Robust technological enhancement of core cognitive capacities is now a realistic possibility. From the perspective of neutralism, the view that justifications for public policy should be neutral between reasonable conceptions of the good, only members of a subset of the ethical concerns serve as legitimate justifications for public policy regarding robust technological enhancement. This paper provides a framework for the legitimate use of ethical concerns in justifying public policy decisions regarding these enhancement technologies by evaluating the ethical concerns that arise (...) in the context of testing such technologies on nonhuman animals. Traditional issues in bioethics, as well as novel concerns such as the possibility of moral status enhancement, are evaluated from the perspective of neutralism. (shrink)

In order to determine whether current (or future) machines have a welfare that we as agents ought to take into account in our moral deliberations, we must determine which capacities give rise to interests and whether current machines have those capacities. After developing an account of moral patiency, I argue that current machines should be treated as mere machines. That is, current machines should be treated as if they lack those capacities that would give rise to psychological interests. Therefore, they (...) are moral patients only if they have non-psychological interests. I then provide an account of what I call teleo interests that constitute the most plausible type of non-psychological interest that a being might have. I then argue that even if current machines have teleo interests, they are such that agents need not concern themselves with these interests. Therefore, for all intents and purposes, current machines are not moral patients. (shrink)

Synthetic organisms are at the same time organisms and artifacts. In this paper we aim to determine whether such entities have a good of their own, and so are candidates for being directly morally considerable. We argue that the good of non-sentient organisms is grounded in an etiological account of teleology, on which non-sentient organisms can come to be teleologically organized on the basis of their natural selection etiology. After defending this account of teleology, we argue that there are no (...) grounds for excluding synthetic organisms from having a good also grounded in their teleological organization. However, this comes at a cost; traditional artifacts will also be seen as having a good of their own. We defend this as the best solution to the puzzle about what to say about the good of synthetic organisms. (shrink)

This paper addresses the foundations of Teleological Individualism, the view that organisms, even non-sentient organisms, are goal-oriented systems while biological collectives, such as ecosystems or conspecific groups, are mere assemblages of organisms. Typical defenses of Teleological Individualism ground the teleological organization of organisms in the workings of natural selection. This paper shows that grounding teleological organization in natural selection is antithetical to Teleological Individualism because such views assume a view about the units of selection on which it is only individual (...) organisms that are units of selection. However, none of the Conventionalist, Reductionist, or Multi-Level Realist theories serve to justify such an assumption. Thus, Teleological Individualism cannot be grounded in natural selection. (shrink)

Our environmental wrongdoings result in a moral debt that requires restitution. One component of restitution is reparative and another is remediative. The remediative component requires that we remediate our characters in ways that alter or eliminate the character traits that tend to lead, in their expression, to environmental wrongdoing. Restitutive restoration is a way of engaging in ecological restoration that helps to meet the remediative requirement that accompanies environmental wrongdoing. This account of restoration provides a new motivation and justification for (...) engaging in restorative practices in addition to the standard pragmatist justification and motivations. (shrink)

Climate negotiations under the United Nations Framework Convention on Climate Change have so far failed to achieve a robust international agreement to reduce greenhouse gas emissions. Game theory has been used to investigate possible climate negotiation solutions and strategies for accomplishing them. Negotiations have been primarily modelled as public goods games such as the Prisoner’s Dilemma, though coordination games or games of conflict have also been used. Many of these models have solutions, in the form of equilibria, corresponding to possible (...) positive outcomes—that is, agreements with the requisite emissions reduction commitments. Other work on large-scale social dilemmas suggests that it should be possible to resolve the climate problem. It therefore seems that equilibrium selection may be a barrier to successful negotiations. Here we use an N-player bargaining game in an agent-based model with learning dynamics to examine the past failures of and future prospects for a robust international climate agreement. The model suggests reasons why the desirable solutions identified in previous game-theoretic models have not yet been accomplished in practice and what mechanisms might be used to achieve these solutions. (shrink)

