Formal Logic

“The repeated sentiment is that formal logic has a unique ability to generate absolute epistemological certainty. It is a neutral and settled discipline…(this) attitude is so easy to acquire in secondary literature or introductions to formal logic, and is so cherished for various reasons, that a serious look at the actual phenomena of logical study, if one has the stamina to carry it out, holds the potential for an awakening which can be described as nothing other than rude. It makes us realize that absolute certainty, full justification, widespread agreement, and presuppositionless neutrality have been mistakenly taken for granted regarding formal logic. Serious disagreement within the discipline of logic threaten it as a model of scientific study, for key conflicts seem Luther – The Foolishness of God; “Monstrous indeed is the madness of men, who desire thus to subject the immeasurable to the puny measure of their own reason…The greatest geniuses are blinder than moles…” Calvin – “But I reply: the testimony of the Spirit is more excellent than all reason.” [1.7.4] irresolvable, especially in the absence of any clear account of the proper object of logical study and the appropriate evidence for claims about it.” “The apparent unity of logic which has been present to many people is usually achieved through revisionist surveys of the field and through sociological prejudice. The ‘logic’ which has been of interest to scholars throughout history is in fact many things, although some writers would hardly let on that it is so. Twenty-three centuries of Indian (Hindu and Buddhist) logic are commonly omitted altogether…The ‘logic’ of thought-hygenic interest (Descartes), of all-encompassing philosophic interest (Kant, Hegel, Bradley, Husserl), of empirical interest (Mill), of mathematical interest (Boole, De Morgan), and of formal interest (Russell and Whitehead) are rarely even mentioned for distinguishing. Logics which deal with other basic concepts than quantity, disjunction, etc. are easily ignored by popular writers (e.g. Deontic, Doxastic, Modal logics). And even when we restrict our attention to recent, Western, formal logic — first order, predicate logic with truth-functional connectives — the illusion of unity often arises either from an unwillingness to raise questions, a concession to pedagogical utility, or from exclusion of those who hold divergent convictions from an academic guild (seeing opponents as not even qualifying as true ‘logicians’ or as being too preposterous to invite to academic conferences on logic). “That ‘formal logic’ is a ‘science’ in the honorific sense will turn out to be a pretense of huge proportions…It will turn out…that there is serious disagreement as to what logic is about and accordingly, how logician’s claims should be warranted…Whatever ‘logical truths’ are, let us at least ask which truths are the logical truths. The history of logic does not encourage us that an agreed upon list can be formulated by all ‘reasonable’ men, for to our embarrassment this history is strewn with bitter controversies and conflicts. The reason for this situation is not hard to find: it turns out that the choice of logical truths is affected by other kinds of questions, for instance the place of ordinary language analysis, the role of intuition the selection of a metaphysical entity as the subject matter of logic, the understanding of reference…etc. Not only must we countenance…disagreements in the study of logic, we must observe that there has been no general agreement even as to the method by which the disagreements could be settled. Since these disagreements effect the acceptance of logical rules or the validity of arguments, they are surely unsettling in a field allegedly characterized by invariant, obvious, and absolute proof.” “The tendency will be for the dogged advocates of an honorific view of the discipline of logic to retrench, I suppose, and contend that at least the ‘three laws of thought’ are objectively certain and beyond question. Identity, contradiction, and excluded middle will be the new, restricted realm of certainty. But little hope can be offered for this revised confidence in ‘scientific’ objectivity and agreement. The ancient Epicureans were vigorous in rejecting the law of excluded middle against Stoic logicians. Medieval scholastics, considering the question of truth in statements expressing future contingencies, were led to reject excluded middle (and to suggest a manyvalued logic, as did Peter de Rivo). And modern physicists who have been concerned with philosophical aspects of quantum mechanics have also rejected the traditional law of excluded middle in logic.” “Now then, we do not have a rational and certain answer to the question, what are logical truths? Nor do we have such an answer for the questions, which are the logical truths? There are embarrassing conflicts over those truths, so we cannot help but go on and ask how logicians come to know or be confident about any particular logical truth. Russell and others have contended that these logical truths are known a priori, independent of experience. Why, then, is there no universal agreement among reasonable men about them?