A VERSION OF CARTESIAN METHOD RODERICK H. CHISHQLM Introduction In one of his many profound discussions of the method of philosophy, Korner makes the ...

This lucid and comprehensive essay by a distinguished philosopher surveys the views of Plato, Aristotle, Leibniz, and Kant on the nature of mathematics. It examines the propositions and theories of the schools these philosophers inspired, and it concludes by discussing the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.

This lucid and comprehensive essay by a distinguished philosopher surveys the views of Plato, Aristotle, Leibniz, and Kant on the nature of mathematics. It examines the propositions and theories of the schools these philosophers inspired, and it concludes by discussing the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.

Lucid and comprehensive essay surveys the views of Plato, Aristotle, Leibniz and Kant on the nature of mathematics; examines the propositions and theories of the schools these philosophers inspired; and concludes with a discussion on the relation between mathematical theories, empirical data and philosophical presuppositions.

Ethical thought experiments such as the trolley dilemma have been investigated extensively in the past, showing that humans act in utilitarian ways, trying to cause as little overall damage as possible. These trolley dilemmas have gained renewed attention over the past few years, especially due to the necessity of implementing moral decisions in autonomous driving vehicles. We conducted a set of experiments in which participants experienced modified trolley dilemmas as drivers in virtual reality environments. Participants had to make decisions between (...) driving in one of two lanes where different obstacles came into view. Eventually, the participants had to decide which of the objects they would crash into. Obstacles included a variety of human-like avatars of different ages and group sizes. Furthermore, the influence of sidewalks as potential safe harbors and a condition implicating self-sacrifice were tested. Results showed that participants, in general, decided in a utilitarian manner, sparing the highest number of avatars possible with a limited influence by the other variables. Derived from these findings, which are in line with the utilitarian approach in moral decision making, it will be argued for an obligatory ethics setting implemented in ADVs. (shrink)

(No abstract is available for this citation).

Is consolidation needed to account for retroactive interference in free recall? Interfering mental activity during the retention interval of a memory task impairs performance, in particular if the interference occurs in temporal proximity to the encoding of the to-be-remembered information. There are at least two rival theoretical accounts of this temporal gradient of retroactive interference. The cognitive neuroscience literature has suggested neural consolidation is a pivotal factor determining item recall. According to this account, interfering activity interrupts consolidation processes that would (...) otherwise stabilize the memory representations of TBR items post-encoding. Temporal distinctiveness theory, by contrast, proposes that the retrievability of items depends on their isolation in psychological time. According to this theory, information processed after the encoding of TBR material will reduce the temporal distinctiveness of the TBR information. To test between these accounts, implementations of consolidation were added to the SIMPLE model of memory and learning. We report data from two experiments utilizing a two-list free recall paradigm. Modeling results imply that SIMPLE was able to model the data and did not benefit from the addition of consolidation. It is concluded that the temporal gradient of retroactive interference cannot be taken as evidence for memory consolidation. (shrink)

Translational research is a buzzword which dominates discussions about the quality, the utilization, and the benefits of medical research. Yet, although translational research has become a prominent topic, no commonly agreed definition of this terminology exists. Instead, experts from different contexts such as biomedical research, clinical practice or nursing discuss translational research in multiple ways depending on how they define the problem that translational research is supposed to be the solution to. In this paper, we do not seek to find (...) a ‘correct’ definition of translational research, but instead ask how actors using this terminology for describing their own research make sense of it. To do so, we asked three questions: Which actors are engaged in the debate about translational research? What kind of different meanings of translational research exist? And, which actors refer to which meaning of translational research when using the term? In answering these questions, we highlight the role this terminology plays in defining what medical science is about today. (shrink)

Translational research is a buzzword which dominates discussions about the quality, the utilization, and the benefits of medical research. Yet, although translational research has become a prominent topic, no commonly agreed definition of this terminology exists. Instead, experts from different contexts such as biomedical research, clinical practice or nursing discuss translational research in multiple ways depending on how they define the problem that translational research is supposed to be the solution to. In this paper, we do not seek to find (...) a ‘correct’ definition of translational research, but instead ask how actors using this terminology for describing their own research make sense of it. To do so, we asked three questions: Which actors are engaged in the debate about translational research? What kind of different meanings of translational research exist? And, which actors refer to which meaning of translational research when using the term? In answering these questions, we highlight the role this terminology plays in defining what medical science is about today. (shrink)