The ongoing explosion of interest in artificial intelligence is fueled in part by recently developed techniques in machine learning. Those techniques allow automated systems to process huge amounts of data, utilizing mathematical methods that depart from traditional statistical approaches, and resulting in impressive advancements in our ability to make predictions and uncover correlations across a host of interesting domains. But as is now widely discussed, the way that those systems arrive at their outputs is often opaque, even to the experts (...) who design and deploy them. Is it morally problematic to make use of opaque automated methods when making high-stakes decisions, like whether to issue a loan to an applicant, or whether to approve a parole request? Many scholars answer in the affirmative. However, there is no widely accepted explanation for why transparent systems are morally preferable to opaque systems. We argue that the use of automated decision-making systems sometimes violates duties of consideration that are owed by decision-makers to decision-subjects, duties that are both epistemic and practical in character. Violations of that kind generate a weighty consideration against the use of opaque decision systems. In the course of defending our approach, we show that it is able to address three major challenges sometimes leveled against attempts to defend the moral import of transparency in automated decision-making. (shrink)

Embedding ethics modules within computer science courses has become a popular response to the growing recognition that CS programs need to better equip their students to navigate the ethical dimensions of computing technologies like AI, machine learning, and big data analytics. However, the popularity of this approach has outpaced the evidence of its positive outcomes. To help close that gap, this empirical study reports positive results from Northeastern’s program that embeds values analysis modules into CS courses. The resulting data suggest (...) that such modules have a positive effect on students’ moral attitudes and that students leave the modules believing they are more prepared to navigate the ethical dimensions they’ll likely face in their eventual careers. Importantly, these gains were accomplished at an institution without a philosophy doctoral program, suggesting this strategy can be effectively employed by a wider range of institutions than many have thought. (shrink)

Many policies and ethical guidelines recommend developing “trustworthy AI”. We argue that developing morally trustworthy AI is not only unethical, as it promotes trust in an entity that cannot be trustworthy, but it is also unnecessary for optimal calibration. Instead, we show that reliability, exclusive of moral trust, entails the appropriate normative constraints that enable optimal calibration and mitigate the vulnerability that arises in high-stakes hybrid decision-making environments, without also demanding, as moral trust would, the anthropomorphization of AI and thus (...) epistemically dubious behavior. The normative demands of reliability for inter-agential action are argued to be met by an analogue to procedural metacognitive competence (i.e., the ability to evaluate the quality of one’s own informational states to regulate subsequent action). Drawing on recent empirical findings that suggest providing reliability scores (e.g., F1-scores) to human decision-makers improves calibration in the AI system, we argue that reliability scores provide a good index of competence and enable humans to determine how much they wish to rely on the system. (shrink)

This paper briefly describes process metaphysics, and argues that it is better suited for describing life than the more standard thing, or substance, metaphysics. It then explores the implications of process metaphysics for conceptualizing evolution. After explaining what it is for an organism to be a process, the paper takes up the Hull/Ghiselin thesis of species as individuals and explores the conditions under which a species or lineage could constitute an individual process. It is argued that only sexual species satisfy (...) these conditions, and that within sexual species the degree of organization varies. This, in turn, has important implications for species' evolvability. One important moral is that evolution will work differently in different biological domains. (shrink)

Time in electromagnetism shares many features with time in other physical theories. But there is one aspect of electromagnetism's relationship with time that has always been controversial, yet has not always attracted the limelight it deserves: the electromagnetic arrow of time. Beginning with a re-analysis of a famous argument between Ritz and Einstein over the origins of the radiation arrow, this chapter frames the debate between modern Einsteinians and neo-Ritzians. It tries to find a clean statement of what the arrow (...) is and then explains how it relates to the cosmological and thermodynamic arrows, representing the most developed and sophisticated attack yet, in either the physics or philosophy literature, on the electromagnetic arrow of time. (shrink)

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...) better thought of as an early stage of a dialogue than as a definitive treatise. (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)

This paper tries to clarify, strengthen and respond to two prominent objections to the development and use of human enhancement technologies. Both objections express concerns about the link between enhancement and the drive for hyperagency. The first derives from the work of Sandel and Hauskeller—and is concerned with the negative impact of hyperagency on social solidarity. In responding to their objection, I argue that although social solidarity is valuable, there is a danger in overestimating its value and in neglecting some (...) obvious ways in which the enhancement project can be planned so as to avoid its degradation. The second objection, though common to several writers, has been most directly asserted by Saskia Nagel, and is concerned with the impact of hyperagency on the burden and distribution of responsibility. Though this is an intriguing objection, I argue that not enough has been done to explain why this is morally problematic. I try to correct for this flaw before offering a variety of strategies for dealing with the problems raised. (shrink)

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless without rigor and objectivity. The logician urging us to be dispassionate is in resonance and harmony with the ethicist urging us to be compassionate.

