Two semantic paradoxes, the Liar and Curry’s paradox, are analysed using a newly developed conception of procedural semantics (semantics according to which the truth of propositions is determined algorithmically), whose main characteristic is its departure from methodological realism. Rather than determining pre-existing facts, procedures are constitutive of them. Of this semantics, two versions are considered: closed (where the halting of procedures is presumed) and open (without this presumption). To this end, a procedural approach to deductive (...) reasoning is developed, based on the idea of simulation. As is shown, closed semantics supports classical logic, but cannot in any straightforward way accommodate the concept of truth. In open semantics, where paradoxical propositions naturally ‘belong’, they cease to be paradoxical; yet, it is concluded that the natural choice—for logicians and common people alike—is to stick to closed semantics, pragmatically circumventing problematic utterances. (shrink)

After presenting Kripke’s criticism to Frege’s ideas on context dependence of thoughts, I present two recent attempts of considering cognitive aspects of context dependent expressions inside a truth conditional pragmatics or semantics: Recanati’s non-descriptive modes of presentation (MOPs) and Kaplan’s ways of having in mind (WHIMs). After analysing the two attempts and verifying which answers they should give to the problem discussed by Kripke, I suggest a possible interpretation of these attempts: to insert a procedural or algorithmic level (...) in semantic representations of indexicals. That a function may be computed by different procedures might suggest new possibilities of integrating contextual cognitive aspects in model theoretic semantic. (shrink)

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.

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)

This article offers an explanation of perhaps Wittgenstein’s strangest and least intuitive thesis – the semantical mutation thesis – according to which one can never answer a mathematical conjecture because the new proof alters the very meanings of the terms involved in the original question. Instead of basing our justification on the distinction between mere calculation and proofs of isolated propositions, characteristic of Wittgenstein’s intermediary period, we generalize it to include conjectures involving effective procedures as well.

We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

Dummett’s justification procedures are revisited. They are used as background for the discussion of some conceptual and technical issues in proof-theoretic semantics, especially the role played by assumptions in proof-theoretic definitions of validity.

In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound and (...) complete three-sided sequent calculus for this expressively rich theory. (shrink)

One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

In this paper I shall deal with the role of "understanding a thought" in the debate on the definition of the content of an assertion. I shall present a well known tension in Frege's writings, between a cognitive and semantic notion of sense. This tension is at the source of some of the major contemporary discussions, mainly because of the negative influence of Wittgenstein's Tractatus, which did not give in-depth consideration to the tension found in Frege. However many contemporary authors, (...) after the first attempt by Carnap himself, have tried to make room both for a cognitive and semantic aspect of meaning. I claim that at least some of these attempts (Dummett, Perry and Chalmers) are seriously flawed, mainly due to the difficulty in making a proper connection between the two different conceptions of sense. I shall outline an alternative project, which takes into consideration Frege's requirements on antipsychologism and of the objectivity of thought, while maintaining a close connection between the two aspects of sense. (shrink)

An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...) which can be used to generate terms instantiating types from this selected set when applied to terms designating certain other Semantic Types, including almost all the terms specifying clinical tasks. Usage of such operators thus provides a useful and economical way of specifying clinical tasks. The operators allow us to define a mapping between those types within the UMLS which do not represent clinical tasks and those which do. This mapping then provides a basis for an ontology of clinical tasks that can be used in the formulation of computer-interpretable clinical guideline models. (shrink)

The logicality of language is the hypothesis that the language system has access to a ‘natural’ logic that can identify and filter out as unacceptable expressions that have trivial meanings—that is, that are true/false in all possible worlds or situations in which they are defined. This hypothesis helps explain otherwise puzzling patterns concerning the distribution of various functional terms and phrases. Despite its promise, logicality vastly over-generates unacceptability assignments. Most solutions to this problem rest on specific stipulations about the properties (...) of logical form—roughly, the level of linguistic representation which feeds into the interpretation procedures—and have substantial implications for traditional philosophical disputes about the nature of language. Specifically, contextualism and semantic minimalism, construed as competing hypotheses about the nature and degree of context-sensitivity at the level of logical form, suggest different approaches to the over-generation problem. In this paper, I explore the implications of pairing logicality with various forms of contextualism and semantic minimalism. I argue that to adequately solve the over-generation problem, logicality should be implemented in a constrained contextualist framework. (shrink)

We examine the proof-theoretic verificationist justification procedure proposed by Dummett. After some scrutiny, two distinct interpretations with respect to bases are advanced: the independent and the dependent interpretation. We argue that both are unacceptable as a semantics for propositional intuitionistic logic.

