A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which (...) assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)
In their historical overview of cognitive science, Bechtel, Abraham- son and Graham (1999) describe the field as expanding in focus be- ginning in the mid-1980s. The field had spent the previous 25 years on internalist, high-level GOFAI (“good old fashioned artificial intelli- gence” [Haugeland 1985]), and was finally moving “outwards into the environment and downards into the brain” (Bechtel et al, 1999, p.75). One important force behind the downward movement was Patricia Churchland’s Neurophilosophy (1986). This book began a movement bearing (...) its name, one that truly came of age in 1999 when Kath- leen Akins won a million-dollar fellowship to begin the McDonnell Project in Philosophy and the Neurosciences. The McDonnell Project put neurophilosophy at the forefront of philosophy of mind and cogni- tive science, yielding proliferating articles, conferences, special journal issues and books. In two major new books, neurophilosophers Patricia Churchland (2002) and John Bickle (2003) clearly feel this newfound prominence: Churchland mocks those who do not apply findings in neuroscience to philosophical problems as “no-brainers”; Bickle mocks anyone with traditional philosophical concerns, including “naturalistic philosophers of mind” and other neurophilosophers. (shrink)
v. 1. Classical roots and medieval discussions -- v. 2. Renaissance controversis, later scholasticism, and the elimination of the intelligible species in modern philosophy.
This paper discusses some aspects of the controversies regarding the operation of the agent intellect on sensory images. I selectively consider views developed between the 13th century and the beginning of the 17th century, focusing on positions which question the need for a (distinct) agent intellect or argue for its essential "inactivity" with respect to phantasms. My aim is to reveal limitations of the Peripatetical framework for analyzing and explaining the mechanisms involved in conceptual abstraction. The first section surveys developments (...) of Aristotelian noetics and abstraction in Ancient and Arabic philosophy. The second section presents a discussion of some "positive" accounts on abstraction and the agent intellect, and some "negative" accounts. (shrink)
In this paper we try to bring some clarification in the recent debate on causal pluralism. Our first aim is to clarify what it means to have a pluralistic theory of causation and to articulate the criteria by means of which a certain theory of causation can or cannot qualify as a pluralistic theory of causation. We also show that there is currently no theory on the market which meets these criteria, and therefore no full-blown pluralist theory of causation exists. (...) Because of this, we offer a general strategy by means of which pluralist theories of causation can be developed. (shrink)
Instances of explanatory reduction are often advocated on metaphysical grounds; given that the only real things in the world are subatomic particles and their interaction, we have to try to explain everything in terms of the laws of physics. In this paper, we show that explanatory reduction cannot be defended on metaphysical grounds. Nevertheless, indispensability arguments for reductive explanations can be developed, taking into account actual scientific practice and the role of epistemic interests. Reductive explanations might be indispensable to address (...) some epistemic interest answering a specific explanation-seeking question in the most accurate, adequate and efficient way. Just like explanatory pluralists often advocate the indispensability of higher levels of explanation pointing at the pragmatic value of the explanatory information obtained on these higher levels, we argue that explanatory reduction—traditionally understood as the contender of pluralism—can be defended in a similar way. The pragmatic value reductionist, lower level explanations might have in the biomedical sciences and the social sciences is illustrated by some case studies. (shrink)
Leibniz's overall view of the relationship between reasoning and computation is discussed on the basis of two broad claims that one finds in his writings, concerning respectively the nature of human reasoning and the possibility of replacing human thinking by a mechanical procedure. A joint examination of these claims enables one to appreciate the wide scope of Leibniz's interests for mechanical procedures, concerning a variety of philosophical themes further developed both in later logical investigations and in methodological contributions to cognitive (...) psychology. (shrink)
This paper approaches the choice between the open and closed nuclear fuel cycles as a matter of intergenerational justice, by revealing the value conflicts in the production of nuclear energy. The closed fuel cycle improve sustainability in terms of the supply certainty of uranium and involves less long-term radiological risks and proliferation concerns. However, it compromises short-term public health and safety and security, due to the separation of plutonium. The trade-offs in nuclear energy are reducible to a chief trade-off between (...) the present and the future. To what extent should we take care of our produced nuclear waste and to what extent should we accept additional risks to the present generation, in order to diminish the exposure of future generation to those risks? The advocates of the open fuel cycle should explain why they are willing to transfer all the risks for a very long period of time (200,000 years) to future generations. In addition, supporters of the closed fuel cycle should underpin their acceptance of additional risks to the present generation and make the actual reduction of risk to the future plausible. (shrink)
Causal pluralism is currently a hot topic in philosophy. However, the consequences of this view on causation for scientific knowledge and scientific methodology are heavily underexposed in the present debate. My aim in this paper is to argue that an epistemological-methodological point of view should be valued as a line of approach on its own and to demonstrate how epistemological- methodological causal pluralism differs in its scope from conceptual and metaphysical causal pluralism. Further, I defend epistemological-methodological causal pluralism and try (...) to illustrate that scientific practice needs diverse causal concepts in diverse domains, and even diverse causal concepts within singular domains. (shrink)
This spectacular discovery attracted a lot of media attention. This edition will be published in Brill's Texts and Sources on Intellectual History (BSIH) in August.
Much work on legal knowledge systems treats legal reasoning as arguments that lead from a description of the law and the facts of a case, to the legal conclusion for the case. The reasoning steps of the inference engine parallel the logical steps by means of which the legal conclusion is derived from the factual and legal premises. In short, the relation between the input and the output of a legal inference engine is a logical one. The truth of the (...) conclusion only depends on the premises, and is independent of the argument that leads to the conclusion.This paper opposes the logical approach, and defends a procedural approach to legal reasoning. Legal conclusions are not true or false independent of the reasoning process that ended in these conclusions. In critical cases this reasoning process consists of an adversarial procedure in which several parties are involved. The course of the argument determines whether the conclusion is true or false. The phenomenon of hard cases is used to demonstrate this essential procedural nature of legal reasoning. (shrink)
