In contemporary natural languages semantics one will often see the use of special brackets to enclose a linguistic expression, e.g. ⟦carrot⟧. These brackets---so-called denotation brackets or semantic evaluation brackets---stand for a function that maps a linguistic expression to its "denotation" or semantic value (perhaps relative to a model or other parameters). Even though this notation has been used in one form or another since the early development of natural language semantics in the 1960s and 1970s, Montague himself (...) didn't make use of this notation in his series of groundbreaking papers on semantics. That raises the question: When was the ⟦.⟧-notation introduced to semantics? This note answers that question. (shrink)

SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject (...) which begins when numerals are mentioned (not just used) and mentioned as names of numbers (not just as syntactic objects). Semantic arithmetic leads to many fascinating and surprising algorithms and decision procedures; it reveals in a vivid way the experiential import of mathematical propositions and the predictive power of mathematical knowledge; it provides an interesting perspective for philosophical, historical, and pedagogical studies of the growth of scientific knowledge and of the role metalinguistic discourse in scientific thought. (shrink)

In this paper I will be concerned with the question of the extent to which semantics can be thought of as a purely formal exercise, which we can engage in in a way that is neutral with respect to how our formal system is to be interpreted. I will be arguing, to the contrary, that the features of the formal systems which we use to do semantics are closely linked, in several different ways, to the interpretation that we give to (...) those formal systems. The occasion for this question, and the main example that I will use to illustrate my answer to it, is the close relationship between the formal systems employed in recent statements of apparently competing accounts of epistemic modals with the dynamic, expressivist, and relativist theoretical paradigms. The structure of the paper will be straightforward. In part 1, I will briefly introduce four theories of epistemic modals – one dynamic theory, two expressivist theories, and one relativist theory. Then in part 2 I’ll show that one expressivist theory is formally equivalent to the dynamic theory, that the other is formally equivalent to the relativist theory, and that the two expressivist theories are themselves essentially notational variants. I’ll use these facts to pose our central question: if these theories have so much formally in common, then doesn’t that suggest that we can separate the task of constructing a formal semantics from the task of deciding between competing interpretations of it? Finally, in part 3 I’ll answer that question in the negative. There are at least three reasons why formal semantics cannot be separated from questions of interpretation that are illustrated by the theories I introduce in part 1. (shrink)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to (...) be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be (...) equivalent; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253). (shrink)

A certain skeptical strategy involves a skeptical hypothesis that closely mirrors the structure of our standard theory of the world; this strategy insulates the skeptical argument from attacks based on standard criteria of theory choice. A standard reply to this strategy is to claim that proffered alternative is just the standard theory expressed in a different notation. But this reply does not succeed, given plausible assumptions about semantics. However, there is an alternative strategy--also semantical--which can deal with the problem, (...) at least in those cases where, intuitively, the skeptic's challenge should fail. (shrink)

In “Semantics of Fictional Terms,” Garcia-Carpintero critically surveys the most recent literature on the topic of fictional names. One of his targets is realism about fictional discourse. Realists about fictional discourse believe that: (a) it contains true sentences that have fictional names as their subjects; (b) sentences containing names can be true only if those names have referents; (c) fictional names have fictional characters – abstract objects – as their referents. The fundamental problem that arises for realists is that not (...) all true sentences containing fictional names are plausibly about abstract objects. This leads to the need to introduce disjunctive conceptions of property attribution that Garcia-Carpintero claims are implausible, and that realism should therefore be rejected. He also maintains, however, that (a) is correct. I agree. Furthermore, I am also committed to anti-realism about fictional discourse – that fictional names have no referents. Garcia-Carpintero claims that my view is simply a notational variant of realism. I argue that this is false – that my view could not possibly be a notational variant of any extant realist theory. (shrink)