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.

Mental (or semantic) holism is the doctrine that the identity of a belief content (or the meaning of a sentence that expresses it) is determined by its place in the web of beliefs or sentences comprising a whole theory or group of theories. It can be contrasted with two other views: atomism and molecularism. Molecularism characterizes meaning and content in terms of relatively small parts of the web in a way that allows many different theories to share those parts. For (...) example, the meaning of 'chase' might be said by a molecularist to be try to catch. Atomism characterizes meaning and content in terms of none of the web; it says that sentences and beliefs have meaning or content independently of their relations to other sentences or beliefs. One major motivation for holism has come from reflections on the natures of confirmation and learning. As Quine (1953) observed, claims about the world are confirmed not individually, but only in conjunction with theories of which they are a part. And typically, one cannot come to understand scientific claims without understanding a significant chunk of the theory of which they are a part. For example, in learning the Newtonian concepts of 'force', 'mass', kinetic energy' and 'momentum', one doesn't learn any definitions of these terms in terms that are understood beforehand, for there are no such definitions. Rather, these theoretical terms were all learned together in conjunction with procedures for solving problems. The major problem with holism is that it threatens to make generalization in psychology virtually impossible. If the content of any state depends on all others, it would be extremely unlikely that any two believers would ever share a state with the same content. Moreover, holism would appear to conflict with our ordinary conception of reasoning. What sentences one accepts influence what one infers. if i accept a sentence and then later reject it, i thereby change the inferential role of that sentence, so the meaning of what i accept wouldn't be the same as what i later reject. but then it would be difficult to understand on this view how one could rationally --or even irrationally!-- change one's mind. and agreement and translation are also problematic for much the same reason. holists have responded (1) by proposing that we should think not in terms of "same/different" meaning but in terms of a gradient of similarity of meaning, (2) by proposing "two factor" theories or (3) by simply accepting the consequence that there is no real difference between changing meanings and changing beliefs. (shrink)

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also (...) decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

The chapter outlines an abstract theoretical framework that is currently (re-)emerging in the course of a theoretical convergence of several disciplines. In the first section, the fundamental problem of perception theory is formulated, namely, the generation, by the perceptual system, of meaningful categories from physicogeometric energy patterns. In the second section, it deals with basic intuitions and assumptions underlying what can be regarded as the current Standard Model of Perceptual Psychology and points out why this model is profoundly inadequate for (...) dealing with the fundamental problem of perception theory. In the third section, it discusses a level of analysis that promises to be fruitful for dealing, in conformity with established procedures of the natural sciences, with the problem of perceptual “meaning” and the problem of what constitutes a “perceptual object.” In the fourth section, it outlines a theoretical perspective on basic principles of the perceptual system which centers on the notions of complex data types and conceptual forms, and draws an entirely different theoretical picture of the role of the sensory input than traditional accounts. The final section focusses on the issue of material qualities and discusses, within the general theoretical framework outlined, some observations and results on the perception of certain material properties, namely, lustrous and glassy appearances. (shrink)

Hume's two definitions of causation have caused an extraordinary amount of controversy. The starting point for the controversy is the fact, well known to most philosophy undergraduates, that the two definitions aren't even extensionally equivalent, let alone semantically equivalent. So how can they both be definitions? One response to this problem has been to argue that Hume intends only the first as a genuine definition—an interpretation that delivers a straightforward regularity interpretation of Hume on causation. By many commentators' lights, however, (...) this is a bug rather than a feature: such an account of the two definitions leaves necessary connection out of Hume's story about the meaning of "cause" .. (shrink)

