The title is meant to emphasize the immense loss of status I take logic to have undergone in recent decades, and to suggest something about its causes. The loss is most obvious in the context of higher education, where almost no post-secondary institutions now have effectual general requirements in standard formal logic, as that was easily understood thirty or more years ago. Courses in so-called 'critical thinking' are, with rare and noble exceptions, only a further illustration of the point, for (...) many of them, if not most, say nothing at all about logical form and formal logic, and proceed as if <span class='Hi'>thought</span> and discourse could be critically understood and appraised in total ignorance of their formal aspects. (shrink)
In this paper I examine William Alston's work on the epistemology of religious belief, focusing on the threat to the epistemic status of Christian belief presented by awareness of religious diversity. I argue that Alston appears to misunderstand the epistemic significance of the ‘practical rationality’ of the Christian mystical practice. I suggest that this error is due to a more fundamental misunderstanding, regarding the significance of practical rationality, in Alston's ‘doxastic practice’ approach to epistemology; an error that leads to arbitrariness (...) among the class of rational doxastic practices. I suggest how one might remedy this weakness, with an additional, epistemic, criterion that rational doxastic practices must satisfy. (shrink)
Is arguing over ontology a mistake? A recent proposal by Karen Bennett suggests that some metaphysical disputes, such as those over constitution and composition, can be dismissed on epistemic grounds. Given that both sides in a dispute try to minimize the differences between them, there are no good metaphysical grounds for choosing between them. In this paper, I expand on her epistemic dismissivism, arguing that given the Quinean conception of the task and method of metaphysics, we are warranted in believing (...) that all ontological disputes will end in a draw, even if they have not yet done so. By a draw, I mean that while both sides in a dispute are genuinely disagreeing about what there is and there are still moves open to them, there are no moves remaining that will advance the discourse further. (shrink)
I undertake to explain how the well known laws of formal logic – Barbara Syllogism, modus ponens, etc. – relate to experience by developing Edmund Husserl's critique ofFormalism and Psychologism in logical theory and then briefly explaining his positive views of the laws of logic. His view rests upon his understanding of the proposition as a complex, intentional property. The laws of formal logic are, on his view (and mine), statements about the truth values of propositions as determined by their (...) formal character and relationships alone. The laws thus understood explain how algorithms set up to mirror them can accomplish what they do to advance knowledge, even though they operate purely mechanically. Further, they explain the proper sense in which formal laws "govern," and may guide, processes of actual thinking. Husserl's theory is a realist theory in the sense that, on his interpretation, the laws of pure or formal logic hold true regardless of what any individual, culture or species may or may not think, or even if no thinking ever occurs. (shrink)
Twentieth Century philosophical thought has expressed itself for the most part through two great Movements: the phenomenological and the analytical. Each movement originated in reaction against idealistic—or at least anti-realistic—views of "the world". And each has collapsed back into an idealism not different in effect from that which it initially rejected. Both movements began with an appeal to meanings or concepts, regarded as objective realities capable of entering the flow of experience without loss of their objective status or of their (...) power to reveal to us an objective world as it would be if there were no subjective apprehensions of it. Both movements ended with a surrender of the objectivity of meanings and concepts in this strong sense, coming to treat them as at most more-or-less shareable components of a somehow communalized experience, but in any case incapable of revealing how things are irrespective of actual human experience. For the old Egocentric Predicament, with its "ideas" etc., is substituted a Lingocentric or Histrocentric Predicament of "language" and its elements. Hilary Putnam speaks for the current consensus: 'Internal realism says that we don't know what we are talking about when we talk about "things in themselves"' (The Many Faces of Realism , p. 36 ). (shrink)
We will study several weak axiom systems that use the Subtraction and Division primitives (rather than Addition and Multiplication) to formally encode the theorems of Arithmetic. Provided such axiom systems do not recognize Multiplication as a total function, we will show that it is feasible for them to verify their Semantic Tableaux, Herbrand, and Cut-Free consistencies. If our axiom systems additionally do not recognize Addition as a total function, they will be capable of recognizing the consistency of their Hilbert-style deductive (...) proofs. Our axiom systems will not be strong enough to recognize their Canonical Reflection principle, but they will be capable of recognizing an approximation of it, called the "Tangibility Reflection Principle". We will also prove some new versions of the Second Incompleteness Theorem stating essentially that it is not possible to extend our exceptions to the Incompleteness Theorem much further. (shrink)