According to Russell, the notation in Principia Mathematica has been designed to avoid the vagueness endemic to our natural language. But what does Russell think vagueness is? My argument is an attempt to show that his views on vagueness evolved and that the final conception he adopts is not coherent. Three phases of his conception of vagueness are identified, the most significant being the view that he articulates on vagueness in his 1923 address to the Jowett Society. My central (...) thesis is that the 1912 conception of vagueness -- what I characterize as "semantic egalitarianism" -- seriously conflicts with the later paradoxical account of vagueness. (shrink)

This paper discusses two notational variance views with respect to indexical singular reference and content: the view that certain forms of Millianism are at bottom notational variants of a Fregean theory of reference, the Fregean Notational Variance Claim; and the view that certain forms of Fregeanism are at bottom notational variants of a direct reference theory, the Millian Notational Variance Claim. While the former claim rests on the supposition that a direct reference theory could be easily turned into a particular (...) version of a neo-Fregean one by showing that it is bound to acknowledge certain senselike entities, the latter claim is based upon the supposition that a neo-Fregean theory could be easily turned into a particular version of a Millian one by showing that De Re senses are theoretically superfluous and hence eliminable. The question how many accounts of singular reference and content are we confronted with here — Two different (and mutually antagonistic) theories? Or just two versions of what is in essence the same theory? — is surely of importance to anyone interested in the topic. And this question should be answered by means of a careful assessment of the soundness of each of the above claims. Before trying to adjudicate between the two accounts, one would naturally want to know whether or not there are indeed two substantially disparate accounts. Grosso modo, if the Fregean Claim were sound then we would have a single general conception of singular reference to deal with, viz. Fregeanism; likewise, if the Millian Claim were sound we would be facing a single general conception of singular reference, viz. Millianism. My view is that both the Fregean Notational Variance Claim and its Millian counterpart are wrong, though naturally on different grounds. I have argued elsewhere that the Fregean Notational Variance Claim - considered in its application to the semantics of propositional-attitude reports involving proper names — is unsound. I intend tosupplement in this paper such a result by trying to show that the Millian Claim - taken in its application to the semantics of indexical expressions — should also be rated as incorrect. I focus on a certain set of arguments for the Millian Claim, arguments which I take as adequately representing the general outlook of the Millian theorist with respect to neo-Fregeanism about indexicals and which involve issues about the cognitive significance of sentences containing indexical terms. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

The purpose of this study is to compile a selection of the various formalisms found in conversation theory to introduce readers to Pask's discursive algebra. In this way, the text demonstrates how concept sharing and concept formation by means of the interaction of two participants may be formalized. The approach taken in this study is to examine the formal notation system used by Pask and demonstrate how such formalisms may be used to represent concept sharing and concept formation through (...) conversation. The compilation of the discursive algebra using the framework provided by conversation theory could potentially be used as an auxiliary framework to study conversational interactions in multi-agent systems theory. (shrink)

My objective is a better comprehension of two theoretically fundamental concepts. One, the concept of a substance in an ordinary (non-Aristotelian) sense, ranging over such things as salt, carbon, copper, iron, water, and methane – kinds of stuff that now count as (chemical) elements and compounds. The other I’ll call the object-concept in the abstract sense of Russell, Wittgenstein, and Frege in their logico-semantical enquiries. The material object-concept constitutes the heart of our received logico / ontic system, still massively influenced (...) by Aristotle after almost 2.5 millennia. On such an account, the fundamentality of material objects and their attributes are the metaphysical basis of the cosmos, as reflected in our received logic, Quine’s ‘canonical notation’ – derived via the empiricism of Russell from Frege’s function-based Begriffschrifft, and consisting of concrete singular terms and variables, quantifiers and predicate-expressions. The inadequacy of Frege’s approach to understanding concepts is reflected in his initial question. Frege enquires of ‘what it is that we are calling an object’, remarking that he regards a regular definition as impossible: “we have here something too simple to admit of logical analysis”. The imagined ultimacy or simplicity of the idea of a single object (arithmetically, just a unit – one as against two, three, four, etc.) as foundational to the calculus is just that – imagined. It is also guaranteed to block the comprehension of the substance-concept. (shrink)