Attempt of trans-disciplinary analysis of the evolutionary value of bioethics is realized. Currently, there are High Tech schemes for management and control of genetic, socio-cultural and mental evolution of Homo sapiens (NBIC, High Hume, etc.). The biological, socio-cultural and technological factors are included in the fabric of modern theories and technologies of social and political control and manipulation. However, the basic philosophical and ideological systems of modern civilization formed mainly in the 17–18 centuries and are experiencing ever-increasing and destabilizing risk-taking (...) pressure from the scientific theories and technological realities. The sequence of diagnostic signs of a new era once again split into technological and natural sciences’ from one hand, and humanitarian and anthropological sciences’, from other. The natural sciences series corresponds to a system of technological risks be solved using algorithms established safety procedures. The socio-humanitarian series presented anthropological risk. Global bioethics phenomenon is regarded as systemic socio-cultural adaptation for technology-driven human evolution. The conceptual model for meta-structure of stable evolutionary strategy of Homo sapiens (SESH) is proposes. In accordance to model, SESH composed of genetic, socio-cultural and techno-rationalist modules, and global bioethics as a tool to minimize existential evolutionary risk. An existence of objectively descriptive and value-teleological evolutionary trajectory parameters of humanity in the modern technological and civilizational context (1), and the genesis of global bioethics as a system social adaptation to ensure self-identity (2) are postulated. -/- . (shrink)

Klein's target article argues that autonoetic consciousness is a necessary condition for memory; this unusually narrow view of the scope of memory implies that only episodic memory is, strictly speaking, memory. The narrow view is opposed to the standard broad view, on which causal connection with past experience is sufficient for memory; on the broad view, both declarative (i.e., episodic and semantic) and procedural memory count as genuine forms of memory. Klein mounts a convincing attack on the broad view, (...) arguing that it opens the "doors of memory" too far, but this commentary contends that the narrow view does not open them far enough. It may be preferable to adopt an intermediate view of the scope of memory, on which causal connection is sufficient for memory only when it involves encoding, storage, and retrieval of content. More demanding than the simple causal condition but less demanding than the autonoesis condition, the encoding-storage-retrieval condition implies that both episodic and semantic memory count as genuine forms of memory but that procedural memory does not. (shrink)

In this paper we give some formal examples of ideas developed by Penco in two papers on the tension inside Frege's notion of sense (see Penco 2003). The paper attempts to compose the tension between semantic and cognitive aspects of sense, through the idea of sense as proof or procedure – not as an alternative to the idea of sense as truth condition, but as complementary to it (as it happens sometimes in the old tradition of procedural semantics).

This paper provides new examples of vagueness phenomena with comparatives. I show that comparatives of the form ‘x is ADJ-er than y’ can be vague due to a fuzziness in how much of some property makes for a difference in ADJ-ness. The sorites examples I provide cannot be assimilated to cases of indiscriminability or fuzziness in relevant dimensions, standards, or measurement procedures. A revised degree-based semantics with semiorders, a well studied threshold structure, is developed. The treatment of equatives captures (...) the truth of the claim that adjacent items in the sorites series are not relevantly distinguishable in ADJ-ness; and it avoids validating transitivities that would yield paradoxical conclusions. (shrink)

Henry Molaison, aged eighty-two, died at the end of 2008, and just after noon on exactly the first anniversary of his death, December 2, 2009, scientists began slicing his brain into 2,500 tissue samples. Known primarily in his lifetime as only H.M., he left his brain to science so that it could be dissected and digitally mapped – a gift much beloved by many scientists. An amnesiac in life, H.M. first rose to prominence in 1962 when Dr. Brenda Milner, a (...) pioneer in the field of neuropsychology, demonstrated that though H.M. was severely amnesic and could not remember past activities, he could nevertheless learn certain habits. The experiment involved the now famous mirror drawing. This article, written by a philosopher/artist and a neuroscientist/neuroaesthetician, argues that artists are unable to verbally articulate thoughts about their own art practice for reasons similar to why H.M. could not. All memories are not stored in the same part of the brain. Different categories of memories i.e., semantic memory or procedural memory, are stored in different parts of the brain. We argue that the procedural memory is not readily accessible to semantic memory. (shrink)

A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.