A counterfactual is a conditional statement in the subjunctive mood. For example: If Suzy hadn’t thrown the rock, then the bottle wouldn’t have shattered. The philosophical importance of counterfactuals stems from the fact that they seem to be closely connected to the concept of causation. Thus it seems that the truth of the above conditional is just what is required for Suzy’s throw to count as a cause of the bottle’s shattering. If philosophers were reluctant to exploit this idea prior (...) to 1970, it was because of a widespread feeling that the truth-conditions of the counterfactual conditional were not sufficiently well understood. The development of a formal semantics for counterfactuals by Robert Stalnaker [1968] and David Lewis [1973b] stands as a major recent achievement in philosophical logic. (shrink)

The meaning of an utterance is often enriched by the pragmatic context in which it is uttered. This is because in ordinary conversations we routinely and uncontroversially compress what we say, safe in the knowledge that those interpreting us will ‘add in’ the content we intend to communicate. Does the same thing hold true in the case of legal utterances like ‘This constitution protects the personal rights of the citizen’ or ‘the parliament shall have the power to lay and collect (...) taxes’? This article addresses this question from the perspective of the constitutional originalist—the person who holds that the meaning of a constitutional text is fixed at some historical moment. In doing so, it advances four theses. First, it argues that every originalist theory is committed to some degree of pragmatic enrichment, the debate is about how much. Second, that in determining which content gets ‘added in’, originalists typically hold to a common knowledge standard for enrichment, protestations... (shrink)

Knowledge entails the truth of the proposition known; that which is merely believed may be false. If I have beliefs about your beliefs, then I may believe that some of your beliefs are false. I may believe, for example, that you mistakenly believe that it is now raining outside. This is a coherent belief for me, though not for you. You cannot coherently believe that you believe falsely that it is raining, and this despite the fact that your having that (...) false belief is clearly a logical possibility. The proposition is, for you, a kind of doxastic blindspot. (shrink)

The aim of this project to expose the reasons behind the pandemic of misinformation (henceforth, PofM) by examining the enabling conditions of epistemic agency and the emerging technologies that threaten it. I plan to research the emotional origin of epistemic agency, i.e. on the origin of our capacity to acquire justification for belief, as well as on the significance this emotional origin has for our lives as epistemic agents in our so-called Misinformation Age. This project has three objectives. First, I (...) plan to expose the degree to which epistemic agency is made possible by an under-researched species of emotion called epistemic feelings. Perhaps, the most epistemically significant is the feeling of confidence. In particular, epistemic feelings make epistemic agency possible by making errors in reasoning salient or the potential lack thereof. -/- Second, in order to diagnose the reasons for PofM, I will analyze the emotional basis of epistemic agency in the context of emerging technologies. Epistemic feelings ought to be construed as motivators of epistemic acts, specifically acts following exposure to misinformation spread by social media. For example, a recent study found that subjects on YouTube have a 6.3% probability in five clicks to go from watching innocuous videos to misogynistic videos. Accordingly, one prominent view holds that social media algorithms lead subjects down the proverbial rabbit hole, producing content that elicits strong emotional reactions. -/- But under-researched is the degree to which these emotions are intertwined with epistemic feelings, so that subjects are likely to misjudge the information as correct due to being primed to do so by processing the AI's suggested media. Thus, when this technology is used in epistemic practices, the result is invariably epistemically bad behavior because of how this manner of producing content motivates epistemic acts through the production of erroneous feelings of confidence, which result from the perceived ease of cognitive processing: the content is easy to process and so, the subject confidently misjudges, it is true. As of yet, an account of this cognitive and emotional decision-making process has not been used to analyze how emerging technologies are threatening epistemic agency, and thus our wellbeing as knowers. -/- Finally, I plan to develop therapeutics for PofM by outlining how to reform our collective epistemic practices. Thus, this project complements existing research in virtue epistemology, specifically by articulating the challenges to cultivating epistemic virtues and warding off the vices of the mind. In summation, the project aims to account for how emerging technologies are committing a form of epistemic injustice through the exploitation of cognitive biases and the production of erroneous epistemic feelings, with the overarching goal being a framework for convalescing from the pandemic of misinformation plaguing our age. (shrink)