Despre necesitatea şi utilitatea dezvoltării unei filosofii specifice tehnologiei blockchain, accentuând pe aspectele ontologice. După o Introducere în care evidenţiez principalele direcţii filosofice pentru această tehnologie emergentă, în Tehnologia blockchain explicitez modul de funcţionare al blockchain, punând în discuţie direcţiile ontologice de dezvoltare în Proiectarea şi Modelarea acestei tehnologii. Următoarea secţiune este dedicată principalei aplicaţii a tehnologiei blockchain, Bitcoin, cu implicaţiile sociale ale acestei criptovalute. Urmează o secţiune de Filosofie în care identific tehnologia blockchain cu conceptul de heterotopie dezvoltat de (...) Michel Foucault şi o interpretez în lumina tehnologiei notaţionale dezvoltată de Nelson Goodman ca sistem notaţional. În secţiunea Ontologii dezvolt două direcţii de dezvoltare considerate de mine ca importante: Ontologia narativă, bazată pe ideea de ordine şi structură a istoriei transmise prin naraţia istoriei a lui Paul Ricoeur, şi un sistem ontologic bazat pe Ontologiile de intreprindere, bazat pe conceptele şi modelele de intreprindere specifice webului semantic, şi pe care eu îl consider cel mai bine dezvoltat şi cel care va deveni, probabil, sistemul ontologic formal, cel puţin în ceea ce priveşte aspectele economice şi juridice ale tehnologiei blockchain. În Concluzii vorbesc despre direcţiile viitoare de dezvoltare a filosofiei tehnologiei blockchain în general ca o teorie explicativă şi robustă din punct de vedere fenomenologic, consistentă şi care să permită testabilitatea, şi a ontologiilor în special, argumentând pentru necesitatea unei adopţii globale a unui sistem ontologic pentru a dezvolta soluţii transversale şi a rentabiliza tehnologia. -/- Cuvinte cheie: filosofie, blockchain, ontologie, bitcoin, proiectare, modele -/- CUPRINS -/- Abstract Introducere Tehnologia blockchain - - - Proiectare - - - Modele Bitcoin Filosofia Ontologii - - - Ontologii narative - - - Ontologii de intreprindere Concluzii Note Bibliografie -/- DOI: 10.13140/RG.2.2.25492.35204. (shrink)

Complex logic is a novel logical framework, which formalizes the semantics of the categories of matter, space, and time in a system of logic that operates with complex logical objects. A complex logical object represents a superposition of a logical statement and its logical negation positioning any statement co-relatively to its logical negation. In the system of logical notations, where S is a logical statement and Not S is its logical negation, complex logic includes co-relative logical positions of S and (...) Not S with the probabilities of their truth within the scale 0... 1, excluding the boundary values of 0 and 1, into a single logical superposition. Thus, the logical superposition, summing up the probabilistic positions of S and Not S, has an invariant truth value equal to 1. In this context, complex logic proves to be invariant to reality, offering a unified logical interpretation of reality, spanning from quantum to cosmological scales. By defining the nature of matter and reality as a complex two-format processual essence with corresponding logical consequences, complex logic enhances our concept and understanding of reality. (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of (...) LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

In a review of Frege's Puzzle1, Graeme Forbes makes the claim that Salmon's account of belief might be seen, under certain conditions, as a mere notational variant of a neo-Fregean theory; and thus that such an account might be reduced to a neo-Fregean one simply by rewriting it in terms of Fregean terminology. With a view to supporting his claim, Forbes offers an outline of an account of belief which, according to him, would satisfy the following conditions: (i) it could (...) be directly obtained from Salmon's own analysis by means of a certain set of substitutions, which presumably would not affect the essential features of Salmon's view; (ii) it could naturally be described as Fregean, in the sense that it would preserve, (at least) the spirit of Frege's doctrines, especially his fundamental intuitions about belief. Of course, the upshot of Forbes's argument is that Salmon's theory would not, at bottom, constitute a genuine alternative to a Fregean semantics for belief ascriptions. In this paper I argue to the effect that Forbes's claim is not in general sound. It seems to me that the sort of indirect argument used by Forbes - that of trying to undermine Salmon's theory by showing that it is just a version of a neo-Fregean account - does not provide someone working within a Fregean framework with an adequate strategy to counter Salmon's neo-Russellian views. It would perhaps be better to concentrate a Fregean attack on certain apparently dubious and highly controversial theses and results which are constitutive of Salmon's view, e.g. the counterintuitive character of a substantial set of consequences which follow from his theory of belief, as well as the associated revisionist stand he is forced to take towards our current patterns of speaking about belief. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) (...) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