The aim of the article is to defi ne a certain type of argumentation, which has been scarcely described so far in either Polish or foreign literature in the fi eld of argumentation theory, and thus to systematize the problems of research on semantic procedures in argumentation. The analysis of the ways in which a modifi cation of meaning can affect the power of arguments inclines to distinguish a new type of argumentation - semantic argumentation. The concepts of persuasive defi (...) nition and classifi cation as well as methods of their application in the formulation of an argument will also be analyzed. The defi nition of semantic argumentation proposed here may give rise to some problems, typical when introducing a new concept, which is why the second part of the article is devoted to the issues related to the proposed shape of the defi nition. The defi nition is necessary for further research on semantic argumentation, its typology and for the assessment of its correctness. (shrink)

ABSTRACT Truth-conditions are systematically determined when they are the output of an algorithmic procedure that takes as input a set of semantic and contextual features. Truth-conditional sceptics have cast doubts on the thesis that truth-conditions are systematic in this sense. Against this form of scepticism, Schoubye and Stokke : 759–793) and Dobler : 451–474.) have provided systematic analyses of utterance truth-conditions. My aim is to argue that these theories are not immune to the kind of objections raised by truth-conditional sceptics. (...) In particular, I argue that the use of Questions Under Discussion and ways of being is problematic. (shrink)

In this paper I will explore the question whether the Trivialization construction of transparent intensional logic (TIL) can be understood in terms of the Execution construction, specifically, in terms of its degenerate case known as the 0-Execution. My answer will be positive and the apparent contrast between the intuitive understanding of Trivialization and 0-Execution will be explained as a matter of distinct yet related informal perspectives, not as a matter of technical or conceptual differences.

There are two kinds of semantic theories of anaphora. Some, such as Heim’s File Change Semantics, Groenendijk and Stokhof’s Dynamic Predicate Logic, or Muskens’ Compositional DRT (CDRT), seem to require full coindexing of anaphora and their antecedents prior to interpretation. Others, such as Kamp’s Discourse Representation Theory (DRT), do not require this coindexing and seem to have an important advantage here. In this squib I will sketch a procedure that the first group of theories may help themselves to so (...) that they can interleave interpretation and coindexing in DRT’s way. (shrink)

ACTION-THEORETICALLY EXPLANATORY INTERPRETATIONS AS A MEANS OF SEMANTIC MEANING ANALYSIS The article first develops a general procedure for semantic meaning analysis in difficult cases where the meaning is very uncertain. The procedure consists of searching for one or more possible hypothetical causal explanations of the text, these explanations containing, among other things, the semantic intention of the author, his subjective reasons for this meaning and for the writing down of the text, but also the path of transmission of the text (...) from the writing down to the respective present text version. These hypothetical explanations (interpretations) are deductive-nomological or probabilistic, therefore presuppose corresponding general law hypotheses. If there is only one possible (hypothetical) explanation of the text at hand, this hypothetical explanation is also true. Very often, however, there are several possible explanations. In this case, the probabilities of these possible explanations must be determined; these probabilities then carry over to the individual hypotheses in the explanation (according to Bayes' law). This general procedure of meaning analysis is used in the second part of the article to reconstruct two famous interpretations (by Wapnewski and Hahn) of a poem by Walther von der Vogelweide ("Nemt, frowe, disen kranz"). -/- GERMAN ABSTRACT In dem Artikel wird zunächst ein allgemeines Verfahren zur semantischen Bedeutungsanalyse in schwierigen Fällen entwickelt, in denen die Bedeutung sehr unsicher ist. Das Verfahren besteht darin, daß eine oder mehrere mögliche hypothetische kausale Erklärungen des Textes gesucht werden, wobei diese Erklärungen u.a. die semantische Intention des Autors enthalten, seine subjektiven Gründe für diese Bedeutung und für die Niederschrift des Textes, aber auch den Weg der Tradierung des Textes von der Niederschrift bis zur jeweils vorliegenden Textversion. Diese hypothetischen Erklärungen (Deutungen) sind deduktiv-nomologisch oder probabilistisch, setzen deshalb entsprechende allgemeine Gesetzeshypothesen voraus. Wenn es nur eine mögliche (hypothetische) Erklärung des vorliegenden Textes gibt, ist diese hypothetische Erklärung auch wahr. Sehr häufig gibt es aber mehrere mögliche Erklärungen. In diesem Fall müssen die Wahrscheinlichkeiten dieser möglichen Erklärungen bestimmt werden; diese Wahrscheinlichkeiten übertragen sich dann auch auf die einzelnen Hypothesen in der Erklärung (nach dem Bayesschen Gesetz). Dieses allgemeine Verfahren der Bedeutungsanalyse wird im zweiten Teil des Artikels zur Rekonstruktion zweier berühmter Interpretationen (von Wapnewski und Hahn) eines Gedichts von Walther von der Vogelweide („Nemt, frowe, disen kranz“) verwendet. (shrink)