This article will study a class of deduction systems that allow for a limited use of the modus ponens method of deduction. We will show that it is possible to devise axiom systems α that can recognize their consistency under a deduction system D provided that: (1) α treats multiplication as a 3-way relation (rather than as a total function) and that (2) D does not allow for the use of a modus ponens methodology above essentially the levels of II₁ (...) and Σ₁ formulae. Part of what will make this boundary-case exception to the Second Incompleteness Theorem interesting is that we will also characterize generalizations of the Second Incompleteness Theorem that take force when we only slightly weaken the assumptions of our boundary-case exceptions in any of several further directions. (shrink)
This study described parent participation in the informed consent conference for randomized clinical trials (RCTs) in childhood leukemia and documented the relationship of physician communication to parent participation. Parents of 140 children with newly diagnosed leukemia who were eligible for RCTs were studied at six sites using comprehensive methods involving direct observation and transcripts of parent-physician communication based on audiotapes. Parent participation during the informed consent conference reflected a wide range of content categories. Consistent with hypotheses, Physician Rapport and Partnership (...) Building related to parent participation in the informed consent conference but Information Giving did not. Higher parent socioeconomic status also was related to greater parent participation for two of three measures of parent participation. Findings suggest that physician behaviors that provide support and facilitate communication may enhance parental participation in the informed consent conference for RCTs in childhood leukemia. (shrink)
We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given $m and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.
Gödel's Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show that axiomatizations for a computer's floating point arithmetic can recognize their cut-free consistency in a stronger respect than is feasible under integer arithmetics. This paper will include both new generalizations of the Second Incompleteness Theorem and techniques for evading it.
Jesus The Logician ABSTRACT: In understanding how discipleship to Jesus Christ works, a major issue is how he automatically presents himself to our minds. It is characteristic of most 20th century Christians that he does not automatically come to mind as one of great intellectual power: as Lord of universities and research institutes, of the creative disciplines and scholarship. The Gospel accounts of how he actually worked, however, challenge this intellectually marginal image of him and help us to see him (...) at home in the best of academic and scholarly settings of today, where many of us are called to be his apprentices. (shrink)
Using a result of Gurevich and Lewis on the word problem for finite semigroups, we give short proofs that the following theories are hereditarily undecidable: (1) finite graphs of vertex-degree at most 3; (2) finite nonvoid sets with two distinguished permutations; (3) finite-dimensional vector spaces over a finite field with two distinguished endomorphisms.
Let K be a finite set of finite structures. We give a syntactic characterization of the property: every element of K is injective in ISP(K). We use this result to establish that A is injective in ISP(A) for every two-element algebra A.
Aquinas’s ’five ways’ are not to be understood as demonstrative proofs, successful or not, for the existence of God. Rather, they provide a necessary step towards supplying licensable surrogates for the essential predications that cannot logically be drawn from the incomprehensible nature of God, yet would seem needed for the ’Summa‘s declared genre of argued theology. (Predication ’secundum analogiam’ provides surrogates for nonrelational accidental predications, likewise unavailable.) What Aquinas is proving in arguing ’deum esse’ in ’St’ I.2.3 is not God’s (...) actual existence (see ’St’ I.3.4 ad 2) but an alternative interpretation of "God’s being something" where "God is something" is a placeholder for, say, "God is prime mover" or, more explicitly, for such (necessary) identities as "The prime mover is the necessitated necessitator," an identity whose necessity depends at more than one place on the assumption of God’s existence from faith, not on demonstrative proof of God’s existen. (shrink)
Let us recall that Raphael Robinson's Arithmetic Q is an axiom system that differs from Peano Arithmetic essentially by containing no Induction axioms , . We will generalize the semantic-tableaux version of the Second Incompleteness Theorem almost to the level of System Q. We will prove that there exists a single rather long Π 1 sentence, valid in the standard model of the Natural Numbers and denoted as V, such that if α is any finite consistent extension of Q + (...) V then α will be unable to prove its Semantic Tableaux consistency. The same result will also apply to axiom systems α with infinite cardinality when these infinite-sized axiom systems satisfy a minor additional constraint, called the Conventional Encoding Property. Our formalism will also imply that the semantic-tableaux version of the Second Incompleteness Theorem generalizes for the axiom system IΣ 0 , as well as for all its natural extensions. (This answers an open question raised twenty years ago by Paris and Wilkie .). (shrink)
