Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...) verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)

They say that argumentative writing skills are best learned through writing argumentative essays. I say that while this is excellent practice for argumentative writing, an important exercise to practice structuring such essays and build critical thinking skills simultaneously is what I call the four-sentence paper. The exercise has the template They say..., I say..., one might object..., I reply... One might object that the assignment oversimplifies argumentative writing, stifles creativity, promotes an adversarial attitude, or that students can’t consider objections (...) well anyway. I reply that a simplified form of argumentative writing is fine for beginners, especially since the template is ubiquitous in philosophy; that any assignment template has room for creativity; that considering objections is consistent with good manners; and that despite some pitfalls of trying to defend a thesis and consider objections, students are capable of considering objections well with proper instruction and practice. (shrink)

The problem concerns quantifiers that seem to hover between universal and existential readings. I argue that they are neither, but a different quantifier that has features of each. NOTE the published paper has a mistake. I have corrected this in the version on this site. A correction note will appear in Analysis.

The Goedelian approach is discussed as a prime example of a science towards the origins. While mere self­referential objectification locks in to its own by­products, self­releasing objectification informs the formation of objects at hand and their different levels of interconnection. Guided by the spirit of Goedel's work a self­reflective science can open the road where old tenets see only blocked paths. “This is, as it were, an analysis of the analysis itself, but if that is done it forms the fundamental (...) of human science, as far as this kind of things is concerned.” G. Leibniz, ('Methodus Nova ...', 1673) . (shrink)

This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system). -- .

We take an argument of Gödel's from his ground‐breaking 1931 paper, generalize it, and examine its validity. The argument in question is this: "the sentence G says about itself that it is not provable, and G is indeed not provable; therefore, G is true".

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this (...) paper is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

Legal theorists have characterized physical evidence of brain dysfunction as a double-edged sword, wherein the very quality that reduces the defendant’s responsibility for his transgression could simultaneously increase motivations to punish him by virtue of his apparently increased dangerousness. However, empirical evidence of this pattern has been elusive, perhaps owing to a heavy reliance on singular measures that fail to distinguish between plural, often competing internal motivations for punishment. The present study employed a test of the theorized double-edge pattern using (...) a novel approach designed to separate such motivations. We asked a large sample of participants (N = 330) to render criminal sentencing judgments under varying conditions of the defendant’s mental health status (Healthy, Neurobiological Disorder, Psychological Disorder) and the disorder’s treatability (Treatable, Untreatable). As predicted, neurobiological evidence simultaneously elicited shorter prison sentences (i.e., mitigating) and longer terms of involuntary hospitalization (i.e., aggravating) than equivalent psychological evidence. However, these effects were not well explained by motivations to restore treatable defendants to health or to protect society from dangerous persons but instead by deontological motivations pertaining to the defendant’s level of deservingness and possible obligation to provide medical care. This is the first study of its kind to quantitatively demonstrate the paradoxical effect of neuroscientific trial evidence and raises implications for how such evidence is presented and evaluated. (shrink)

Reading the Phenomenology onto-grammatically means interpreting its constitutive forms of consciousness as grammatical iterations of the speculative proposition, where the subject-object relations can be read as dialogical encounters between subject and predicate, where the predicate “talks back”, creating a discursive space of hermeneutical ambiguity and openness, at play in the copula. The article begins with a brief presentation of Hegel’s general theory of language, as it pertains to the distinction between the linguistic sign (Zeichen) and the word (Wort), drawn from (...) his later writings, before applying these grammatical terms to the ontological reading of the speculative sentence, as presented in the Preface to the Phenomenology and discussed by Jere Surber. Then, the article puts its dialogical insights into practice, examining how the onto-grammatical reading of the speculative sentence plays out in the Phenomenology’s famous "lordship and bondage" (aka "master/slave") dialectic. (shrink)

In this paper Timothy Williamson’s argument that the knowledge norm of assertion is the best explanation of the unassertability of Morrean sentences is challenged and an alternative account of the norm of assertion is defended.