In this paper, I critique arguments made by philosopher David Buller against central evolutionary-psychological explanations of human mating. Specifically, I aim to rebut his criticisms of Evolutionary Psychology regarding (1) women's long-term mating preferences for high-status men; (2) the evolutionary rationale behind men's provisioning of women; (3) men's mating preferences for young women; (4) women's adaptation for extra-pair sex; (5) the sex-differentiated evolutionary theory of human jealousy; and (6) the notion of mate value. In sum, I aim to demonstrate that (...) Buller's arguments contra Evolutionary Psychologists are left wanting. (shrink)

This paper attempts to reconcile two apparently opposed ways of thinking about the imagination and its relationship to literature, one which casts it as essentially concerned with fiction-making and the other with culture-making. The literary imagination’s power to create fictions is what gives it its most obvious claim to “autonomy”, as Kant would have it: its freedom to venture out in often wild and spectacular excess of reality. The argument of this paper is that we can locate the literary imagination’s (...) complementary power of cultural articulation in this fictional activity. The suggestion is that we should conceive of the literary imagination as expressing its interests in culture not mimetically but by producing a certain kind of meaning. This meaning is irreducibly narratological, and understanding it helps us to see the role of narrative in bringing into harmony the literary imagination’s interests in both the imaginary and the real. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and Sriram (...) Nambiar, I have written several publications trying to set the record straight—but so far to little avail. This encyclopedia entry is one more attempt to set the record straight in a way that can be appreciated by non-experts.Also see https://www.academia.edu/10161999/Booles_criteria_of_validity_and_invalidity . (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

English translation of an entry on pages 137–42 of the Spanish-language dictionary of logic: Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta. -/- DEDICATION: To my friend and collaborator Kevin Tracy. -/- This short essay—containing careful definitions of ‘counterargument’ and ‘counterexample’—is not an easy read but it is one you’ll be glad you struggled through. It contains some carefully chosen examples suitable for classroom discussion. -/- Using the word ‘counterexample’ instead of ‘counterargument’ in connection with Aristotle’s invalidity (...) proofs leads to a misinterpretation of Aristotle’s intentions. The two relations expressed by these two words are drastically different—as explained in this essay. There is however a subtle overlap: Every argument that is a counterargument for a given argument is a counterexample to the universal proposition that every argument in the same form as the given argument is valid. The word ‘counterexample’ was coined in the 1800s. The word ‘counterargument’ was given this sense in the 1960s. Saying that one argument is a counterexample for another argument is bad English—taking the word ‘counterexample’ in its Standard English sense. The word ‘counterinstance’ is an exact synonym for ‘counterexample’. Which logic books define ‘counterinstance’ or ‘counterexample’? Who started using ‘counterinstance’ or ‘counterexample’ in the sense of ‘counterargument’? Did they note that they were not using the word in the Standard sense? Why did it catch on? -/- Also see: https://www.academia.edu/8840909/Argumentations_and_logic_1989_ . (shrink)