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational content is (...) extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

In this thesis I argue that the psychological study of concepts and categorisation, and the philosophical study of reference are deeply intertwined. I propose that semantic intuitions are a variety of categorisation judgements, determined by concepts, and that because of this, concepts determine reference. I defend a dual theory of natural kind concepts, according to which natural kind concepts have distinct semantic cores and non-semantic identification procedures. Drawing on psychological essentialism, I suggest that the cores consist of externalistic placeholder essence (...) beliefs. The identification procedures, in turn, consist of prototypes, sets of exemplars, or possibly also theory-structured beliefs. I argue that the dual theory is motivated both by experimental data and theoretical considerations. The thesis consists of three interrelated articles. Article I examines philosophical causal and description theories of natural kind term reference, and argues that they involve, or need to involve, certain psychological elements. I propose a unified theory of natural kind term reference, built on the psychology of concepts. Article II presents two semantic adaptations of psychological essentialism, one of which is a strict externalistic Kripkean-Putnamian theory, while the other is a hybrid account, according to which natural kind terms are ambiguous between internalistic and externalistic senses. We present two experiments, the results of which support the strict externalistic theory. Article III examines Fodor’s influential atomistic theory of concepts, according to which no psychological capacities associated with concepts constitute them, or are necessary for reference. I argue, contra Fodor, that the psychological mechanisms are necessary for reference. (shrink)

The arguments of Fodor, Garret, Walker and Parkes [(1980) Against definitions, Cognition, 8, 263-367] are the source of widespread skepticism in cognitive science about lexical semantic structure. Whereas the thesis that lexical items, and the concepts they express, have decompositional structure (i.e. have significant constituents) was at one time "one of those ideas that hardly anybody [in the cognitive sciences] ever considers giving up" (p. 264), most researchers now believe that "[a]ll the evidence suggests that the classical [(decompositional)] view is (...) wrong as a general theory of concepts" [Smith, Medin & Rips (1984) A psychological approach to concepts: comments on Rey, Cognition, 17, 272], and cite Fodor et al. (1980) as "sounding the death knell for decompositional theories" [MacNamara & Miller (1989) Attributes of theories of meaning, Psychological Bulletin, 106, 360]. I argue that the prevailing skepticism is unmotivated by the arguments in Fodor et al. Fodor et al. misrepresent the form, function and scope of the decompositional hypothesis, and the procedures they employ to test for the psychological reality of definitions are flawed. I argue, further, that decompositional explanations of the phenomena they consider are preferable to their primitivist alternatives, and, hence, that there is prima facie reason to accept them as evidence for the existence of decompositional structure. Cognitive scientists would, therefore, do well to revert to their former commitment to the decompositional hypothesis. (shrink)

A central theme in Wittgenstein’s post-Tractatus remarks on the limits of language is that we ‘cannot use language to get outside language’. One illustration of that idea is his comment that, once we have described the procedure of teaching and learning a rule, we have ‘said everything that can be said about acting correctly according to the rule’; ‘we can go no further’. That, it is argued, is an expression of anti-reductionism about meaning and rules. A framework is presented for (...) assessing the debate between reductionist and anti-reductionist readings of Wittgenstein’s views about meaning and use. It is argued that that debate cannot be settled merely by reference to Wittgenstein’s general opposition to reductionism. An important argument for anti-reductionism about rules and meaning, from Remarks on the Foundations of Mathematics, is discussed. Putative evidence of reductionism about meaning in the Brown Book is considered; an alternative reading is proposed. The nature of Wittgenstein’s anti-reductionism is examined. It is argued, first, that Wittgenstein accepts that semantic and normative facts supervene on non-semantic, non-normative facts and, second, that at many points his treatment of meaning and rules goes beyond the kind of pleonastic claim that is often taken to define non-reductionist, quietist, positions in philosophy. (shrink)