Bishop sentences such as “If a bishop meets a bishop, he blesses him” have long been considered problematic for the descriptivist (or E-type) approach of donkey anaphora (e.g. Evans, 1977; Heim, 1990; and Neale, 1990). Elbourne (2005) offers a situational descriptivist analysis that allegedly solves the problem, and furthermore extends its explanatory coverage to bishop sentence with coordinate subjects. However, I throw serious doubts on Elbourne’s analysis. Specifically, I argue that the purported solution is committed to the use of (...) unbound anaphora, and it cannot sustain the claimed empirical adequacy. (shrink)

Automated decision making for sentencing is the use of a software algorithm to analyse a convicted offender’s case and deliver a sentence. This chapter reviews the moral arguments for and against employing automated decision making for sentencing and finds that its use is in principle morally permissible. Specifically, it argues that well-designed automated decision making for sentencing will better approximate the just sentence than human sentencers. Moreover, it dismisses common concerns about transparency, privacy and bias as unpersuasive or (...) inapplicable. The chapter also notes that moral disagreement about theories of just sentencing are plausibly resolved by applying the principle of maximising expected moral choiceworthiness, and that automated decision making is better suited to the resulting ensemble model. Finally, the chapter considers the challenge posed by penal populism. The dispiriting conclusion is that although it is in theory morally desirable to use automated decision-making for criminal sentencing, it may well be the case that we ought not to try. (shrink)

How does fiction work? How can mere words create realities that exist only in the mind of the writer and the reader, yet seem so tangible in their realness? How can the first sentence of a novel transport one into a very real, yet purely objective, world — literally word-by-word? How do the subjective worlds of the writer and reader interact with the words on the page to create similar, yet always highly individualized, objective worlds? How can semiotics function (...) as a means to analyzing a written text in order to answer these questions about how the processes of writing and reading work? These, amongst others, are the questions explored in this paper, “Mrs. Dalloway and the Semiotics of a First Sentence”. In it I analyze Virginia Woolf ’s classic novel from a semiotic stance. Through exploring the semiotics of the novel’s first sentence, I attempt to show how we can read even the first nine words of a book and find ourselves transported to a whole, new, highly detailed world — the world of fiction. (shrink)

The chapter considers two semantic issues concerning will-sentences: Stalnaker’s Asymmetry and modal subordination in Karttunen-type discourses. The former points to a distinction between will and modal verbs, seeming to show that will does not license non-specific indefinites. The latter, conversely, suggests that will-sentences involve some kind of modality. To account for the data, the chapter proposes that will is semantically a tense, hence it doesn’t contribute a quantifier over modal alternatives; a modal feature, however, is introduced in the interpretation of (...) a will-sentence through a supervaluational strategy universally quantifying over possible futures. That this is not part of will’s lexical semantics is shown to have consequences that ultimately contribute to explain Stalnaker’s Asymmetry. Furthermore, that a modal quantification is present in the interpretation of a will-sentence is shown to imply the availability of modal subordination in Karttunen-type discourses. (shrink)

Evaluative sentences (moral judgments, expressions of taste, epistemic modals) are relative to the speaker's standards. Lately, a phenomenon has challenged the traditional explanation of this relativity: whenever two speakers disagree over them they contradict each other without being at fault. Hence, it is thought that the correction of the assertions involved must be relative to an unprivileged standard not necessarily the speaker's. I will claim instead that so far, neither this nor any other proposal has provided an explanation of the (...) phenomenon. I will point out several problems presented by them and I will hint to how this phenomenon could be explained by making minor adjustments to our semantic theory. Sentenças avaliativas (julgamentos morais, expressões de gosto, modos epistêmicos) são relativas aos padrões do falante. Recentemente, um fenômeno desafiou a explicação tradicional dessa relatividade: sempre que dois falantes discordam entre si, eles contradizem um ao outro sem estarem errados. Por isso, pensa-se que a correção das asserções envolvidas deve ser relacionada a um padrão desprovido de privilégio e não necessariamente ao padrão do falante. Eu sustentarei, ao contrário, que até agora nem esta nem alguma outra proposta forneceu uma explicação do fenômeno. Eu assinalarei diversos problemas apresentados por essas propostas e sugerirei o modo como este fenômeno poderia ser explicado ao fazer pequenos ajustes em nossa teoria semântica. (shrink)