… Furthermore, if logical truths are justified a priori and are thereby universal, unchanging, eternal truths, why should they in fact (or why should they be thought to) apply repeatedly in the realm of contingent experience? Why should they have anything to do with history, or why should reasoning about history have these ‘laws of thought’ imposed upon it?” “The justification of logical truth along a posteriori lines was proposed by Mill; we gain confidence in them through repeated experience, which is then generalized. But…it should be seen that if their truth cannot be decided independently of experience, then they actually become contingent and lose their necessity. Why should a law of logic which is verified in one domain of experience be taken as true for unexperienced domains as well?…” “Although the preceding discussion only suggest a program for cross-examining various alternative ways of justifying logical truths, it does give some reason to think that this issue is not an absolutely clear and certain matter in philosophy, and it does remind us that the approaches taken to the question are far from uniform…Anyone who reads the relevant contemporary literature in the philosophy of logic will once again be impressed with two things regarding such questions about the type of evidence available for logicians’ claims: first, some authors fail even to reflect upon them, and second, among those who do there is rank disagreement. Is this really the paradigm of objective, settled, rationality?” “The variant approaches to the type of evidence we have for logicians’ claims really traces back quite naturally to another question of what kind of entity is mentioned in logicians; claims…For instance, should a materialist and a spiritualist agree as to the evidential basis for the claims they will make, one would surely be confused. Plato’s realism and rationalism go hand in hand, just as do Hobbes’ nominalism and empiricism. Thus metaphysical commitments regarding logicians’ claims will be quite relevant to the types of rational support logicians offer for those claims. (Those who wish to resist this truth should consider if their view, that the nature of reality has no bearing whatsoever on logical truths and functions, is not itself a highly dogmatic, metaphysical commitment.)” “When we turn to the specification of the ultimate subject matter in the study of logic, we find unquestioned invariance (e.g. Peirce claimed that there were at least a hundred definitions of logic). To the general question, what basic type of entity is mentioned in logicians’ claims?, traditional answers include: (1) inferences, which are comprised of judgments made up of concepts (e.g. L.J.Russell, Wm. Thomson. J.G. Hibben), (2) arguments, comprised of propositions made up of terms (Bolzano, Mill, Bosanquet, W.E. Johnson, C.I. Lewis), or (3) proofs, comprised of sentences made up of names (Hilbert Carnap, Quine). Especially today in the philosophy of logic do the best minds in the field, by their own admission, talk about utterly different things with radically divergent kinds of properties, relations, and modes of cognition….” “The unsettled nature of the discipline of logic is nowhere more clearly indicated than in the fact that the leading scholars in the field cannot even agree as to (1) what their claims are about, or (2) what kind of rational evidence can be offered for those claims. What little, trivial agreement might appear to be found in certain inscriptional sequences similar from writer to writer (e.g. ‘If A is B, and if B is C, then A is C’) are emptied of any rational significance by differences which are as fundamental as those that have been noted. Morris Cohen, in A Preface to Logic, freely admits; ‘if by logic is meant a clear, accurate, and orderly intellectual procedure, then the subject of logic, as presented in current textbooks, comes near being the most illogical in our chaotic curriculum.’ Logic does not turn out to be an invariant field of elementary self-evident beliefs and set procedures by which all reasonable and educated men have arrived uniformly and with absolute certainty at agreed upon truths, rules, and evaluations of arguments. Nor has it been found that logic sustains a relationship to all other fields of study (including epistemology and metaphysics) which is solely and uniquely a one-way foundational relationship to them; we have seen that epistemological and metaphysical presuppositions significantly influence positions taken in ‘formal logic’ — in which case the discipline can hardly be said to be utterly neutral and objective…Even as with the other disciplines of scholarly study, logic is found wanting in thorough justification and lacking in unity. Given the honorific conception, not even formal logic can truly count as scientific.”

Bahnsen, Article: “Science, Subjectivity and Scripture,”


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