View more Abstract If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. ‘Televisions are televisions’ and ‘TVs are televisions’ neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical (...) sentences and their synomic interceptions have identical factual content, which seems to exhaust semantic content. However, intercepting alters syntax by eliminating term recurrence, the sole strictly syntactic means of ensuring necessary term coextension, and thereby syntactically securing necessary truth. Interceptional necessity is lexical, a notational artifact. The denial of interception nonsynonymy and the disregard of term recurrence in logic link with many misconceptions about propositions, logical form, conventions, and metalanguages. Mathematics is distinct from logic: its truth is not syntactic; it is transmitted by synonym substitution; term recurrence has no essential role. The ‘=’ of mathematics is an objectual relation between numbers; the ‘=’ of logic marks a syntactic relation of coreferring terms. -/- . (shrink)

Complex systems like literacy and numeracy emerge through multigenerational interactions of brains, behaviors, and material forms. In such systems, material forms – writing for language and notations for numbers – become increasingly refined to elicit specific behavioral and psychological responses in newly indoctrinated individuals. These material forms, however, differ fundamentally in things like semiotic function: language signifies, while numbers instantiate. This makes writing for language able to represent the meanings and sounds of particular languages, while notations for numbers are semantically (...) meaningful without phonetic specification. This representational distinction is associated with neurofunctional and behavioral differences in what neural activity and behaviors like handwriting contribute to literacy and numeracy. In turn, neurofunctional and behavioral differences place written representations for language and numbers under different pressures that influence the forms they take and how those forms change over time as they are transmitted across languages and cultures. (shrink)

Paul Pietroski has developed a powerful minimalist and internalist alternative to standard compositional semantics, where meanings are identified with instructions to fetch or assemble human concepts in specific ways. In particular, there appears to be no need for Fregean Function Application, as natural language composition only involves processes of combining monadic or dyadic concepts, and Pietroski’s theory can then, allegedly, avoid both singular reference and truth conditions. He also has a negative agenda, purporting to show, roughly, that the vocabulary of (...) standard truth conditional semantics is far too powerful to plausibly describe the linguistic competence of mere human minds. In this paper, I explain some of the basics of Pietroski’s compositional semantics and argue that his major objection to standard compositionality is inconclusive, because a similar argument can be mounted against his own minimalist theory. I argue that we need a clear distinction between the language of the theorist---theoretical notation---and the language whose nature we are trying to explain. The theoretical notation should in fact be as expressively powerful as possible. It does not follow that the notation cannot be used to explain mere human linguistic competence, even if human minds are limited in various ways. (shrink)

The article contains a critical analysis of Wittgenstein’s theory of logical symbolism. According to an influential interpretation, Wittgenstein presented in the Tractatus a new method of solving paradoxes. This method seems a simple and effective alternative to Russell’s type theory. Wittgenstein’s theory of logical symbolism is based on the requirement of clear notation and the context principle: the type of a symbol only “shows” itself in the way we use the signs of our language. The function sign φ(φx) does (...) not express any paradox, because the syntactic rules for its use, written in clear notation, should “show” us that φ(φx) = ψ(φx). Many researchers (Davant, Ishiguro, Mounce, Ruffino, Friedlander, Jolley, Livingston, Ladov, et al.) follow this interpretation. However, the difficulty of such a view on Wittgenstein’s theory of logical symbolism is that there hides the fallacy of petitio principii. Indeed, in examples of a functional sign of the form φ(φx), we are interested not only in the question of whether the functions φ are different symbols, but also in how this functional sign φ(φx) itself excludes the symbolization of the same object by different ways. This interpretation is contrasted with the idea that Wittgenstein’s theory of logical symbolism is in fact a modified analogue of Russell’s simple theory of types. The reciprocality principle becomes the core of Wittgenstein’s theory: the combinatorial potential of the “prototype” of a functional sign is identical to the combinatorial potential of the “prototype” of an argument. According to Wittgenstein, only describing the combinatorial potential of linguistic expressions (symbols) can vanish the illusion of paradoxes. The function cannot be its argument, because the function sign φ(φx) already contains the “prototype” of its argument, “showing” us that φ(φx) = φx. The correctness of this interpretation does not exclude the possibility that the differences between Russell and Wittgenstein are in fact nothing more than façon de parler. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of (...) formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

