This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, (...) both logically and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

In PI 189, Wittgenstein's interlocutor asks, ‘But are the steps then not determined by the algebraic formula?’. Wittgenstein responds, ‘The question contains a mistake’. What is the mistake contained in the interlocutor's question? Wittgenstein's elaboration is neither explicit nor its intended upshot transparent. In this paper, I offer a reading on which the interlocutor's question arises from illicitly crossing different pictures of ‘determination’. I begin by working through Wittgenstein's machine analogy in PI 193, which illustrates picture‐crossing in our ways (...) of talking about a machine. Using the lessons from this analogy, I show how the interlocutor's ‘mistake’ can be diagnosed in similar terms: their confusion about the power of a rule to determine its applications rests on mistakenly crossing a behavioural and a mathematical sense of ‘determine’—thereby concocting a mystifying picture of rule‐following. (shrink)

Abstract This paper offers an appraisal of Phillip Pettit's approach to the problem how a merely finite set of examples can serve to represent a determinate rule, given that indefinitely many rules can be extrapolated from any such set. I argue that Pettit's so-called ethnocentric theory of rule-following fails to deliver the solution to this problem he sets out to provide. More constructively, I consider what further provisions are needed in order to advance Pettit's general approach to the problem. (...) I conclude that what is needed is an account that, whilst it affirms the view that agents' responses are constitutively involved in the exemplification of rules, does not allow such responses the pride of place they have in Pettit's theory. (shrink)

The article contains a critical analysis of the skeptical solution to the rule- following problem. The skeptical solution denies the existence of “superlative” R-facts that would make statements of the form “P means R by ‘+’ ” true. The role of the sources for the meaning of ‘+’ here is played by the patterns of solidarity behavior of members of some community to which P belongs. The correct use of ‘+’ would be one that is approved by the competent majority (...) of this community, and there can be no other sense in which it would be correct or wrong. Boyd’s hypothesis denies the communal character of the ‘+’ meaning. While there are no “superlative” R-facts, there should be C-facts not about the R as the standard that P or its community follows in their practice of using ‘+’, but about whether they do it correctly. The proof of the Boyd hypothesis is based on the example of an imaginary Ω-community, whose agents use a finite set of simple symbols for the needs of their arithmetic: ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’. Each symbol denotes a subset of identical, from the Ω-community point of view, numerical values. The symbol ‘A’ is used, for ex- ample, for a subset of the natural numbers 1, 10, 19, 28, 37, 46, etc.; ‘B’ for 2, 11, 20, 29, 38, 47, etc.; ‘C’ for 3, 12, 21, 30, 39, 48, etc. The Ω-community’s arithmetic uses the only local function ⊕ whose range of values forms a finite set of mathematical propositions {α} that are true. The Ω-community’s arithmetic, like our own, is open to many skeptical challenges. Is there a fact that determines the meaning of ‘⊕’? What do agents do when they calculate with ‘⊕’ (say, solve examples ‘A⊕B = ?’, ‘C⊕E=?’, etc.)? Do they Add, Badd or Dadd? To answer them would require a “superlative” R-fact. For the calculation practice with ‘⊕’, it could be a certain R-fact that determines the only possible order for the sequence of numerals ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’ such that {α} is true. An analysis of the calculation practice using the local arithmetic function ⊕ shows that for it there are no such R-facts that would determine the only correct standard R – even if the agents in the Ω-community were trained in such calculations on a full set of cases for the application of that function. However, for such practice there are C-facts (independent in their existence from R-facts) that make it possible to distinguish between what seems to be right and what is right. The solitary agent P and the Ω-community are in the same position regarding the knowledge of C-facts. The Ω-community’s point of view has no advantage in matters of C-facts knowledge over the solitary agent P’s point of view. The Ω-community arithmetic shows that if a solitary agent P had the suitable knowledge of C-facts about the practice of calculations with ‘⊕’, it would allow him/her to disagree with the not correct answers of other members of the community even when they would constitute an absolute majority. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the (...) categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

