where controversy was raging are disappearing from collective memory, and the whole intuitionistic enterprise nowadays tends to be merely considered one place in the whole landscape of logic, mathematics, and philosophy. This place can be specified in various ways.

Belief and Acceptance: A Logical Point of View

The concept of belief seems to crystallise most of the vexed issues of contemporary philosophy, and the numerous and seemlingly unrelated debates around this notion give today the impression of an ubiquitous brownian motion rather than of an even modest progression in some definite direction. Perhaps this feeling simply results of not standing at the right distance, perhaps after the time will have accomplished its cruel work of decantation, it will be possible to get some clearer perspective, and eventually to grasp the genuine problem to which so many solutions had been proposed. But perhaps not so. Perhaps most of the current debate rests on a fundamental equivocation, and there is simply no minimally coherent concept able to play so many roles as today attributed to “belief”: to underly sincere utterances in public languages, to be entertainable by animals and infra-linguals too, to represent, when true or justified, the final aim of science, to be also responsible for overt behavior, articulated with desire according to some pragmatic formula, and so on. If inconsistency is the case, the best thing to do is to divide this unmanageable empire of beliefehood into separate provinces: on one hand belief stricto sensu (if one dare say), and various non-credal attitudes on the other hand.