In this article, I show why it is necessary to abolish the use of predictive algorithms in the US criminal justice system at sentencing. After presenting the functioning of these algorithms in their context of emergence, I offer three arguments to demonstrate why their abolition is imperative. First, I show that sentencing based on predictive algorithms induces a process of rewriting the temporality of the judged individual, flattening their life into a present inescapably doomed by its past. Second, I demonstrate (...) that recursive processes, comprising predictive algorithms and the decisions based on their predictions, systematically suppress outliers and progressively transform reality to match predictions. In my third and final argument, I show that decisions made on the basis of predictive algorithms actively perform a biopolitical understanding of justice as management and modulation of risks. In such a framework, justice becomes a means to maintain a perverse social homeostasis that systematically exposes disenfranchised Black and Brown populations to risk. (shrink)

This paper considers one of the most significant and controversial attempts to account for the meaning of pejoratives as lexical items, namely Hom and May’s. After outlining the theory, we pinpoint sets of pejorative sentences that come out true on their account and for which the question as to whether they are compatible with the view advocated by them (so-called Moral and Semantic Innocence) remains open. Helping ourselves to the standard model-theoretical framework Hom and May (presumably) work in, we prove (...) they are compatible with the view. Given that the issues of both the moral import of pejoratives and the practical effects of their utterance are not settled by the proof, we then highlight unwelcome moral and pragmatic implications for some of the pejorative sentences under scrutiny, thereby showing that the view, broadly understood, is not as morally and semantically innocuous as it is meant to be. (shrink)

This paper shows that Russell’s theory of descriptions gives the wrong se-mantics for definite descriptions occurring in questions and imperatives. Depending on how that theory is applied, it either assigns nonsense to per-fectly meaningful questions and assertions or it assigns meanings that di-verge from the actual semantics of such sentences, even after all pragmatic and contextual variables are allowed for. Given that Russell’s theory is wrong for questions and assertions, it must be wrong for assertoric state-ments; for the semantics of (...) ‘the phi’ obviously doesn’t vary depending on whether it occurs in a question or an assertion or a command. (shrink)

It is often thought that traditional recidivism prediction tools used in criminal sentencing, though biased in many ways, can straightforwardly avoid one particularly pernicious type of bias: direct racial discrimination. They can avoid this by excluding race from the list of variables employed to predict recidivism. A similar approach could be taken to the design of newer, machine learning-based (ML) tools for predicting recidivism: information about race could be withheld from the ML tool during its training phase, ensuring that the (...) resulting predictive model does not use race as an explicit predictor. However, if race is correlated with measured recidivism in the training data, the ML tool may ‘learn’ a perfect proxy for race. If such a proxy is found, the exclusion of race would do nothing to weaken the correlation between risk (mis)classifications and race. Is this a problem? We argue that, on some explanations of the wrongness of discrimination, it is. On these explanations, the use of an ML tool that perfectly proxies race would (likely) be more wrong than the use of a traditional tool that imperfectly proxies race. Indeed, on some views, use of a perfect proxy for race is plausibly as wrong as explicit racial profiling. We end by drawing out four implications of our arguments. (shrink)

A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".

In this article, I seek to answer the following cluster of questions: What would a characteristically African, and specifically relational, conception of a criminal trial’s final end look like? What would the Afro-relational approach prescribe for sentencing? Would its implications for this matter forcefully rival the kinds of penalties that judges in South Africa and similar jurisdictions typically mete out? After pointing out how the southern African ethic of ubuntu is well understood as a relational ethic, I draw out of (...) it a certain conception of reconciliation that I advance as a strong candidate for being the proper final end of a criminal trial. I argue that, far from requiring forgiveness, seeking reconciliation can provide strong reason to punish offenders. Specifically, a reconciliatory sentence is one that roughly has offenders reform their characters and compensate their victims in ways the offenders find burdensome, thereby disavowing the crime and tending to foster cooperation and mutual aid. I argue that this novel account of punishment is a prima facie attractive alternative to more familiar retributive and deterrence rationales, and that it entails that widespread practices such as imprisonment and mandatory minimum sentences are unjust. (shrink)

This essay addresses one of the open questions of proof-theoretic semantics: how to understand the semantic values of atomic sentences. I embed a revised version of the explanatory proof system of Millson and Straßer (2019) into the proof-theoretic semantics of Francez (2015) and show how to specify (part of) the intended interpretation of atomic sentences on the basis of their occurrences in the premises and conclusions of inferences to and from best explanations.