The level of enjoyment in participating in sports activities is one component that causes young athletes to decide to stop or become more motivated to pursue sports activities. Practicing and participating in competitions are the main activities in sports coaching interactions towards optimal performance. This study aims to determine the effect of modifying the match rules implemented in youth soccer competitions on the level of enjoyment of players. Using an experimental method with 20 soccer schools participating in a competition (...) with modified game rules. Players registered by his team amounted to an average of 13.8 players aged 9-12 years. The number of players who are willing to fill out the pleasure level questionnaire is 238 players. Each player was asked to fill out a questionnaire before and after the competition, the questionnaire was analyzed using the mean and percentage test technique. The results of data analysis showed the average score before participating in the competition was 4.10 while after participating in the competition it was 4.47, which means an increase of 8.88%. The results showed that the level of enjoyment of the players increased after participating in the competition. Modification of the rule of the game in competition affects the level of enjoyment of players in the interaction of youth soccer coaching. Coaches, administrators, and match organizers are expected to have a positive paradigm of thinking and policy making towards the organization of competitions for young soccer players. (shrink)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett (...) and his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

Free trade agreements are about reducing tariffs, market access in services, protection of intellectual property rights, streamlining customs procedures, trade remedy measures, and dispute settlement mechanism. Equally important if not even more important than these provisions is the designation of rules of origin. Many benefits can be lost if restrictive rules of origin are incorporated. Rules of origin are supposed to be straightforward and easy-to-follow methods used to determine origin of imported goods. The policy question that arises (...) is how to improve trade integration among Arab countries through more effective rules of origin. (shrink)

Traditional rule consequentialism faces a problem sometimes called the ideal world objection—the worry that by looking only at the consequences in worlds where rules are universally adhered to, the theory fails to account for problems that arise because adherence to rules in the real world is inevitably imperfect. In response, recent theorists have defended sophisticated versions of rule consequentialism which are sensitive to the consequences in worlds with less utopian levels of adherence. In this paper, I argue that (...) these attempts underestimate the problem they are designed to avoid—the worry about ideal worlds is only one manifestation of a deeper and more general problem, the distant world objection, which threatens not only the sophisticated revisions of rule consequentialism, but any view which determines what we ought to do by evaluating worlds that differ from ours in more than what is up to us. (shrink)

Rule-consequentialists tend to argue for their normative theory by claiming that their view matches our moral convictions just as well as a pluralist set of Rossian duties. As an additional advantage, rule-consequentialism offers a unifying justification for these duties. I challenge the first part of the ruleconsequentialist argument and show that Rossian duties match our moral convictions better than the rule-consequentialist principles. I ask the rule-consequentialists a simple question. In the case that circumstances change, is the wrongness of acts determined (...) by the ideal principles for the earlier circumstances or by the ideal ones for the new circumstances? I argue that whichever answer the rule-consequentialists give the view leads to normative conclusions that conflict with our moral intuitions. Because some set of Rossian duties can avoid similar problems, rule-consequentialism fails in the reflective equilibrium test advocated by the rule-consequentialists. (shrink)

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)

This paper is about what we call Deontically-flavored Nominal Constructions (DNCs) in English, such as "No ice cream" or "Dogs on leash only". DNCs are often perceived as commands and have been argued to be a type of non-canonical imperative, much like root infinitives in German or Russian. We argue instead that DNCs at their core are declaratives that cite a rule but can be used performatively in the right context. We propose that DNCs contain an elided deontic modal, i.e., (...) allowed, whose presence explains their distributional restrictions and interpretational properties. Among other things, we speculate on the licensing conditions of DNCs (the presence of 'only' or the negative determiner 'no'), suggesting that these are tied to the properties of discourses in which rules can be used naturally. (shrink)

