Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

According to the well-known Bradley’s Regress argument, one cannot explain the unity of states of affairs by referring to relations combining objects with properties. This argument has been widely discussed within analytic metaphysics, but has not been recognized as relevant for the philosophy of perception. I argue that the mainstream characterization of visual content is threatened by the Bradley’s Regress, and the most influential metaphysical solutions to the regress argument cannot be applied in the context of visual content. However, I (...) show that a proper solution to Bradley’s Regress can be formulated by taking into consideration features of visual content suggested by empirical research in vision science. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of automated (...) theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

Within a literary ontology, YHWH in the Hebrew Bible is technically also a fictional entity or object. In Hebrew Bible scholarship, a variety of philosophical issues surrounding fiction have received sustained and in-depth attention. However, the mainstream research on these matters tends to focus on the philosophical foundations of or backgrounds to a particular literary theory, rather than on metaphysical puzzles as encountered in the philosophy of fiction proper. To fill this gap, the present article seeks to provide a meta-theoretical (...) overview of the main contemporary philosophical perspectives on the metaphysics of fictional objects. Three views are discussed, namely possibilism, Meinongianism and creationism. Each view's theory is introduced and critically appropriated with reference to what is implied to be an answer to the question of what exactly the biblical character YHWH can meaningfully be said to be in the context of the metaphysics of fictional objects. In this way, the present study also goes beyond the traditional concern with the nature of God in Old Testament theology. (shrink)

Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.

In this paper, we describe "metaphysical reductions", in which the well-defined terms and predicates of arbitrary mathematical theories are uniquely interpreted within an axiomatic, metaphysical theory of abstract objects. Once certain (constitutive) facts about a mathematical theory T have been added to the metaphysical theory of objects, theorems of the metaphysical theory yield both an analysis of the reference of the terms and predicates of T and an analysis of the truth of the sentences of T. The well-defined terms and (...) predicates of T are analyzed as denoting abstract objects and abstract relations, respectively, in the background metaphysics, and the sentences of T have a reading on which they are true. After the technical details are sketched, the paper concludes with some observations about the approach. One important observation concerns the fact that the proper axioms of the background theory abstract objects can be reformulated in a way that makes them sound more like logical axioms. Some philosophers have argued that we should accept (something like) them as being logical. (shrink)

Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting (...) system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an over-simplification: one can't assimilate predication to functional application.<br>. (shrink)

This paper contains answers to the following Five questions, posed by the editors are answered: (1) Why were you initially drawn to the foundations of mathematics and/or the philosophy of mathematics? (2) What example(s) from your work (or the work of others) illustrates the use of mathematics for philosophy? (3) What is the proper role of philosophy of mathematics in relation to logic, foundations of mathematics, the traditional core areas of mathematics, and science? (4) What do you consider the most (...) neglected topics and/or contributions in late 20th century philosophy of mathematics? (5) What are the most important open problems in the philosophy of mathematics and what are the prospects for progress? (shrink)

Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we (a) develop results in modal metaphysics whose discovery was computer assisted, and (b) conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that (...) led to these results may be more broadly applicable within computer science. The paper includes a description of our background methodology and how it evolved, and a discussion of our new results. (shrink)

In this paper, we compare two theories, modal Meinongianism and object theory, with respect to several issues that have been discussed recently in the literature. In particular, we raise some objections for MM, undermine some of the objections that its defenders raise for OT, and we point out some virtues of the latter with respect to the former.

This paper provides an original approach to research on the logical processes that determine how certain forms participate in others. By introducing the concept of relational participation, the problems of self-referentiality of the Platonic forms can be dealt with more effectively. Applying this to the forms of likeness and unlikeness in Parmenides 132d-133a reveals a possible way to resolve different versions of the Third Man Argument. The method of generating numbers from oddness and evenness may also be of interest; relational (...) participation in these forms clarifies the interpretation of Parmenides 143e-144a. (shrink)

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

Because the label "computing and philosophy" can seem like an ad hoc attempt to tie computing to philosophy, it is important to explain why it is not, what it studies (or does) and how it differs from research in, say, "computing and history," or "computing and biology". The American Association for History and Computing is "dedicated to the reasonable and productive marriage of history and computer technology for teaching, researching and representing history through scholarship and public history" (http://theaahc.org). More pervasive, (...) work in computing and biology enjoys the convenient name of "bioinformatics...the science of using information to understand biology..., a subset of the larger field of computational biology, the application of quantitative analytical techniques in modeling biological systems" (http://oreilly.com/catalog/bioskills/chapter/ ch01.html). The recent venture of the Association for Computing Machinery and the Institute of Electrical and Electronics Engineers to publish the Transactions on Computational Biology and Bioinformatics (TCBB) bears witness to the reach of computing and biology and underscores its objective. TCBB intends to report "archival research results related to the algorithmic, mathematical, statistical, and computational methods that are central in bioinformatics and computational biology; the development and testing of effective computer programs in bioinformatics; the development and optimization of biological databases; and important biological results that are obtained from the use of these methods, programs, and databases" (http://tcbb.acm.org). In the case of "computing and history" and "bioinformatics," each discipline stands in a particular relationship to computers that raises questions unique to itself. But both are devoted to the development of computational tools to aid discovery.. (shrink)

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in PROVER9 (a first-order automated reasoning system which is the successor to OTTER). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in PROVER9's first-order syntax, and (2) how (...) PROVER9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research. (shrink)

This paper serves as a kind of field guide to certain passages in the literature which bear upon the foundational theory of abstract objects. The foundational theory assimilates ideas from key philosophers in both the analytical and phenomenological traditions. I explain how my foundational theory of objects serves as a common ground where analytic and phenomenological concerns meet. I try to establish how the theory offers a logic that systematizes a well-known phenomenological kind of entity, and I try to show (...) the various ways the theory systematizes the ideas of many analytic philosophers. The ideas of Plato, Leibniz, Frege, Russell, Goedel and even Kripke become connected through those of Brentano, Meinong, Husserl, and Mally. -/- The field guide will not only document the passages in which the distinction between two kinds of predication originates, but also document the other surprising, and often unrelated, contexts where the distinction reappears in the work of others. It will also document ways in which the theory can be used to represent precisely the ideas of the philosophers mentioned above. The resulting guide will bring together the works of many different authors, including some clearly within the analytic tradition, some clearly within the phenomenological tradition, and some who straddle the divide. (shrink)

The arguments of the dialetheists for the rejection of the traditional law of noncontradiction are not yet conclusive. The reason is that the arguments that they have developed against this law uniformly fail to consider the logic of encoding as an analytic method that can resolve apparent contradictions. In this paper, we use Priest [1995] and [1987] as sample texts to illustrate this claim. In [1995], Priest examines certain crucial problems in the history of philosophy from the point of view (...) of someone without a prejudice in favor of classical logic. For each of these problems, the logic of encoding offers an alternative explanation of the phenomena---this alternative is not considered when Priest describes what options there are in classical logic for analyzing the problem at hand. (shrink)

Journal Name: Apeiron Issue: Ahead of print.