About the necessity and usefulness of developing a philosophy specific to the blockchain technology, emphasizing on the ontological aspects. After an Introduction that highlights the main philosophical directions for this emerging technology, in Blockchain Technology I explain the way the blockchain works, discussing ontological development directions of this technology in Designing and Modeling. The next section is dedicated to the main application of blockchain technology, Bitcoin, with the social implications of this cryptocurrency. There follows a section of Philosophy in which (...) I identify the blockchain technology with the concept of heterotopia developed by Michel Foucault and I interpret it in the light of the notational technology developed by Nelson Goodman as a notational system. In the Ontology section, I present two developmental paths that I consider important: Narrative Ontology, based on the idea of order and structure of history transmitted through Paul Ricoeur's narrative history, and the Enterprise Ontology system based on concepts and models of an enterprise, specific to the semantic web, and which I consider to be the most well developed and which will probably become the formal ontological system, at least in terms of the economic and legal aspects of blockchain technology. In Conclusions I am talking about the future directions of developing the blockchain technology philosophy in general as an explanatory and robust theory from a phenomenologically consistent point of view, which allows testability and ontologies in particular, arguing for the need of a global adoption of an ontological system for develop cross-cutting solutions and to make this technology profitable. -/- CONTENTS: -/- Abstract Introducere Tehnologia blockchain - Proiectare - Modele Bitcoin Filosofia Ontologii - Ontologii narative - Ontologii de intreprindere Concluzii Note Bibliografie -/- DOI: 10.58679/MM73548, ISBN 978-606-033-222-0. (shrink)

This work is a attempt to describe various braches of mathematics and the analogies betwee them. Namely: 1) Symbolic Analogic 2) Lateral Algebraic Expressions 3) Calculus of Infin- ity Tensors Energy Number Synthesis 4) Perturbations in Waves of Calculus Structures (Group Theory of Calculus) 5) Algorithmic Formation of Symbols (Encoding Algorithms) The analogies between each of the branches (and most certainly other branches) of mathematics form, ”logic vectors.” Forming vector statements of logical analogies and semantic connections between the di↵erentiated (...) branches of math- ematics is useful. It’s useful, because it gives us a linguistic notation from which we can derive other insights. These combined insights from the logical vector space connections yield a combination of Numeric Energy and the logic space. Thus, I have derived and notated many of the most useful tangent ideas from which even more correlations and connections ca be drawn. Using AI, these branches can be used to form even more connections through training of lan- guage engines on the derived models. Through the vector logic space and the discovery of new sheaf (Limbertwig), vast combinations of novel, mathematical statements are derived. This paves the way for an AGI that is not rigid, but flex- ible, like a Limbertwig. The Limbertwig sheaf is open, meaning it can receive other mathematical logic vectors with di↵erent designated meanings (of infi- nite or finite indicated elements). Furthermore, the articulation of these syntax forms evolves language away from imperative statements into a mathematically emotive space. Indeed, shown within, we see how the supramanifold of logic is shared with the supramanifold of space-time mathematically. Developing clean mathematical spaces can help meditation, thought pro- cess, acknowledgment of ideas spoken into that cognitive-spacetime and in turn, methods by which paradoxes can be resolved linguistically. This toolkit should be useful to all in the sciences as well as those bridging the humantities to mathematics. Using our memories as a toolkit to aggregate these ideas breaks down bound- aries between them in a new, exciting way. Merging philosophy and Quantum Mechanics together through the lens of symbolic analogies gives the tools to unravel this mystery of all mysteries. Mathematics thus exists as a bridge al- beit a complex one between the two disciplines, giving life to a composite art of problem-solving. Furthermore, mathematics yields to millions of other applications that are potentially limited only by our imagination. From massive data sets used for predictive analytics to emerging fields in medicine, mathematics is an energy and force at the center of possibilities. The power of mathematics to help manage life exists in its ability to shape and model the world in which we live and interact with one another. In conclusion, mathematics is a powerful tool that creates bridges and con- nections between many disciplines and serves as a powerful form of analytical data consumption. It provides language-rich bridges from which to assemble vast fields of theoretical investigations and create groundbreaking innovations. As we approach new horizons in the technology timeline, mathematics will con- tinue to be a powerful driver of creativity and progress. (shrink)