Predicativists hold that proper names have predicate-type semantic values. They face an obvious challenge: in many languages names normally occur as, what appear to be, grammatical arguments. The standard version of predicativism answers this challenge by positing an unpronounced determiner in bare occurrences. I argue that this is a mistake. Predicativists should draw a distinction between two kinds of semantic type—underived semantic type and derived semantic type. The predicativist thesis concerns the underived semantic type of proper names and underdetermines a (...) view about the semantic type of bare occurrences. I’ll argue that predicativists should hold that bare names are derived individual-denoting expressions. I end by considering what this result means for the relationship between predicativism and other metalinguistic theories of names. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the (...) categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Vann McGee has recently argued that Belnap’s criteria constrain the formal rules of classical natural deduction to uniquely determine the semantic values of the propositional logical connectives and quantifiers if the rules are taken to be open-ended, i.e., if they are truth-preserving within any mathematically possible extension of the original language. The main assumption of his argument is that for any class of models there is a mathematically possible language in which there is a sentence true in just (...) those models. I show that this assumption does not hold for the class of models of classical propositional logic. In particular, I show that the existence of non-normal models for negation undermines McGee’s argument. (shrink)

Big Data is a large-sized and complex dataset, which cannot be managed using traditional data processing tools. Mining process of big data is the ability to extract valuable information from these large datasets. Association rule mining is a type of data mining process, which is indented to determine interesting associations between items and to establish a set of association rules whose support is greater than a specific threshold. The classical association rules can only be extracted from binary data (...) where an item exists in a transaction, but it fails to deal effectively with quantitative attributes, through decreasing the quality of generated association rules due to sharp boundary problems. In order to overcome the drawbacks of classical association rule mining, we propose in this research a new neutrosophic association rule algorithm. The algorithm uses a new approach for generating association rules by dealing with membership, indeterminacy, and non-membership functions of items, conducting to an efficient decision-making system by considering all vague association rules. To prove the validity of the method, we compare the fuzzy mining and the neutrosophic mining. The results show that the proposed approach increases the number of generated association rules. (shrink)

It is often argued that inferential role semantics (IRS) entails semantic holism as long as theorists fail to answer the question about which inferences, among the many, are meaning-constitutive. Since analyticity, as truth in virtue of meaning, is a widely dismissed notion in indicating which inferences determine meaning, it seems that holism follows. Semantic holism is often understood as facing problems with the stability of content and many usual explanations of communication. Thus, we should choose between giving up IRS, to (...) avoid these holistic entailments, and defending holism against this charge, to rescue IRS. I try to pursue the second goal by analyzing certain patterns of counterfactual reasoning. Wilfrid Sellars and Robert Brandom claim that, to defend IRS, content-constitutive inferences are those counterfactually robust. While it is difficult to assess the goodness of such a view, it nonetheless entails that counterfactually non-robust inferences (which I call “modally ruled out inferences”) are not content-constitutive. If this is true, and if we take certain remarks about the grasp of concepts on board, there is a way to restrict the scope of the holism entailed by IRS to the extent of reshaping problems with the stability of content. (shrink)

This article responds to a case-based argument by Mark Richard that rule of reference is not essential to meaning. It objects that the argument requires shifting between understanding the relevant term in the case, ‘marriage,’ as a determinable, in order to support one premise, and a determinate, in order to support another. On no univocal interpretation can both premises be made true.

ABSTRACT If acting morally can be viewed as acting consistently with a moral principle or rule, then being a person with moral integrity can be viewed as consistently applying moral principles or rules across different types of situations. We advance a view of moral integrity that incorporates three distinct, but interrelated, types of moral consistency: cognitive, emotional and motivational moral consistency. Our approach is based on Self-Determination Theory, a motivational theory that can explain when a moral rule becomes (...) the primary motive for behavior. We argue that moral integrity is achieved when a person acts on the basis of an internal moral system of principles, emotions and motives and provide an account of the way that it develops during a person’s interaction with the environment. (shrink)

