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Shifting sands: An interestrelative theory of vagueness
 Philosophical Topics
, 2000
"... Please quote or cite page numbers from published version only. Saul Kripke pointed out that whether or not an utterance gives rise to a liarlike paradox cannot always be determined by checking just its form or content. 1 Whether or not Jones’s utterance of ‘Everything Nixon said is true ’ is parado ..."
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Please quote or cite page numbers from published version only. Saul Kripke pointed out that whether or not an utterance gives rise to a liarlike paradox cannot always be determined by checking just its form or content. 1 Whether or not Jones’s utterance of ‘Everything Nixon said is true ’ is paradoxical depends in part on what Nixon said. Something similar may be said about the sorites paradox. For example, whether or not the predicate ‘are
THF0 – the core of the TPTP language for higherorder logic
 Automated Reasoning, 4th International Joint Conference, IJCAR 2008
"... Abstract. One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higherorder logic – THF0, based on Church’s simple type the ..."
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Abstract. One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higherorder logic – THF0, based on Church’s simple type theory. THF0 is a syntactically conservative extension of the untyped firstorder TPTP language. 1
Chapter 2 The Logical Notation:
, 2003
"... A very large body of work in AI begins with the assumptions that information and knowledge should be represented in firstorder logic and that reasoning is theoremproving. On the face of it, this seems implausible as a model for people. It certainly doesn’t seem as if we are using logic when we are ..."
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A very large body of work in AI begins with the assumptions that information and knowledge should be represented in firstorder logic and that reasoning is theoremproving. On the face of it, this seems implausible as a model for people. It certainly doesn’t seem as if we are using logic when we are thinking, and if we are, why are so many of our thoughts and actions so illogical? In fact, there are psychological experiments that purport to show that people do not use logic in thinking about a problem (e.g., Wason and JohnsonLaird 1972). I believe that the claim that logic is the language of thought comes to less than one might think, however, and that thus it is more controversial than it ought to be. It is the claim that a broad range of cognitive processes are amenable to a highlevel description in which six key features are present. The first three of these features characterize propositional logic and the next two firstorder logic. The last carries us beyond standard logic. I will express these features in terms of “concepts”, but one can just as easily substitute
Abstractions and Metaphors on the Internet
"... Abstractions and metaphors seem necessary for human and software agents to operate on the Internet. We hear about (virtual) desktops, classrooms, universities, sales rooms, shopping baskets, etc. We investigate this from a logical point of view emphasizing the syntax/semantics distinction and the us ..."
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Abstractions and metaphors seem necessary for human and software agents to operate on the Internet. We hear about (virtual) desktops, classrooms, universities, sales rooms, shopping baskets, etc. We investigate this from a logical point of view emphasizing the syntax/semantics distinction and the use of abstractions to handle logical and computational complexity.
Frege, Boolos, and Logical Objects
"... Objects In this section, we discuss the following kinds of logical object: natural cardinals, extensions, directions, shapes, and truth values. The material concerning the latter four kinds of logical objects are presented here as new results of OT. However, before introducing those results, we fir ..."
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Objects In this section, we discuss the following kinds of logical object: natural cardinals, extensions, directions, shapes, and truth values. The material concerning the latter four kinds of logical objects are presented here as new results of OT. However, before introducing those results, we first briefly rehearse the development of number theory in Zalta [1999].
Epistemic truth and excluded middle*
"... Abstract: Can an epistemic conception of truth and an endorsement of the excluded middle (together with other principles of classical logic abandoned by the intuitionists) cohabit in a plausible philosophical view? In PART I I describe the general problem concerning the relation between the epistemi ..."
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Abstract: Can an epistemic conception of truth and an endorsement of the excluded middle (together with other principles of classical logic abandoned by the intuitionists) cohabit in a plausible philosophical view? In PART I I describe the general problem concerning the relation between the epistemic conception of truth and the principle of excluded middle. In PART II I give a historical overview of different attitudes regarding the problem. In PART III I sketch a possible holistic solution. Part I The Problem §1. The epistemic conception of truth. The epistemic conception of truth can be formulated in many ways. But the basic idea is that truth is explained in terms of epistemic notions, like experience, argument, proof, knowledge, etc. One way of formulating this idea is by saying that truth and knowability coincide, i.e. for every statement S
The grammar of meanings in Ibn Sīnā and
, 2013
"... This is not yet the paper; in fact it is barely more than a set of notes. But in submitting a precis of the paper to the journal AlMukhtabat I undertook to make the acknowledgements and references available here. It will turn into a proper paper covering all the required references as soon as I can ..."
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This is not yet the paper; in fact it is barely more than a set of notes. But in submitting a precis of the paper to the journal AlMukhtabat I undertook to make the acknowledgements and references available here. It will turn into a proper paper covering all the required references as soon as I can manage. The listing follows the sections of the precis. I thank Manuela Giolfo, Ahmad Hasnaoui, Amirouche Moktefi, Zia Movahed and Kees Versteegh for information, corrections and comments that relate directly to things discussed below. I should also thank Kais Dukes of the Arabic Language Computing group at Leeds University, who sent me some very useful information before going silent — I hope I didn’t make myself a nuisance to him. None of these people are responsible for any errors of fact or judgment below. 1 Ibn Sīnā and Frege as logicians Gottlob Frege’s books Begriffsschrift [8] and Grundgesetze der Arithmetik [13] mark the beginning and the end of his main involvement with giving formal proofs for arithmetical truths. Ibn Sīnā’s logical writings are in nearly all cases first sections of works covering other disciplines as well. Gutas ([20] Chapter 2) discusses and defends what is now the standard dating of these works. The earliest that I use is Kitāb alNajāt [37], or Najāt for short, which was written in around 1 1013 when Ibn Sīnā was around 33, but it was published a dozen or so years later, probably after some light editing. His major surviving work in logic is the first few volumes of his encyclopedic ˇSifā’, which take the form of commentaries on Aristotle’s Organon and were written in the early to mid 1020s. From this work we will use Madk al [29] (commentary on Porphyry’s
Edward N. Zalta 2 Essence and Modality ∗
"... In the course of research on modal logic over the past 60 years, it has become traditional to define an essential property in modal terms as follows: (E) F is essential to x =df ✷(E!x → Fx), where ‘E!x ’ asserts existence and abbreviates ‘∃y(y = x)’. Kit Fine has ..."
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In the course of research on modal logic over the past 60 years, it has become traditional to define an essential property in modal terms as follows: (E) F is essential to x =df ✷(E!x → Fx), where ‘E!x ’ asserts existence and abbreviates ‘∃y(y = x)’. Kit Fine has