The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one is (...) greater than the other or the one is greater than the other [sc. in appropriate correlated senses of ‘equals’, ‘is greater than’ and ‘is less than’]. In case there are two or more appropriate senses of ‘equals’, the one intended is often indicated by an adverb. For example, one plane figure may be said to be equal in area to another and, in certain cases, one plane figure may be said to be equal in length to another. Each sense of ‘equality’ is tied to a specific domain and is therefore non-logical. Notice that in every cases ‘equality’ is definable in terms of ‘is greater than’ and also in terms of ‘is less than’ both of which are routinely considered domain specific, non-logical. The word ‘identity’ in the logical sense does not require disambiguation. Moreover, it is not correlated ‘is greater than’ and ‘is less than’. If it is not the case that a certain designated triangle is [sc. is identical to] an otherwise designated triangle, it is not necessary for the one to be greater than or less than the other. Moreover, if two magnitudes are equal then a unit of measure can be chosen and, no matter what unit is chosen, each magnitude is the same multiple of the unit that the other is. But identity does not require units. In this regard, congruence is like identity and unlike equality. In arithmetic, the logical concept of identity is coextensive with the arithmetic concept of equality. The logical concept of identity admits of an analytically adequate definition in terms of logical concepts: given any number x and any number y, x is y iff x has every property that y has. The arithmetical concept of equality admits of an analytically adequate definition in terms of arithmetical concepts: given any number x and any number y, x equals y iff x is neither less than nor greater than y. As Aristotle told us and as Frege retold us, just because one relation is coextensive with another is no reason to conclude that they are one. (shrink)

This 4-page review-essay—which is entirely reportorial and philosophically neutral as are my other contributions to MATHEMATICAL REVIEWS—starts with a short introduction to the philosophy known as mathematical structuralism. The history of structuralism traces back to George Boole (1815–1864). By reference to a recent article various feature of structuralism are discussed with special attention to ambiguity and other terminological issues. The review-essay includes a description of the recent article. The article’s 4-sentence summary is quoted in full and then analyzed. The point (...) of the quotation is to make clear how murky, incompetent, and badly written the paper is. There is no way to determine from the article whether the editor or referees suggests improvements. (shrink)

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...) for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical. This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that in 1831, De Morgan was still in the grips of the allegedly Aristotelian paradigm. (shrink)

The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...) it. Two such discourse-texts are said to have the same grammatical form, in this sense, if a uniform one-one substitution of content words transforms the one exactly into the other. The sentence ‘Abe properly respects every agent who respects himself’ may be regarded as having the same grammatical form as the sentence ‘Ben generously assists every patient who assists himself’. (shrink)

The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact fallacy if (...) they think that a proposition has different consequences were it true than it would have if false. C. I. Lewis said that confusing logical consequence with material consequence leads to this fallacy. See Corcoran’s 1973 “Meanings of implication” [available on Academia. edu]. -/- The premise-fact confusion occurs in a written passage that implies the premise-fact fallacy or that suggests that the writer isn’t clear about the issues involved in the premise-fact fallacy. Here are some examples. -/- E1: If Abe is Ben and Ben swims, then it would follow that Abe swims. -/- Comment: The truth is that from “Abe is Ben and Ben swims”, the proposition “Abe swims” follows. Whether in fact Abe is Ben and Ben swims is irrelevant to whether “Abe swims” follows from “Abe is Ben and Ben swims”. -/- E1 suggests that maybe “Abe swims” wouldn’t follow from “Abe is Ben and Ben swims” if the latter were false. -/- E2: The truth of “Abe is Ben and Ben swims” implies that Abe swims. -/- E3: Indirect deduction requires assuming something false. -/- Comment: If the premises of an indirect deduction are true the conclusion is true and thus the “reductio” assumption is false. But deduction, whether direct or indirect, does not require true premises. In fact, indirect deduction is often used to determine that the premises are not all true. -/- Anyway, the one-page paper accompanying this abstract reports one of dozens of premise-fact errors in PRIOR ANALYTICS. In the session, people can add their own examples and comment on them. For example, is the one at 25b32 the first? What is the next premise-fact error after 25b32? Which translators or commentators discuss this? -/- . (shrink)

This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does (...) not follow from its premises? This result does nothing to vitiate the theories of distribution developed over the period beginning in medieval times. What it does vitiate is many if not all attempts to use distribution in tests of invalidity outside of the standard two-premise categorical arguments—where they were verified on a case-by-case basis without further theoretical grounding. In addition it shows that there was no theoretical basis for many if not all claims of fundamental status of rules of distribution. These results are further support for approaching historical texts using mathematical archeology. (shrink)