Terry Horgan and John Tienson have suggested that connectionism might provide a framework within which to articulate a theory of cognition according to which there are mental representations without rules (RWR) (Horgan and Tienson 1988, 1989, 1991, 1992). In essence, RWR states that cognition involves representations in a language of thought, but that these representations are not manipulated by the sort of rules that have traditionally been posited. In the development of RWR, Horgan and Tienson attempt to forestall (...) a particular line of criticism, theSyntactic Argument, which would show RWR to be inconsistent with connectionism. In essence, the argument claims that the node-level rules of connectionist networks, along with the semantic interpretations assigned to patterns of activation, serve to determine a set of representation-level rules incompatible with the RWR conception of cognition. The present paper argues that the Syntactic Argument can be made to show that RWR is inconsistent with connectionism. (shrink)

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between (...) schemata of first order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

This chapter reviews fundamental ethical controversy surrounding the ongoing effort to revise the Uniform Determination of Death Act in the United States. Instead of focusing on the process of the revision itself, the chapter explores the underlying ethical debate over brain death that has been ongoing for many decades and finally culminated in this revision. Three issues are focused: the requirement for consent and personal exemptions before applying brain death for the diagnosis of death; redefining the areas of the (...) brain that have ceased to function in the definition of brain death; and codifying the American Academy of Neurology as the authority to issue the standards of the diagnosis of brain death. The chapter concludes that allowing the personal choice of death determination gives a pragmatic compromise to the disputed definition and practice of diagnosing brain death. So long as all risks and imperfections of the diagnosis are accepted through the consenting process, there is nothing ethically objectionable to continuing the current practice of diagnosing brain death as a successful tool to facilitate heart-beating organ donation without violating the dead-donor rule. By contrast, precluding personal choice and imposing legal restrictions to consent and exemptions would further erode public trust. (shrink)

Pufendorf makes a clear distinction between the physical constitution of human beings and their value as human beings, stressing that the latter is justified exclusively by the regular use of the free will. According to Pufendorf, the regular use of free will requires certain inventions (divine as well as human) imposed on the free will and called moral entities. He claims that these inventions determine the moral quality of a human being as well as the standards according to which human (...) beings and their actions are able to be judged. This article examines the normative aspects of Pufendorf’s concepts of moral value and moral estimation in regard to the epistemological question of the accessibility of moral entities for human beings. In the first part, it reconstructs Pufendorf’s doctrine of moral entities and the place of moral estimation in this doctrine. In the second part, it presents Pufendorf’s account of the moral philosophy as a science in order to explain his theory of moral normativity as imposed, and the role of a person in regard to the own moral status. In the last part, it illustrates some consequences in regard to the problem of slavery in Pufendorf. (shrink)

The author considers the model-theoretic character of proofs and disproofs by means of attempted counterexample constructions, distinguishes this proof format from formal derivations, then contrasts two approaches to semantic tableaux proposed by Beth and Lambert-van Fraassen. It is noted that Beth's original approach has not as yet been provided with a precisely formulated rule of closure for detecting tableau sequences terminating in contradiction. To remedy this deficiency, a technique is proposed to clarify tableau operations.

In this perspective paper, I tried to explain that what will be the possible prospect of multiple functions in one and another through the chain rule of differentiation? The chain rule is a formula to compute the derivative of the functional composition of two or more functions. The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. The chain rule (...) in that what changes I noted, how it can be modified to reduce the differentiation process of multiple functions in one and another and implementing that process in the inverse of multiple functions in one and another, further proceedings them through the chain rule of differentiation with all prospects. Here I claim that the differentiation’s chain rule is not changed but the sequences of finding the derivative of multiple functions are changed. (shrink)