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship (...) between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

This paper presents a diagrammatic notation for visualizing epistemic entities and relations. The notation was created during the Visualizing Worldviews project funded by the University of Toronto’s Jackman Humanities Institute and has been further developed by the scholars participating in the university’s Research Opportunity Program. Since any systematic diagrammatic notation should be based on a solid ontology of the respective domain, we first outline the current state of the scientonomic ontology. We then proceed to providing diagrammatic tools (...) for visualizing the epistemic entities and relations of this ontology. These basic diagramming techniques allow us to construct diagrams of various types for both synchronic and diachronic visualizations. The paper concludes by highlighting some future research directions. As the notation presented here is de facto accepted and used in scientonomy, the paper suggests no modifications. (shrink)

This paper considers a now familiar argument that the ubiquity of context -dependence threatens the project of natural language semantics, at least as that project has usually been conceived: as concerning itself with `what is said' by an utterance of a given sentence. I argue in response that the `anti-semantic' argument equivocates at a crucial point and, therefore, that we need not choose between semantic minimalism, truth-conditional pragmatism, and the like. Rather, we must abandon the idea, familiar from (...) Kaplan and others, that utterances express propositions `relative to contexts' and replace it with the Strawonian idea that speakers express propositions by making utterances in contexts. The argument for this claim consists in a detailed investigation of the particular case of demonstratives, which I argue demand such a Strawsonian treatment. I then respond to several objections, the most important of which allege that the Strawsonian account somehow undermines the project of natural language semantics, or threatens the semantics -pragmatics distinction. Please note that the paper posted here is an extended version of what was published. (shrink)

Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...) are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’. I argue that, properly applied, the principle of logical realism is no threat to the claim that the languages in question are notational variants. Indeed, there seems to be every reason to think that they are. (shrink)

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these (...) notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for linear or partial orders conflicts (...) with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

Tagging is the phenomenon in which regions of a picture, map, or diagram are annotated with words or other symbols, to provide descriptive information about a depicted object. The interpretive principles that govern tagged images are not well understood, due in part to the difficulty of integrating pictorial and linguistic semantic rules. Rather than directly combining these rules, I propose to use the framework of perspectival feature maps as an intermediary representation of content, in which the outputs of pictorial (...) and linguistic interpretation may be assimilated. The result is a simple and compositional semantics for tagged images. (shrink)

In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, (...) we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine’s proposed solution to Frege’s puzzle. We argue that Fine has mis-diagnosed his own solution–his attempted solution does not deny compositionality. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle. (shrink)

I argue that semantics is the study of the proprietary database of a centrally inaccessible and informationally encapsulated input–output system. This system’s role is to encode and decode partial and defeasible evidence of what speakers are saying. Since information about nonlinguistic context is therefore outside the purview of semantic processing, a sentence’s semantic value is not its content but a partial and defeasible constraint on what it can be used to say. I show how to translate this thesis (...) into a detailed compositional-semantic theory based on the influential framework of Heim and Kratzer. This approach situates semantics within an independently motivated account of human cognitive architecture and reveals the semantics–pragmatics interface to be grounded in the underlying interface between modular and central systems. (shrink)

Our aim in this paper is to extend the semantics for the kind of logic of ground developed in (deRosset and Fine, 2023). In that paper, we very briefly suggested a way of treating universal and existential quantification over a fixed domain of objects. Here we explore some options for extending the treatment to allow for a variable domain of objects.