Translational research is a buzzword which dominates discussions about the quality, the utilization, and the benefits of medical research. Yet, although translational research has become a prominent topic, no commonly agreed definition of this terminology exists. Instead, experts from different contexts such as biomedical research, clinical practice or nursing discuss translational research in multiple ways depending on how they define the problem that translational research is supposed to be the solution to. In this paper, we do not seek to find (...) a ‘correct’ definition of translational research, but instead ask how actors using this terminology for describing their own research make sense of it. To do so, we asked three questions: Which actors are engaged in the debate about translational research? What kind of different meanings of translational research exist? And, which actors refer to which meaning of translational research when using the term? In answering these questions, we highlight the role this terminology plays in defining what medical science is about today. (shrink)

The breadth-first search adopted by Bayesian researchers to map out the conceptual space and identify what the framework can do is beneficial for science and reflective of its collaborative and incremental nature. Theoretical pluralism among researchers facilitates refinement of models within various levels of analysis, which ultimately enables effective cross-talk between different levels of analysis.

We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.

There exist valuable methods for theorem proving in non classical logics based on translation from these logics into first-order classical logic (abbreviated henceforth FOL). The key notion in these approaches istranslation from aSource Logic (henceforth abbreviated SL) to aTarget Logic (henceforth abbreviated TL). These methods are concerned with the problem offinding a proof in TL by translating a formula in SL, but they do not address the very important problem ofpresenting proofs in SL via a backward translation. We propose a (...) framework for presenting proofs in SL based on a partial backward translation of proofs obtained in a familiar TL: Order-Sorted Predicate Logic. The proposed backward translation transfers some formulasF TL belonging to the proof in TL into formulasF SL , such that the formulasF SL either (a) belong to a corresponding deduction in SL (in the best case) or, (b) are semantically related in some precise way, to formulas in the corresponding deduction in SL (in the worst case). The formulasF TL andF SL can obviously be considered aslemmas of their respective proofs. Therefore the transfer of lemmas of TL gives at least a skeleton of the corresponding proof in SL. Since the formulas of a proof keep trace of the strategy used to obtain the proof, clearly the framework can also help in solving another fundamental and difficult problem:the transfer of strategies from classical to non classical logics. We show how to apply the proposed framework, at least to S5, S4(p), K, T, K4. Two conjectures are stated and we propose sufficient (and in general satisfactory) conditions in order to obtain formulas in the proof in SL. Two particular cases of the conjectures are proved to be theorems. Three examples are treated in full detail. The main lines of future research are given. (shrink)

We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, (...) so we have the second characterization of K-triviality.The proof of the first characterization uses a new cupping result. We prove that if A≰LRB, then for every set X there is a B-random set Y such that X is computable from Y⊕A. (shrink)

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)

This paper considers reductions between types of numberings; these reductions preserve the Rogers Semilattice of the numberings reduced and also preserve the number of minimal and positive degrees in their semilattice. It is shown how to use these reductions to simplify some constructions of specific semilattices. Furthermore, it is shown that for the basic types of numberings, one can reduce the left-r.e. numberings to the r.e. numberings and the k-r.e. numberings to the k+1-r.e. numberings; all further reductions are obtained by (...) concatenating these reductions. (shrink)