This dissertation provides a careful reading of the later Wittgenstein’s philosophy of mathematics centered around three major themes: reality, determination, and infinity. The reading offered gives pride of place to Wittgenstein’s therapeutic conception of philosophy. This conception views questions often taken as fundamental in the philosophy of mathematics with suspicion and attempts to diagnose the confusions which lead to them. In the first essay, I explain Wittgenstein’s approach to perennial issues regarding the alleged reality to which mathematical truths or (...) propositions correspond. Wittgenstein diagnoses exotic pictures of mathematical reality as stemming from misleading analogies formed across empirical and mathematical propositions. The second essay explains Wittgenstein’s treatment of perplexity regarding the ability of a mathematical rule to determine its applications in advance. This too is found to depend on a misleading analogy, in this case across behavioral and mathematical senses of ‘determine’. The third and final essay discusses Wittgenstein’s general critical approach to “the infinite”. Philosophical perplexity about infinity is shown to depend on the verbal imagery regularly associated with proofs and their power to take hold of one’s imagination. Wittgenstein dampens the imaginative excesses often associated with “the infinite” by offering a sober redescription of Cantor’s famous method of diagonalization. (shrink)

In this article, the authors try to answer the following questions: How can an object/instance seen for the first time extend a category or update a concept? How is it possible to determine the reference of a concept that represents a behaviour? In the first case, the authors discuss the learning of inferential linguistic competence used to update a concept through an approach based on prototype theory. In the second case, the authors discuss the learning of referential linguistic competence used (...) to determine the reference of a concept (i.e., determination of an actual behaviour) through an approach based on embodied cognition. The authors show how combining prototype-based and embodied categorization in Wittgenstein’s rule-following praxis (the individual and community dimension), linguistic learning of a concept (inferential competence), and determination of its reference (referential competence) can be traced back to the same model. Keywords Action, Categorization, Embodied Cognition, Embodiment, Linguistic Inferential Competence, Linguistic Referential Competence, Perception, Prototype Theory, Reference, Sign. (shrink)

In their Introduction to Logic, Copi and Cohen suggest that students construct a formal proof by "working backwards from the conclusion by looking for some statement or statements from which it can be deduced and then trying to deduce those intermediate statements from the premises. What follows is an elaboration of this suggestion. I describe an almost mechanical procedure for determining from which statement(s) the conclusion can be deduced and the rules by which the required inferences can be made. (...) This method is designed to forestall the quandary in which many beginners find themselves: not knowing how to get started. (shrink)

This essay (a revised version of my undergraduate honors thesis at Stanford) constructs a theory of analogy as it applies to argumentation and reasoning, especially as used in fields such as philosophy and law. The word analogy has been used in different senses, which the essay defines. The theory developed herein applies to analogia rationis, or analogical reasoning. Building on the framework of situation theory, a type of logical relation called determination is defined. This determination relation solves a (...) puzzle about analogy in the context of logical argument, namely, whether an analogous situation contributes anything logically over and above what could be inferred from the application of prior knowledge to a present situation. Scholars of reasoning have often claimed that analogical arguments are never logically valid, and that they therefore lack cogency. However, when the right type of determination structure exists, it is possible to prove that projecting a conclusion inferred by analogy onto the situation about which one is reasoning is both valid and non-redundant. Various other properties and consequences of the determination relation are also proven. Some analogical arguments are based on principles such as similarity, which are not logically valid. The theory therefore provides us with a way to distinguish between legitimate and illegitimate arguments. It also provides an alternative to procedures based on the assessment of similarity for constructing analogies in artificial intelligence systems. (shrink)

This Essay analyzes an essay by H. L. A. Hart about discretion that has never before been published, and has often been considered lost. Hart, one of the most significant legal philosophers of the twentieth century, wrote the essay at Harvard Law School in November 1956, shortly after he arrived as a visiting professor. In the essay, Hart argued that discretion is a special mode of reasoned, constrained decisionmaking that occupies a middle ground between arbitrary choice and determinate rule application. (...) Hart believed that discretion, soundly exercised, provides a principled way of coping with legal indeterminacy that is fully consistent with the rule of law. This Essay situates Hart’s paper – Discretion – in historical and intellectual context, interprets its main arguments, and assesses its significance in jurisprudential history. In the context of Hart’s work, Discretion is notable because it sketches a theory of legal reasoning in depth, with vivid examples. In the context of jurisprudential history, Discretion is significant because it sheds new light on long-overlooked historical and theoretical connections between Hart’s work and the Legal Process School, the American jurisprudential movement dominant at Harvard during Hart’s year as a visiting professor. Hart’s Discretion is part of our jurisprudential heritage, advancing our understanding of legal philosophy and its history. (shrink)