This paper challenges the negative attitudes towards labelled proof systems, usually referred to as semantic pollution, by arguing that such critiques overlook the full potential of labelled calculi. The overarching objective is to develop a practice-based philosophical analysis of labelled calculi to provide insightful considerations regarding their proof-theoretic and philosophical value. To achieve this, successful applications of labelled calculi and related results will be showcased, and comparisons with other relevant works will be discussed. The paper ends by advocating for (...) a more practice-based approach towards the philosophical understanding of proof systems and their role in structural proof theory. (shrink)

nated discussion of the semantics of such verbs. I will call this view.

A semantics of pictorial representation should provide an account of how pictorial signs are associated with the contents they express. Unlike the familiar semantics of spoken languages, this problem has a distinctively spatial cast for depiction. Pictures themselves are two-dimensional artifacts, and their contents take the form of pictorial spaces, perspectival arrangements of objects and properties in three dimensions. A basic challenge is to explain how pictures are associated with the particular pictorial spaces they express. Inspiration here comes from recent (...) proposals that analyze depiction in terms of geometrical projection. In this essay, I will argue that, for a central class of pictures, the projection-based theory of depiction provides the best explanation for how pictures express pictorial spaces, while rival perceptual and resemblance theories fall short. Since the composition of pictorial space is itself the basis for all other aspects of pictorial content, the proposal provides a natural foundation for further pictorial semantics. (shrink)

Epistemic Contextualism is the view that “knows that” is semantically context-sensitive and that properly accommodating this fact into our philosophical theory promises to solve various puzzles concerning knowledge. Yet Epistemic Contextualism faces a big—some would say fatal—problem: The Semantic Error Problem. In its prominent form, this runs thus: speakers just don’t seem to recognise that “knows that” is context-sensitive; so, if “knows that” really is context-sensitive then such speakers are systematically in error about what is said by, or how (...) to evaluate, ordinary uses of “S knows that p”; but since it's wildly implausible that ordinary speakers should exhibit such systematic error, the expression “knows that” isn't context-sensitive. We are interested in whether, and in what ways, there is such semantic error; if there is such error, how it arises and is made manifest; and, again, if there is such error to what extent it is a problem for Epistemic Contextualism. The upshot is that some forms of The Semantic Error Problem turn out to be largely unproblematic. Those that remain troublesome have analogue error problems for various competitor conceptions of knowledge. So, if error is any sort of problem, then there is a problem for every extant competitor view. (shrink)

Situated semantics can be regarded as an attempt at placing situational context (context of situation) at the center of all discussions of meaning. Situation theory is a theory of information content that takes context very seriously. Individuals, properties, relations, and spatiotemporal locations are basic constructs of situation theory. Individuals are conceived as invariants; having properties and standing in relations, they tend to persist in time and space. An anchoring function binds the location parameters to appropriate objects present in the grounding (...) situation. Anchoring plays a major role in the working of constraints that include nomic constraints, conventional constraints and conditional constraints. Situation semantics develops a theory of meaning that is based on relations between situations. Situation semantics provides a fundamental framework for realistic semantics. The ideas emerging from research into situation semantics have been combined with linguistic work and have led to numerous useful proposals. (shrink)