It is argued that human needs are not facts (properties, states, processes, relations) about people, but are values. The reasons presented for this position are (1) that needs are goal oriented and goals are things people value, (2) that ‘need’ functions as a basic motivational term, and (3) that disagreements about what people need are disagreements in attitude toward, and emotional attachment to, things variously considered to be valuable. If human needs are not facts, then, of course, health or medical (...) needs are not. Viewing health or medical needs as discoverable facts, rather than values, engenders certain difficulties in the following areas of concern: (a) Deciding when surgery is necessary and when unnecessary; (b) Defining the concepts of health and disease; (c) Evaluating some consequences of the development of medical science and technology; and (d) Understanding the alleged conflict between patients' health needs and their human rights. CiteULike Connotea Del.icio.us What's this? (shrink)
I consider and reject four possible arguments directed against the preservation of natural aesthetic conditions. (1) Beauty is not out there in nature, but is “in the eye ofthe beholder.” I argue that since ingredients ofnature cause aesthetic experiences, we cannot justifiably disregard and exploit nature. Preservation of aesthetic conditions is compatible with both objective and nonobjective theories of aesthetic value. (2) Frequent aesthetic disagreements bring about irresolvable disputes concerning which segments of nature to preserve. I claim that these disputes (...) are not irresolvable. Not all disputes about nature’s aesthetic values are purely aesthetic disputes: ecological balance, community identity, historic continuity, and economics are relevant; aesthetic experts can help; and such disputes can be put to a vote. (3) Natural beauty is not important compared to nonaesthetic values of nature. I show that this is questionable. Current awareness of environmental problems includes a rapidly growing concern for natural aesthetics. Moreover, even if majority preference is for nonaesthetic uses of nature, this does not settle the question of whether we ought to preserve nature’s attractive features. (4) From neither a utilitarian nor a deontological viewpoint do we have an obligation to preserve natural aesthetic conditions for future generations. I argue that even if we do not have a strict obligation, it does not follow that it makes no moral difference whether we preserve. Not yet existing people may have no rights against us, but this does not mean that we do no wrong in polluting and destroying aesthetic conditions of the natural world in which future people will live. (shrink)
This paper deals with Quine's several attempts To define the concept of underdetermination of scientifics theories in some of his articles and with the dependence of this definition on other concepts of Quine's semantic holism. To define "underdetermination”, Quine needs to explain the relationship between theory and observation. His position concerning this subject can be criticized, on the one hand, by saying that it gives an insufficient criterion for "underdetermination", and, on the other hand, by asserting that it is still (...) too close to the reductionist's conception of truth. (shrink)
One of the main contributions of philosophers at the end of the 19th century and beginning of the 20th century to philosophy of science and semantics was the thesis inspired in the scientific advances of natural and exact sciences, that there is not a single true theory of what goes on in the empirical world, but rather the possibility of constructing multiple versions, equally satisfac-tory, of an explanation of the world. In the Vienna Circle, more specifically, the conventionalist movement showed (...) its influence primarily in the writings of Neurath, but also, more subtly, in the texts of Carnap. In this paper, I shall examine the theoretical relations between Quine’s holistic thesis and the conventionalist aspects of his work. In order to do this I will discuss Neurath’s holistic coherentism and of the conventionalist and holistic aspects present in Camap’s work, which merge, mainly in the Aufbau, with reduc-tionist aims. Thus, I intend to help to clarify to what extent Quine’s holism depends on a conventionalist position and to what extent conventionalism, in its turn, can get along with reductionist epistemological remains. (shrink)
Terms such as ‘exist’, ‘actual’, etc., (hereafter, “ontic terms”) are recognized as having ontologically neutral or non-commissive uses, besides their standard commissive uses. (Consider, e.g., the two interpretations of ‘There is an even prime.’) In this paper, I identify six different non-commissive uses for ontic terms, and along the way I attempt to define (by a kind of via negativa) the commissive use of an ontic term, specifically, the commissive use of ‘actual’. The problem, however, is that the resulting definiens (...) for the commissive ‘actual’ is itself equivocal between a commissive and a non-commissive reading, and thus I consider other proposals for defining the commissive use, including two proposals from David Lewis. However, each proposal is found to be equivocal in the same way--and eventually I argue that it is impossible to define an ontic term unequivocally. Even so, this is not meant to overshadow the fact that we can understand an ontic term as univocally commissive, in certain conversational contexts. I close by applying these observations to the Hirsch-Sider debate in metaontology. (shrink)