Cusanus, Abstract As a rule Cusanus is interpreted in a theological way, under strong theological presuppositions and within the range of religion. This may be quite understandable since he was a cardinal and had important functions in the Papal States. But, what are the results, when we read his texts under pure philosophical conditions? We may see then that some of his texts are meant neither to assert a belief nor to search for reasons for it, but only to reflect (...) upon the presuppositions of this belief and its different traditions. Instead of asserting his belief Cusanus is beginning to reflect upon his presupositions. We try to give an exemple for this shift with the first proposition in the collection of propositions that follow the dialog De non aliud: „definitio quae se et omnia definit, ea est, quae per omnem mentem quaeritur.“ We will see a quite another Cusanus. Cusanus picks up „definitio“ in the sense of self-determination, developped in the dialog. He begins in quite a traditional manner and ends in a supremely abstract and speculative intuition. The 'Not-other' determines itself in a vision; this vision is an order in which every thing gets its proper place; we as human beings aspire to repeat this vision in our mental life in contact with the world. In this way Cusanus does what all great philosophers do: he reflects in a given set of opinions what is the meaning of „to be“. (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction (...) class='Hi'>rules for the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

This paper is based on Ludwig Wittgenstein's (late) teaching on language and meaning, and its aim is to show how we can avoid the anthropomorphization of artificial intelligence or interpreting the work (the question of giving meaning) of AI as similar to or the same as the work of a human being. The way of determining the meaning of certain linguistic units performed by an AI and a human differs because the languages they operate with have a different set of (...) rules or criteria that are indicators of what a certain linguistic entity means. The core of AI in terms of meaning is its logical base, according to which it operates/calculates/manipulates the given information. On the other hand, a human being finds his/her criteria in the language activity performed in the language communities. (shrink)

Until the late 19th century scientists almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore been assumed (...) that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system. Hence the main trait in the theoretical development in the 20th-century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly with the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale. While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) or biology (ge¬netic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.). While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognized, others seem to give rise to the question of whether there are »systems« and relations between different systems in the world which are not rule-based? For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based sy¬stem. While there are no difficulties implied concerning the stability of rule-based systems, the notion of unstable states of a system raises the question of how there can be a system at all if there are no invariant stabilising principles? This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allow the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers. Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability. A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems share some features with an¬ticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems. (shrink)

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (...) (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premisebased procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms. (shrink)

Brain tumors pose significant challenges in modern healthcare, with accurate and timely diagnosis crucial for determining appropriate treatment strategies. Artificial intelligence has made significant advancements in recent years. Rule-based expert systems (if-then rule-based systems) have emerged as a promising approach for clinical decision-making in brain tumor diagnosis. In this paper, we present "A CLIPS-Based Expert System for Brain Tumor Diagnosis," which leverages a set of 14 if-then rules to diagnose brain tumors with three possible outcomes: 1) Confirm the diagnosis (...) of a brain tumor, 2) Consider the possibility of a brain tumor that has metastasized, and 3) Consider the possibility of a brain tumor. Our expert system offers a user-friendly interface, enabling users to select symptoms and receive a diagnosis based on the provided information. This paper discusses the expert system's development, implementation, and evaluation, highlighting its potential to facilitate brain tumor diagnosis and decision-making in clinical settings. Additionally, we provide a literature review that contextualizes our expert system within the broader landscape of rule-based expert systems for brain tumor diagnosis, examining their effectiveness, limitations, and challenges. (shrink)