This study proposes a framework by which grammatically and syntactically sound sentences are classified through the perceptual measurement in noise of multilinguals and monolinguals, using an objective measure called SPERI and an interpretivist measure called SPIn, with results evaluated using Shortlist models and the BLINCS model. Hereby filling a knowledge gap on the perception of sentences that combine in varying levels of contextual meaning, linguistic load and cognitive load, this study used sentence clustering methods to find limitations of the (...) proposed framework in determining an absolute and accurate prediction of performance between sentences in the proposed different categories, with factors such as sentence predictability and word frequency taking precedence. There were unintended findings including a relationship between the number of languages spoken and performance, proficiency in other languages decreasing performance despite being an English Native, and how mistakes by multilinguals were more semantically and phonetically influenced than monolinguals. (shrink)

Traditionally, ‘that’-clauses occurring in attitude attributions are taken to denote the objects of the attitudes. Prior raised a famous problem: even if Frege fears that the Begriffsschrift leads to a paradox, it is unlikely that he fears a proposition, a sentence or what have you as the alleged object denoted by the ‘that’-clause. The usual way out is to say that ‘that’-clauses do not contribute the objects of the attitudes but their contents. I will show that, if we accept (...) this answer, either we’d better stop working on attitude attributions or we’d better work harder on them. (shrink)

In this paper I discuss the Newman problem in the context of contemporary epistemic structural realism (ESR). I formulate Newman’s objection in terms that apply to today’s ESR and then evaluate a defence of ESR based on Carnap’s use of Ramsey sentences and Hilbert’s ε-operator. I show that this defence improves the situation by allowing a formal stipulation of non-structural constraints. However, it fails short of achieving object individuation in the context of satisfying the Ramsified form of a theory. Thus, (...) while limiting the scope of Newman’s argument, Carnap sentences do not fully solve the problem. (shrink)

This paper examines the practice of using predictive systems to lengthen the prison sentences of convicted persons when the systems forecast a higher likelihood of re-offense or re-arrest. There has been much critical discussion of technologies used for sentencing, including questions of bias and opacity. However, there hasn’t been a discussion of whether this use of predictive systems makes sense in the first place. We argue that it does not by showing that there is no plausible theory of punishment that (...) supports it. (shrink)

The paper defends a variant of the material implication approach to the meaning of conditional sentences against some arguments that are considered to be widely subscribed to and/or important in the philosophical, psychological and linguistic literature. These arguments are shown to be wrong, debatable, or to miss their aim if the truth conditions defining material implication are viewed as determining nothing but the denotation of conditional sentences and if the function of conditional sentences in deduction (logic) is focused on rather (...) than in inferencing (reasoning). It is shown that some ‘paradoxes of material implication’ are due to inconsistent premises of deductions introduced by semantic relations between clauses constituting the premises, a fact which does not invalidate the approach. Other ‘paradoxes’ are shown to arise because they are based on uninformative deductions, violating a basic pragmatic principle. In addition, the paper introduces the distinction between the set of possible states of a mental model of the actual world and of alternative worlds. It is argued that material implication determines the denotation of an indicative conditional as a subset of the former set and the denotation of a subjunctive conditional as a subset of the latter set, thus unifying these two types of conditionals. (shrink)

Based on the notion of a trope, this paper gives a novel analysis of identificational sentences such as 'this is Mary','this is a beautiful woman', 'this looks like Mary', or 'this is the same lump of clay, but not the same statue as that'.

In English, in order to speak about Arthur’s attitudes, we use sentences like “Arthur believes that natural language is messy”. For sentences of this kind we have a standard theory, according to which the ‘that’-clause ‘that natural language is messy’ denotes a proposition. As Prior showed for the first time, the standard theory appears to be at odds with some linguistic data. Geach and Prior both assumed that linguistic data are to be taken as reliable guides to a correct semantic (...) account and I will start by raising some worries concerning their methodology. Because of these data, Prior and Geach suggested some non-standard accounts. I will then show that if we take linguistic data seriously, their non-standard accounts do not fare any better than the standard theory. My general conclusion will thus not only be that Prior’s and Geach’s methodology is disputable, but also that their conclusions do not seem to follow even if we grant the reliability of their methodology. (shrink)

The influential proposal that the analytical component of a theory is captured by its ‘Carnap sentence’ is critically scrutinized. A counterexample which makes the suggestion problematic is presented.