This paper is a commentary on the target article by Lokendra Shastri & Venkat Ajjanagadde [S&A]: “From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony” in same issue of the journal, pp.417–451. -/- It puts S&A's temporal-synchrony binding method in a broader context, comments on notions of pointing and other ways of associating information - in both computers and connectionist systems - and mentions types of reasoning that are a challenge to (...) S&A's system (amongst many other connectionist systems, recognizing that S&A's is much more capable as regards reasoning than most other contemporary systems). (shrink)

The paper is a commentary on the target article by Christine A. Skarda & Walter J. Freeman, “How brains make chaos in order to make sense of the world”, in the same issue of the journal, pp.161–195. -/- I confine my comments largely to some philosophical claims that Skarda & Freeman make and to the relationship of their model to connectionism. Some of the comments hinge on what symbols are and how they might sit in neural systems.

This paper is a commentary on the target article by Dana H. Ballard, “Cortical connections and parallel processing: Structure and function”, in the same issue of the journal, pp. 67–120. -/- I raise some issues about the connectionist or neural-network implementation of information and information processing. Issues include the sharing of information by different parts of a connectionist/neural network, the copying of complex information from one place to another in a network, the possibility of connection weights not being synaptic weights, (...) and the possibility of fast communication within single neurons as complex systems in their own right. (shrink)

This paper is a commentary on the target article by Michael Arbib, “Levels of modeling of mechanisms of visually guided behavior”, in the same issue of the journal, pp. 407–465. -/- I focus on the importance of the inclusion of an ability of a system to entertain, at a given time, multiple instantiations of a given schema (situation template, frame, script, action plan, etc.), and complications introduced into neural/connectionist network systems by such inclusion.

Following Quine [] and others we take deductions to produce knowledge of implications: a person gains knowledge that a given premise-set implies a given conclusion by deducing—producing a deduction of—the conclusion from those premises. How does this happen? How does a person recognize their desire for that knowledge of a certain implication, or that they lack it? How do they produce a suitable deduction? And most importantly, how does their production of that deduction provide them with knowledge of the implication. (...) What experienceable sign reveals to the reasoner that they achieved the desired knowledge? If a deduction is an array of inscriptions constructed by following syntactical—mechanical, machine-performable—rules as suggested by Tarski, Carnap, Church, and others, the epistemic question becomes even more pressing and more challenging. Moreover, deduction, the ability to produce deductions and to recognize them when produced, is operational knowledge that presupposes other component operations such as recognizing characters, making assumptions, inferring conclusions from premises, chaining inferences [AL]. (shrink)

What are laws, and do they necessarily have any basis in morality? The present work argues that laws are governmental assurances of protections of rights and that concepts of law and legal obligation must therefore be understood in moral terms. There are, of course, many immoral laws. But once certain basic truths are taken into account – in particular, that moral principles have a “dimension of weight”, to use an expression of Ronald Dworkin’s, and also that principled relations are not (...) always expressed by perfect statistical concomitances – the existence of iniquitous laws poses no significant threat to a moralistic analysis of law. Special attention is paid to the debate between Ronald Dworkin and H.L.A. Hart. Dworkin’s over-all position is argued to be correct, but issue is taken with his argument for that position. Hart’s analysis is found to be vitiated by an impoverished conception of morality and also of the nature of government. Our analysis of law enables us to answer three questions that, at this juncture of history, are of special importance: Are there international laws? If not, could such laws exist? And if they could exist, would their existence necessarily be desirable? The answers to these questions are, respectively: “no”, “yes”, and “no.” Our analysis of law enables us to hold onto the presumption that so-called legal interpretation is a principled endeavor, and that some legal interpretations are truer to existing laws than others. At the same time, it accommodates the obvious fact that the sense in which a physicist interprets meter-readings, or in which a physician interprets a patient’s symptoms, is different from the sense in which judges interpret the law. So our analysis of law enables us to avoid the extreme views that have thus far dominated debates concerning the nature of legal interpretation. On the one hand, it becomes possible to avoid the cynical view (held by the so-called “legal realists”) that legal interpretation is mere legislation and that no legal interpretation is more correct than any other. On the other hand, it becomes possible to avoid Blackstone’s view (rightly descried by Austin as a “childish fiction”) that judges merely discover, and do not create, the law. (shrink)