In this paper, I engage with a recent contextualist account of gender terms proposed by Díaz-León, E. 2016. “Woman as a Politically Significant Term: A Solution to the Puzzle.” Hypatia 31 : 245–58. Díaz-León’s main aim is to improve both on previous contextualist and non-contextualist views and solve a certain puzzle for feminists. Central to this task is putting forward a view that allows trans women who did not undergo gender-affirming medical procedures to use the gender terms of their choice (...) to self-identify. My goal is to investigate Díaz-León’s proposal, point out several shortcomings of the view and discuss possible replies on her part. (shrink)

This essay is divided into two parts. In the first part (§2), I introduce the idea of practical meaning by looking at a certain kind of procedural systems — the motor system — that play a central role in computational explanations of motor behavior. I argue that in order to give a satisfactory account of the content of the representations computed by motor systems (motor commands), we need to appeal to a distinctively practical kind of meaning. Defending the explanatory (...) relevance of semantic properties in a computationalist explanation of motor behavior, my argument concludes that practical meanings play a central role in an adequate psychological theory of motor skill. In the second part of this essay (§3), I generalize and clarify the notion of practical meaning, and I defend the intelligibility of practical meanings against an important objection. (shrink)

Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are (...) given for claiming that syllogistic validity is relevant validity. (shrink)

Timothy Williamson has defended the claim that the semantics of the indicative ‘if’ is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by a fallible cognitive heuristic, called the Suppositional Procedure. Williamson’s Suppositional Conjecture has it that the Suppositional Procedure is humans’ primary way of prospectively assessing conditionals. This paper raises some doubts on the Suppositional Procedure and Conjecture.

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

In artificial intelligence (AI), responses generated by machine-learning models (most often large language models) may be unfactual information presented as a fact. For example, a chatbot might state that the Mona Lisa was painted in 1815. Such phenomenon is called AI hallucinations, seeking inspiration from human psychology, with a great difference of AI ones being connected to unjustified beliefs (that is, AI “beliefs”) rather than perceptual failures). -/- AI hallucinations may have their source in the data itself, that is, the (...) source content, or in the training procedure, i.e. the way the knowledge was encoded in the model’s parameters, so that errors in encoding and decoding textual and non-textual representations can cause hallucinations. In this paper, we will observe how such errors come to life and how they might be mitigated. For this purpose, we will analyze the usability of justification logics, to behave as a proof checker for validating the correctness of large language models’ (LLM) responses. Justification logic was developed by S. Artemov, and later on mostly by Artemov and M. Fitting, deriving its main idea from the logic of proofs (LP): knowledge and belief modalities are seen as justification terms, i.e. t:X stands for t is a (proper) justification for X. Justification logic originated from attempts to create semantics for intuitionistic logic where proofs were the most proper justifications, but in further development, justification logic could be applied to different kinds of justifications). With the recent attempts to mitigate incorrect LLM responses, we will analyze various guardrails that are currently used for LLM responses, and see how the logic of justification may provide its benefits as an AI safety layer against false data. (shrink)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

Inventing novel knowledge to solve problems is a crucial, creative, mechanism employed by humans, to extend their range of action. In this paper, we present TCL (typicality-based compositional logic): a probabilistic, non monotonic extension of standard Description Logics of typicality, and will show how this framework is able to endow artificial systems of a human-like, commonsense based, concept composition procedure that allows its employment in a number of applications (ranging from computational creativity to goal-based reasoning to recommender systems and affective (...) computing). -/- The framework relies on 3 main ingredients: a non monotonic extension of standard Description Logics (allowing to reason on exceptions to inheritance in standard knowledge bases) a probabilistic extension coming from the field of logic programming (the DISPONTE semantics) a cognitive heuristics known ad HEAD-Modifier determining preference rules for the inheritance mechanisms of the novel concepts to be generated via commonsense rules. -/- We report the obtained results and the lessons learned of this research path in the context of model-based AI applications. -/- . (shrink)