Abstract: This research included the design of an initial expert system which helps farmers and specialists to diagnose and provide appropriate advice on onion plant diseases; furthermore, the management of knowledge used in the expert system was discussed. One of the key elements of this research was to find the appropriate language to diagnose the onion disease and the current situation in the knowledge base. Expert systems to be able to effectively implement the consultation, production rules were used to (...) capture knowledge. The expert system was developed using CLIPS with the Delphi language interface. The expert system has produced good results in the analysis of onion disease cases that have been tested and enable the system to determine the correct diagnosis in all cases. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity theorem (...) for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, (...) the problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

English law is unambiguous that legal personality, and with it all legal rights and protections, is assigned at birth. This rule is regarded as a bright line that is easily and consistently applied. The time has come, however, for the rule to be revisited. This article demonstrates that advances in fetal surgery and (anticipated) artificial wombs do not marry with traditional conceptions of birth and being alive in law. These technologies introduce the possibility of ex utero gestation, and/or temporary existence (...) ex utero, and consequently developing human beings that are novel to the law. Importantly, therefore, the concepts of birth and born alive no longer distinguish between human beings deserving of legal protection in the way originally intended. Thus, there is a need for reform, for a new approach to determining the legal significance of birth and what being legally alive actually encompasses. Investigating the law of birth is of crucial importance, because of the implications of affording or denying the subjects of new reproductive technologies rights and protections. A determination of the legal status of the subject of fetal surgery or an artificial womb will determine what can and cannot be done to each entity. Moreover, the status afforded to these entities will drastically impact on the freedoms of pregnant women. (shrink)

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental (...) rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

In his early works, Derek Parfit famously defended revisionary reductionism about personhood. According to this view, facts about personal identity consist in the holding of more particular psychological facts, which can be described wholly impersonally. He also argued that, in some cases, the truth of this view makes questions about diachronic personal identity empty questions to which no meaningful answers can be given. Yet, in his later works, Parfit defends several ethical theories such as contractualism and rule-consequentialism, which seem to (...) rely on exactly the kind of determinate notion of personal identity to which he objected earlier. Parfit, furthermore, never explored reductionism’s consequences for such theories in his later works. In order to solve this interpretative puzzle, this chapter tries to argue that, even if they are seemingly conflicting, Parfit’s views on personal identity and rule-consequentialism, Scanlonian contractualism, and Kantian contractualism do form a coherent and unified whole. (shrink)

The paper defends the argument that the Resemblance Paradox (RP), or the problem of the ‘under-determination of meaning’, and the Rule-Following Paradox (RFP) are two sides of the same paradox threatening meaning from opposite extremes. After presenting the case, the paradox is reconsidered anew and the supposition that the threat is a pervasive one is challenged.

In Republic 8–9, Socrates describes four main kinds of vicious people, all of whose souls are “ruled” by an element other than reason, and in some of whom reason is said to be “enslaved.” What role does reason play in such souls? In this paper, I argue, based on Republic 8–9 and related passages, and in contrast to some common alternative views, that for Plato the “enslavement” of reason consists in this: instead of determining for itself what is good, reason (...) is forced to desire and pursue as good a goal determined by the soul’s ruler. (shrink)

Many jurisdictions prohibit or severely restrict the use of evidence about a defendant’s character to prove legal culpability. Situationists, who argue that conduct is largely determined by situational features rather than by character, can easily defend this prohibition. According to situationism, character evidence is misleading or paltry. -/- Proscriptions on character evidence seem harder to justify, however, on virtue ethical accounts. It appears that excluding character evidence either denies the centrality of character for explaining conduct—the situationist position—or omits probative evidence. (...) Situationism is, after all, presented as antithetical to virtue ethics. -/- This essay provides a virtue ethical defense of character evidence exclusion rules. We show that existing virtue ethical rebuttals to situationism themselves support prohibitions on character evidence; even if behavior arises from stable character traits, character evidence should be prohibited. In building our case, we provide a taxonomy of kinds of character judgment and reconcile the ubiquity and reasonableness of character judgments in ordinary life with the epistemic legitimacy of character evidence prohibitions in law. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. (...) To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