This publication of the proceedings of the first of a new series of colloquia to be held at the University of Western Ontario contains an opening address on existence and quantification by W. V. Quine and three symposia. The paper discussed in the first of these symposia, "Descartes' Ontological Argument" by Anthony Kenny, follows closely one chapter of Kenny's recent book on Descartes. Kenny's paper contains both an interesting account of Descartes' views and some challenging remarks about ontological arguments in (...) general. His paper is discussed in separate commentaries by Norman Malcolm and Terence Penelhum. An interesting feature of this volume is that some comments from the floor are recorded and included along with the regular commentaries. Ernest Sosa and Bernard Williams comment on Kenny's paper along with Malcolm and Penelhum. Kenny responds to all four commentators. The other two symposia follow a similar format. The second, "On Events and Event-descriptions," features a paper by R. M. Martin which focuses on the logic of event descriptions and their role in scientific explanation. Events for Martin are extensional entities, unlike facts, but like facts they are "fictitious in the sense of being handled on virtually." His views are discussed by Donald Davidson, R. J. Butler and Wesley Salmon. In the third symposium on "Existence Assumptions in Practical Thinking," Stephan Körner elaborates on his view of effective choice, relating his account to those of Hume, Kant, and Peirce on the specific topic of the relationship of choice and natural necessity. The commentaries of J. J. Thomson and Bernard Williams are helpful here in getting Körner to clarify his interesting views. In sum, this first colloquium at the University of Western Ontario features genuine philosophical communication on some important issues.--R. H. K. (shrink)

We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal (...) value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left$ is rational. (shrink)

This anthology assembles original contributions by leadinganalytical philosophers to a broad range of topics on whichSuppes set out ideas which still point the way ahead. All the papersincluded were originally given at the 1st International LauenerSymposium on Analytical Philosophy, which accompanied the Presentationof the first Lauener Prize to Patrick Suppes. His detailedcommentaries on each of the revised articles as well as the addedinterview elicit a spirit of constructive academic conversation.The book joins together contributions by Patrick Suppes, DagfinnFllesdal, Nancy Cartwright, Wilhelm (...) K. Essler, Steven French,Stephan Hartmann, and Michael Frauchiger. The collection as awhole puts a different and stimulating perspective on a varietyof issues in the methodology of science and philosophy. (shrink)

This article reflects a conversation between Jan G. van der Watt and Stephan Joubert. The article serves as the introduction to the Special Collection: ‘From timely exegesis to contemporary ecclesiology: Relevant hermeneutics and provocative embodiment of faith in a Corona-defined world – Festschrift for Stephan Joubert, sub-edited by Willem Oliver ’. Following a brief bio-statement as introduction, the following issues are discussed: the collection for the Jerusalem church; relevance of theology for society; social-scientific exegesis; the ancient concept of (...) grace; Bible translation in South Africa; public theology on the electronic platform; biblical examples of leadership and electronic media in religious activities and education.Contribution: This Festschrift represents current trends in biblical scholarship and ecclesial leadership. It contributes to the public discourse in church and society, especially the role of the electronic media in current Fourth Industrial Revolution. (shrink)

This anthology assembles original contributions by leadinganalytical philosophers to a broad range of topics on whichSuppes set out ideas which still point the way ahead. All the papersincluded were originally given at the 1st International LauenerSymposium on Analytical Philosophy, which accompanied the Presentationof the first Lauener Prize to Patrick Suppes. His detailedcommentaries on each of the revised articles as well as the addedinterview elicit a spirit of constructive academic conversation.The book joins together contributions by Patrick Suppes, DagfinnFllesdal, Nancy Cartwright, Wilhelm (...) K. Essler, Steven French,Stephan Hartmann, and Michael Frauchiger. The collection as awhole puts a different and stimulating perspective on a varietyof issues in the methodology of science and philosophy. (shrink)

These papers originated as lectures, three each by Stephan Kröner, [[sic]] Martinus Versfeld, A. J. Ayer, Stephen Pepper, and O. K. Bouswma, [[sic]] in a year-long series at the University of Notre Dame. Kröner [[sic]] and Pepper see philosophy in terms of conceptual structures, Kröner [[sic]] as the production of "categorial frameworks" and Pepper as the systematization of an intuition he calls a "root metaphor." Versfeld says philosophy is Socratic dialectic, that is, the light-hearted testing of hypotheses. For Ayer, (...) philosophy is analysis aimed at reconstructing the unsatisfactory presuppositions of common sense. Bouswma [[sic]] offers three demonstrations of how philosophical problems are dissolved by showing them to be instances of the misuse of words. Interested readers may wish to look at papers on this topic by Rorty, MacQuarrie, Harris, and Johann, read at Notre Dame in the spring of 1967 and published in the Proceedings of the American Catholic Philosophical Association.--L. G. (shrink)