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What Is Logic?
"... It is far from clear what is meant by logic or what should be meant by it. It is nevertheless reasonable to identify logic as the study of inferences and inferential relations. The obvious practical use of logic is in any case to help us to reason well, to draw good inferences. And the typical form ..."
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It is far from clear what is meant by logic or what should be meant by it. It is nevertheless reasonable to identify logic as the study of inferences and inferential relations. The obvious practical use of logic is in any case to help us to reason well, to draw good inferences. And the typical form the theory of any part of logic seems to be a set of rules of inference. This answer already introduces some structure into a discussion of the nature of logic, for in an inference we can distinguish the input called a premise or premises from the output known as the conclusion. The transition from a premise or a number of premises to the conclusion is governed by a rule of inference. If the inference is in accordance with the appropriate rule, it is called valid. Rules of inference are often thought of as the alpha and omega of logic. Conceiving of logic as the study of inference is nevertheless only the first approximation to the title question, in that it prompts more questions than it answers. It is not clear what counts as an inference or what a theory of such inferences might look like. What are the rules of inference based on? Where do we find them? The ultimate end
Interoperability between biomedical ontologies through relation expansion, upperlevel ontologies and automatic reasoning
 PLOS ONE
, 2011
"... Researchers design ontologies as a means to accurately annotate and integrate experimental data across heterogeneous and disparate data and knowledge bases. Formal ontologies make the semantics of terms and relations explicit such that automated reasoning can be used to verify the consistency of kn ..."
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Researchers design ontologies as a means to accurately annotate and integrate experimental data across heterogeneous and disparate data and knowledge bases. Formal ontologies make the semantics of terms and relations explicit such that automated reasoning can be used to verify the consistency of knowledge. However, many biomedical ontologies do not sufficiently formalize the semantics of their relations and are therefore limited with respect to automated reasoning for large scale data integration and knowledge discovery. We describe a method to improve automated reasoning over biomedical ontologies and identify several thousand contradictory class definitions. Our approach aligns terms in biomedical ontologies with foundational classes in a toplevel ontology and formalizes composite relations as class expressions. We describe the semiautomated repair of contradictions and demonstrate expressive queries over interoperable ontologies. Our work forms an important cornerstone for data integration, automatic inference and knowledge discovery based on formal representations of knowledge. Our results and analysis software are available at
BERNAYS AND SET THEORY
"... We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higherorder reflection principles. ..."
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We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higherorder reflection principles.
This is a preliminary version of a review which will appear in Research in the History of Economic Thought and Methodology, Volume 24A (2006), edited by
"... formalist revolution or what happened to orthodox economics after World War II?”, the specter of mathematician David Hilbert has haunted economists’s discussions of formalization and axiomatization. Briefly, if one looks upon formalized economics, or formalism, with a loathing built on fear (or a fe ..."
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formalist revolution or what happened to orthodox economics after World War II?”, the specter of mathematician David Hilbert has haunted economists’s discussions of formalization and axiomatization. Briefly, if one looks upon formalized economics, or formalism, with a loathing built on fear (or a fear based on loathing), one demonizes Hilbert since the philosophical notion of formalism, in the history of metamathematics, is usually associated with Hilbert. That is, in the history of philosophy of mathematics, there appears to be a distinction between formalists and empiricists, on the nature of mathematical objects. The ontological reflections in that arcane literature has Hilbert holding the position that mathematics is simply a formal system, and its symbols are simply marks on paper. It is an easy step then to look for traces of David Hilbert in the development of mathematical economics in the 20 th century. Seek, and ye shall find, and critics of mainstream economics have found Hilbertian connections in Vienna with Menger’s seminar. As a result Hilbert gets caught up in the origin stories of general equilibrium theory which lead all the way to von Neumann and the development of game theory. From Vienna and general equilibrium theory it is a short step, though a false step, to have Hilbert as the spiritual advisor to the Cowles Commission and thence to ArrowDebreu. From there of course one can launch tirades about the formalist revolution in economics and have Hilbert bearing some of the blame for a misguided economics.
Realism for scientific ontologies
"... Abstract. Science aims to develop an accurate understanding of reality through a variety of rigorously empirical and formal methods. Ontologies are used to formalize the meaning of terms within a domain of discourse. The Basic Formal Ontology (BFO) is an ontology of particular importance in the bio ..."
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Abstract. Science aims to develop an accurate understanding of reality through a variety of rigorously empirical and formal methods. Ontologies are used to formalize the meaning of terms within a domain of discourse. The Basic Formal Ontology (BFO) is an ontology of particular importance in the biomedical domains, where it provides the toplevel for numerous ontologies, including those admitted as part of the OBO Foundry collection. The BFO requires that all classes in an ontology are actually instantiated in reality. Despite the fact that it is hard to show whether entities of some kind exist or do not exist in reality (especially for unobservable entities like elementary particles), this criterion fails to satisfy the need of scientists to communicate their findings and theories unambiguously. We discuss the problems that arise due to the BFO’s realism criterion and suggest viable alternatives.
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"... David Hilbert opened ‘Axiomatic Thought ’ [15] with the observation that ‘the most important bearers of mathematical thought, ’ for ‘the benefit of mathematics itself have always [...] cultivated the relations to the domains of physics and the [philosophical] theory of knowledge. ’ We have in L.E.J. ..."
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David Hilbert opened ‘Axiomatic Thought ’ [15] with the observation that ‘the most important bearers of mathematical thought, ’ for ‘the benefit of mathematics itself have always [...] cultivated the relations to the domains of physics and the [philosophical] theory of knowledge. ’ We have in L.E.J. Brouwer 3 and Kurt Gödel 4 two of those ‘most important bearers of mathematical thought ’ who cultivated the relations to philosophy for the benefit of mathematics (though not only for that). And both went beyond philosophy, cultivating relations to mysticism for the benefit of mathematics (though not for that alone). There is a basic conception of mysticism that is singularly relevant here. (’Mysticism ’ labels that.) That corresponds to a basic conception of philosophy (’Philosophy’), also singularly relevant here. Both Mystic and Philosopher begin in a condition of seriously unpleasant, existential unease, and aim at a condition of abiding ease. For Mystic and Philosopher the way to that ease is through being enlightened about the real and true good of all things. Thus Mysticism and Philosophy are triply optimistic: there is a real, true good of all things,