In the last forty years Dummett, Hanks, Künne, and Bobzien have claimed that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question [Satzfrage] was not a thought [Gedanke] ((Dummett 1981: 307–308); (Hanks 2007: 142–143); (Künne 2010: 427–429); (Bobzien 2021: 163–164)). Recently, Textor has claimed that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question was not a question [Frage] (Textor 2021: 227 fn.2). I think it is (...) possible that when Frege wrote ‘Über Sinn und Bedeutung’, he thought that the sense of a sentence-question was a question and a thought. To show that this possibility should not be overlooked, I have written a dialogue in which Frege responds to Dummett, Hanks, Künne, Bobzien, and Textor. -/- Bobzien seems to think that when Frege wrote ‘Die Verneinung’, he thought that the sense of a sentence-question was not a question (Bobzien 2021: 163–165). I think it is possible that when Frege wrote ‘Die Verneinung’, he thought that the sense of a sentence-question was a question and a thought. Hence, I have also written the dialogue to show that this possibility should not be overlooked either. (shrink)

In Tractatus, Wittgenstein held that there are null sentences – prominently including logical truths and the truths of mathematics. He says that such sentences are without sense (sinnlos), that they say nothing; he also denies that they are nonsensical (unsinning). Surely it is what a sentence says which is true or false. So if a sentence says nothing, how can it be true or false? The paper discusses the issue.

Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...) Gödel’s sentence becomes neither true nor false. The similarity of this outcome with Goldstein and Gaifman’s solution of the Liar paradox, which is discussed in section 4, is emphasized. Section 5 returns to the definition of meaningfulness; the meaninglessness of certain sentences with empty subjects and of the Liar sentence is discussed. The objective of this paper is to show how all of the above-mentioned concepts are interrelated. (shrink)

In this essay, I follow the lead of recent scholarship in Saussure linguistics and critically examine the Saussurean doctrine associated with the Course in General Linguistics, which later became a hallmark of structuralism. Specifically, I reconstruct the history of the concluding sentence in the Course which establishes the priority of la langue over everything deemed external to it. This line assumed the status of an oft-cited ‘famous formula’ and became a structuralist motto. The ‘famous formula’ was, however, freely inserted (...) by the editors of the Course who effectively ghostwrote the book after Saussure’s death, and authored a series of early book-reviews of the same text in dedicated scholarly venues. I argue that the editorial success turning their vision of Saussure’s teaching into official doctrine was enabled in part by the dominant social structures regulating twentieth-century European academia. (shrink)

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ (PG, p.346) There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The (...) above quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.

I discuss what I call practical Moore sentences: sentences like ‘You must close your door, but I don’t know whether you will’, which combine an order together with an avowal of agnosticism about whether the order will be obeyed. I show that practical Moore sentences are generally infelicitous. But this infelicity is surprising: it seems like there should be nothing wrong with giving someone an order while acknowledging that you do not know whether it will obeyed. I suggest that this (...) infelicity points to a striking psychological fact, with potentially broad ramifications concerning the structure of norms of speech acts: namely, when giving an order, we must act as if we believe we will be obeyed. (shrink)

This paper replies to Himmelreich's ‘The Paraphrase Argument Against Collective Actions’ [2017], which presents three putative counterexamples to the multiple agents analysis of plural action sentences. The paper shows that the argument from the first example, the discursive dilemma, fails because it relies crucially on a simplification of the target analysis, and that the others don't bear on the question because they turn out on examination to be about individual rather than group action sentences.

The purpose of this paper is to communicate - as a proposal - a general method of assigning a 'truthmaker' to any 1st order sentence in each of its models. The respective construct is derived from the standard model theoretic (recursive) satisfaction definition for 1st order languages and is a conservative extension thereof. The heuristics of the proposal (which has been somewhat idiosyncratic from the current point of view) and some more technical detail of the construction may be found (...) in my article on part I of Spinoza's 'ethica, ordine geometrico demonstrata', which is the context within which I elaborated the assignment. But this context need not be repeated here, the presentation of the truthmaker assignment will be comprehensible to anybody with solid basic knowledge in 1st order model theory, anything used is standard and no advanced techniques are required. (shrink)