This paper argues that many so-called digital technologies can be construed as notational technologies, explored through the example of Monegraph, an art and digital asset management platform built on top of the blockchain system originally developed for the cryptocurrency bitcoin. As the paper characterizes it, a notational technology is the performance of syntactic notation within a field of reference, a technologized version of what Nelson Goodman called a “notational system.” Notational technologies produce abstracted entities through positive and reliable, or (...) constitutive, tests of socially acceptable meaning. Accordingly, this account deviates from typical narratives of blockchains, instead demonstrating that blockchain technologies are effective at managing digital assets because they produce abstracted identities through the performance of notation. Since notational technologies rely on configurations of socially acceptable meaning, this paper also provides a philosophical account of how blockchain technologies are socially embedded. (shrink)

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of their semantics. This paper (...) is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I then (...) investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)

There is a wealth of resources— ideas, insights, discoveries, inventions, traditions, cultures, languages, arts, religions, sciences, narratives, stories, poems, customs and norms, music and songs, games and personal experiences, and advertisements—that we produce, curate, consume, transmit, and inherit as humans. This wealth, which I define as semantic capital, gives meaning to, and makes sense of, our own existence and the world surrounding us. It defines who we are and enables humans to develop an individual and social life. This paper (...) discusses the shift from analog to digital semantic capital, and the extent to which this might affect the semanticisation of our identities, our lives and our realities. -/- . (shrink)

This chapter examines the “externalist” claim that semantics should include theorizing about representational relations among linguistic expressions and (purported) aspects of the world. After disentangling our main topic from other strands in the larger set of externalist-internalist debates, arguments both for and against this claim are discussed. It is argued, among other things, that the fortunes of this externalist claim are bound up with contentious issues concerning the semantics-pragmatics border.

I propose a unified solution to two puzzles: Ross's puzzle and free choice permission. I begin with a pair of cases from the decision theory literature illustrating the phenomenon of act dependence, where what an agent ought to do depends on what she does. The notion of permissibility distilled from these cases forms the basis for my analysis of 'may' and 'ought'. This framework is then combined with a generalization of the classical semantics for disjunction — equivalent to Boolean disjunction (...) on the diagonal, but with a different two-dimensional character — that explains the puzzling facts in terms of semantic consequence. (shrink)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

There is no consensus yet on the definition of semantic information. This paper contributes to the current debate by criticising and revising the Standard Definition of semantic Information (SDI) as meaningful data, in favour of the Dretske‐Grice approach: meaningful and well‐formed data constitute semantic information only if they also qualify as contingently truthful. After a brief introduction, SDI is criticised for providing necessary but insufficient conditions for the definition of semantic information. SDI is incorrect because truth‐values (...) do not supervene on semantic information, and misinformation (that is, false semantic information) is not a type of semantic information, but pseudo‐information, that is not semantic information at all. This is shown by arguing that none of the reasons for interpreting misinformation as a type of semantic information is convincing, whilst there are compelling reasons to treat it as pseudo‐information. As a consequence, SDI is revised to include a necessary truth‐condition. The last section summarises the main results of the paper and indicates some interesting areas of application of the revised definition. (shrink)

Miriam Schoenfield argues that moral realism and moral vagueness imply ontic vagueness. In particular, she argues that neither shifty nor rigid semantic accounts of vagueness can provide a satisfactory explanation of moral vagueness for moral realists. This paper constitutes a response. I argue that Schoenfield's argument against the shifty semantic account presupposes that moral indeterminacies can, in fact, be resolved determinately by crunching through linguistic data. I provide different reasons for rejecting this assumption. Furthermore, I argue that Schoenfield's (...) rejection of the rigid semantic account is based on a presupposition that ultimately implies the very same claim that is under dispute: the vagueness of moral predicates in imperfect languages persists in the perfect language, as well. (shrink)

Temporal Externalism posits the counterintuitive claim that the semantic properties of terms are influenced not only by present and past linguistic practices but also by future linguistic practices. In this paper, I primarily introduce a new challenge to Temporal Externalism, arguing that it presupposes a meta-belief about future linguistic practices but fails to explain how this belief relates to future properties. I then briefly highlight that Jussi Haukioja’s recent defense of Temporal Externalism still does not address the challenges posed (...) by this meta-belief. Therefore, I conclude that Temporal Externalism is untenable. (shrink)

This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as (...) 'whole', 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)