According to an influential reading of his later philosophy, Wittgenstein thinks that nonsense can result from combining expressions in ways prohibited by the rules to which their use is subject. According to another influential reading, the later Wittgenstein thinks that nonsense only ever results from privation—that is, from a failure to assign a meaning to one or more of the relevant expressions. This chapter challenges Glock’s defence of the view that the later Wittgenstein allows for combinatorial nonsense. In doing (...) so, it defends a version of the privation view. According to it, Wittgenstein thinks that nonsense results, not so much from a failure to assign a meaning to an expression, as a failure to use an expression in a way that has a point or purpose. As the chapter shows, this interpretation is consistent with prominent themes in Wittgenstein’s later philosophy, such as that meaning and explanation are coordinate notions, that for a word to have a meaning is for there to be a rule-governed practice of using it, that the rules of the practice are arbitrary, and that they determine the bounds of sense. (shrink)

Hylomorphists hold that substances are, in some sense, composites of matter and form. The form of a substance is typically taken to play a fundamental role in determining the unity or identity of the whole. Staunch hylomorphists think that this role is of a kind that precludes the ontological reduction of form to the physical and thus take their position to be inconsistent with physicalism. Forms, according to staunch hylomorphism, play a fundamental role in grounding their bearers’ proper parts and (...) that, it seems, rules out the physical grounding of form itself. I shall develop a physicalist version of hylomorphism that treats form as geometric structure and which, I shall argue, entails many of the central theses endorsed by staunch hylomorphists. Based on Shoemaker’s notion of conditional powers, I shall argue that the geometric structures of complex wholes are the conditions on at least some of the conditional powers of their bearers’ proper parts, transforming those powers into powers simpliciter. Thus, forms play a fundamental role in the dynamical evolution of the physical world, but without bestowing causal powers themselves and hence without violating the causal closure of the physical domain. If a substance’s proper parts are taken to be individuated by their powers simpliciter, then they derive their identities from their places in the substantial whole, which thus determines the identities of its proper parts without changing their intrinsic natures. (shrink)

It is common to think that what theory of linguistic vagueness is correct has implications for debates in philosophy of law. I disagree. I argue that the implications of particular theories of vagueness on substantive issues of legal theory and practice are less far-reaching than often thought. I focus on four putative implications discussed in the literature concerning (i) the value of vagueness in the law, (ii) the possibility and value of legal indeterminacy, (iii) the possibility of the rule of (...) law, and (iv) strong discretion. I conclude with some methodological remarks. Delineating questions about conventional meaning, the metaphysics/metasemantics of (legal) content determination, and norms of legal interpretation and judicial practice can motivate clearer answers and a more refined understanding of the space of overall theories of vagueness, interpretation, and law. (shrink)

We are on Mars again – the favourite laboratory for philosophical experiments. Our host colleagues introduce us to some Martian stuff referred to as “T”, and ask us to help them to identify T on other possible worlds. Or, technically speaking, we are asked to determine the intension of “T”, i.e., what the term designates with respect to different possible worlds. Following a short series of experiments on the planet, we conclude that the intension of “T” depends upon three factors: (...) (1) The semantic rule linked with the term, i.e., the way in which the term is designed to pick out its referent with respect to different possible worlds (e.g., as a definite description, or as a proper name, or as an actualised description etc.); (2) The properties of the referent of “T” in the actual world; and, (3) What we shall call ‘the metaphysical background of the universe’, i.e., what counts as a thing vs. what counts as a property of things (e.g., whether the universe is such that it contains material objects that merely happen to have their manifest properties, or whether the universe primarily contains manifest objects that merely happen to have their material constitution). As our experiments show, changing the values of any of these variables will result in a change in the reference of the term with respect to different possible worlds, viz., it will result in a change in the intension of the term. We then demonstrate how the three variables are interrelated, and specify how exactly they combine to produce a particular intension of a term. We conclude with a general “formula” that determines what will deserve to be called “T” relative to the different values of the above variables, i.e., we come up with a calculator of intensions. Finally, we also draw some morals about rigidity. (shrink)