Proposition and sentence are two separate entities indicating their specific purposes, definitions and problems. A proposition is a logical entity. A proposition asserts that something is or not the case, any proposition may be affirmed or denied, all proportions are either true (1’s) or false (0’s). All proportions are sentences but all sentences are not propositions. Propositions are factual contains three terms: subject, predicate and copula and are always in indicative or declarative mood. While sentence is a grammatical (...) entity, a unit of language that expresses a complete thought; a sentence may express a proposition, but is distinct from the proposition it may be used to express: categories, declarative sentences, exclamatory, imperative and interrogative sentences. Not all sentences are propositions, propositions express sentence. Sentence is a proposition only in condition when it bears truth values i.e. true or false. We use English sentences governed by imprecise rule to state the precise rules of proposition. In logic we use sentence as logical entity having propositional function but grammatical sentences are different from logical sentences while the former are having only two divisions namely subject and predicate and may express wishes, orders, surprise or facts and also have multiple subjects and predicates and the latter must be in a propositional form which states quantity of the subject and the quality of the proposition and multiple subjects and multiple predicate make the proposition multiple. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being (...) true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

Contrary to nouns and verbs that either do not include a co-positing of parts, including nouns and some verbs, or if they are, their parts do not significate separately, a sentence (λόγος) is a ‘significant portion of speech by co-positing, its parts signify something separately, though not as a positive or negative judgment but as utterance.’ (OI ., I, 4, 16b26-28). Therefore, every utterance in language that i) includes parts, ii) its signification is based on the co-positing of its (...) parts, iii) each of its parts is separately significant but iv) the signification of its parts is the signification of an utterance and not a judgment, is a sentence. This definition distinguishes a sentence from: a) Nouns: because they do not have parts; b) Verbs: because they either do not have parts or if they have, their parts do not significate separately; c) Those co-positings of words whose significance is not based on their co-positing. Thus a co-positing like ‘wall tree house’ is not a sentence because it has no significance on the basis of its co-positing; d) Those co-positings that the signification of at least some of their parts is the signification of judgments. Thus, ‘Socrates is from Athens and is a philosopher’ is not a sentence because at least one of its parts, e.g. ‘Socrates is from Athens’ signifies a judgment. Those sentences that either of truth or falsity belongs to them are propositions (ἀπόφανσις or λόγος ἀπόφαντικὸς). (OI., I, 4, 17a2-3) It is this and only this kind of sentence that is the subject of study in philosophy. (OI., I, 4, 17a5-7) The primary forms of a proposition are, firstly, an affirmation (κατάφασις) and then a negation (ἀπόφασις). (OI., I, 4, 17a8-9) To have an affirmation or a denial and, thus, a proposition, what firstly is necessary is a verb or the tense of a verb (OI, I, 4, 17a9-12; I, 10, 19b12-13; OI, I, 4, 16b28-30) and a noun (OI, I, 10, 19b10-12). Aristotle draws a contrast between single and plural proposition: a) Single proposition: a proposition that ‘indicate a single fact, or the conjunction of the parts of which results in unity.’ (OI., I, 5, 17a15-16) b) Plural propositions: a proposition that ‘are separate and many in number, which indicate many facts, or whose parts have no conjunction.’ (OI., I, 5, 17a16-17) He also differentiates between simple and composite propositions (OI, I, 5, 17a20-22): a) Simple proposition: ‘that which asserts or denies something of something’; b) Composite propositions: ‘that which is compounded of simple propositions.’ A simple (ἁπλῆ) proposition is a statement about the belonging or not belonging of something (OI, I, 5, 17a22-24). Affirmation and denial are indeed kinds of simple proposition, one affirming the belonging and the other not belonging. An affirmation or denial may be single or non-single. A single affirmation or denial ‘signifies some one fact about some one subject. This singularity is destroyed neither by the universality of subject nor by the universal character of the statement. The only thing that destroys this singularity is that one part signifies more than one thing, which makes the proposition more than one proposition (OI, I, 8, 18a13-27). In other words, neither ‘predication of one thing of many subjects’ nor ‘many things of the same subject’ results in a unitary proposition. (OI., II, 11, 20b13-16) There is also another cause that might destroy the unity of predicate and thus the unity of proposition, namely when one of the parts of the predicate is implicit in the other. Thus, e.g. animal-man does not form a unity because the notion ‘animal’ is implicit in ‘man.’ (OI., II, 11, 21a16-18) The following are characteristics of propositions: 1. That about which an affirmation signifies something is a noun, whether definite or indefinite. (OI., I, 10, 19b5-12) Moreover, there can be no affirmation or denial without a verb. (OI., I, 10, 19b12-19) Therefore, a proposition must involve at least a noun and a verb. 2. Contrary propositions: since both belonging and not belonging of something to something is possible, we are able to make a negative proposition out of an affirmative one and vice versa. (OI., I, 5, 17a26-31) Therefore, ‘every affirmation has an opposite denial’ and vice versa. (OI., I, 6, 17a31-33) The contradictory of each proposition is made by changing the positivity or negativity of the verb ‘to be’ to its opposite but not by changing the subject to its opposite. Thus, the contradictory of ‘man is white’ is ‘man is not white’ and not ‘not-man is white.’ (OI., II, 11, 21a38-b5) What happens in the mentioned wrong form of contradictory propositions is that they change the subject while the denial must be the contrary of the affirmation about the same subject. (cf. OI., II, 14, 24b1-6) This is made plain in propositions involving a verb other than ‘to be’. What must be changed in these propositions is the verb and not the noun or the subject. Thus, the contradictory of ‘Socrates runs’ is ‘Socrates does not run’ and not ‘not-Socrates runs.’ 3. Conversion possible: ‘Out of conversion (μετατιθεμένου) of the name and the verb, the same affirmation and denial is generated. (OI., I, 10, 20b10-12) In other words, the two affirmations or denials ‘signify the same thing.’ (OI, I, 10, 20b1-2) . (shrink)