This chapter argues that Davidson's truth-theoretic semantics was not intended to replace the traditional pursuit of providing a compositional meaning theory but rather to achieve the same aim indirectly by placing conditions on a truth theory that would enable someone who understood it to understand its object language. The chapter argues that by placing constraints on the axioms of a Tarski-style truth theory, namely, that they interpret the terms for which they give satisfaction conditions, and specifying a suitable canonical (...) proof procedure that issues in T-sentence that remove all the metalanguage semantic terms from the right hand side and draw intuitively only on the content of the axioms, we can use the theory to interpret object language sentences. It further argues that if we ask what body of knowledge one must be in possession of to interpret the language, it turns out to be a set of propositions about the truth theory but not the axioms of the truth theory itself. This shows how to avoid the problem of the semantic paradoxes and the problem of vagueness. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in (...) Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

This article concentrates on a couple of semiotic approaches working out, on the one hand, the mediated character of reducing interpretative trajectories to the actual translation into the language of narratives (A. J. Greimas) or the language of textuality (F. Rastier), and, on the other, the direct, apparently unmediated passage to the visceral physicality of the verbal signifying system, which make semantic and syntactic components perfunctory to interpretation in a way (J. Kristeva). Greimassian universal narrative grammar dismantles signifying units, navigating (...) in the network of narrative utterances. Rastier's approach structures textual artifacts by unearthing semantic constituents crucial for semiotic analysis. Kristeva examines what is behind the curtain instead of sorting out the significance of the text's content as a special category and the possibility of procedure allowing its interpretation. These three authors are compared in the context of two approaches that come to grips with the author/reader pair. (shrink)

In this work we present an explainable system for emotion attribution and recommendation (called DEGARI (Dynamic Emotion Generator And ReclassIfier) relying on a recently introduced probabilistic commonsense reasoning framework (i.e. the TCL logic, see Lieto & Pozzato 2020) which is based on a human-like procedure for the automatic generation of novel concepts in a Description Logics knowledge base (see also Lieto et al. 2019, Chiodino et al. 2020 for other applications). In particular, in order to model human-like forms of concept (...) combinations, the TCL logic combines a probabilistic description logics of typicality with the HEAD-MODIFIER heuristics coming from cognitive semantics. In the context of our application of such framework, our system exploits the logic TCL to automatically generate novel commonsense semantic representations of compound emotions (e.g. Love as derived from the combination of Joy and Trust according to Plutchik’s theory of emotions, see Plutchik 2001). The generated emotions corresponds to prototypes, i.e. commonsense representations of given concepts, and have been used to reclassify emotion-related contents in a variety of artistic domains. We have tested our system in the context of the H2020 EU project SPICE for providing artistic recommendations of museum items in the Galleria di Arte Moderna (GAM) of Turin. The obtained results (reported in Lieto et al, 2021 and Lieto at al., to appear) show promising results for what concerns both the acceptance of the provided affective recommendation and the explainability associated to each suggestion made by the users. Here we discuss, the open problems and the lessons learned. -/- . (shrink)

The Neo-Fregean view individuates concepts at the level of Fregean senses. It is an internalist view according to which concepts can be described as ways of thinking that imply classifications and epistemic/normative inferences. In this paper, I argue that the Neo-Fregean view of concepts adequately characterises the targets of conceptual engineering (CE), which I depict as the activity of purposefully changing our concepts in order to change classifications and/or concept-implicit inferences. I discuss and reject rival views that either reduce the (...) targets of CE to linguistic meanings or classification procedures or characterise concepts in a psychological or concept-externalist manner. I argue that the Neo-Fregean view is a more encompassing and adequate characterisation of the targets of CE. (shrink)

In this paper I provide support for the view that at least some forms of adversariality in argumentation are legitimate. The support comes from Aristotle’s theory of illegitimate adversarial argumentation in dialectical contexts: his theory of eristic in his work On Sophistical Refutations. Here Aristotle develops non-epistemic standards for evaluating the legitimacy of dialectical procedures, standards which I propose can be understood in terms of the pragmatic notion of context as common ground. Put briefly, Aristotle makes the answerer’s meaning in (...) giving assent in dialectical contexts the basis for further moves in the game of dialectic. Moves which subvert the answerer’s meaning or do not solicit the answerer’s consent are marked as eristic, i.e. adversarial in a problematic sense. I conclude with remarks on what Aristotle’s theory may teach us about how semantic features relate to the normative evaluation of argumentation. (shrink)