Consider the opening sentence of Tolkien’s The Hobbit: In a hole in the ground there lived a hobbit. By writing this sentence, Tolkien is making a fictional statement. There are two influential views of the nature of such statements. On the pretense view, fictional discourse amounts to pretend assertions. Since the author is not really asserting, but merely pretending, a statement such as Tolkien’s is devoid of illocutionary force altogether. By contrast, on the alternative make-believe view, fictional discourse (...) prescribes that the reader make-believe the content of the statement. In this paper, we argue that neither of these views is satisfactory. They both fail to distinguish the linguistic act of creating the fiction, for instance Tolkien writing the sentence above, from the linguistic act of reciting it, such as reading The Hobbit out loud for your children. As an alternative to these views, we propose that the essential feature of the author’s speech act is its productive character, that it makes some state of affairs obtain in the fiction. Tolkien’s statement, we argue, has the illocutionary force of a declaration. (shrink)

The analytic/synthetic distinction can be conceived from two points of view: from within or from without; from the perspective of one's own language or from the perspective of the language of others. From without, the central question is which sentences of a foreign language are to be classified as analytic. From within, by contrast, the question concerning the synthetic and the analytic acquires a normative dimension: which sentences am I not permitted to reject—if I want to avoid talking nonsense? Both (...) perspectives on analytic sentences do not mutually exclude but supplement and illuminate each other. In "Two Dogmas", Quine's criticism of the analytic/synthetic distinction comes from within, whereas in Word and Object, Quine repeats his earlier criticism from without. His criticism is directed against Carnap's views on our understanding of theoretical terms. I challenge Quine's criticism in both of its versions and provide two definitions for analyticity that are immune to Quine's arguments. Using the first of these definitions (the one from without) I try to show how it is possible to distinguish (genuine) belief revision from linguistic change—even in case of a scientific revolution. (shrink)

Serious actualists take it that all properties are existence entailing. I present a simple puzzle about sentence tokens which seems to show that serious actualism is false. I then consider the most promising response to the puzzle. This is the idea that the serious actualist should take ordinary property-talk to contain an implicit existential presupposition. I argue that this approach does not work: it fails to generalise appropriately to all sentence types and tokens. In particular, it fails to (...) capture the right distinctions we ought to make between what I call _typographical sentence types_—an interesting and previously undiscussed class of fine-grained sentence types which are partially individuated by their typography, or how they look when written out. (shrink)

We demonstrate that, in itself and in the absence of extra premises, the following argument scheme is fallacious: The sentence A says about itself that it has a property F, and A does in fact have the property F; therefore A is true. We then examine an argument of this form in the informal introduction of Gödel’s classic (1931) and examine some auxiliary premises which might have been at work in that context. Philosophically significant as it may be, (...) that particular informal argument plays no rôle in Gödel’s technical results. Going deeper into the issue and investigating truth conditions of Gödelian sentences (i.e., those sentences which are provably equivalent to their own unprovability) will provide us with insights regarding the philosophical debate on the truth of Gödelian sentences of systems—a debate which goes back to Dummett (1963). (shrink)