Discerning the decisionmaking of Kim Jong-Un and the North Korean regime on issues of peaceful engagement and warlike actions endures as a mighty challenge for U.S. intelligence analysts and policymakers. In this report, we seek to inform analysis of Democratic People’s Republic of Korea (DPRK) leadership decisionmaking. To do so, we use three discussion papers that were written to facilitate discussion of an interagency working group. The three papers are assembled here in a single report. The first discussion paper describes (...) decisionmaking among different authoritarian regimes, including North Korea, and the opening up of those economies to outside engagement. The second paper outlines two different scenarios that might occur when conventional deterrence on the Korean Peninsula breaks down and the resulting decisions that North Korea’s leadership could face. The third paper assesses DPRK decisionmaking about nuclear weapon use. The report concludes with some observations, drawn from the issues covered in these three discussion papers, about DPRK decisionmaking and stability on the Korean Peninsula. (shrink)

Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08. -/- Constance Reid was an insider of the Berkeley-Stanford logic circle. Her San Francisco home was in Ashbury Heights near the homes of logicians such as Dana Scott and John Corcoran. Her sister Julia Robinson was one of the top mathematical logicians of her generation, as was Julia’s husband Raphael Robinson for whom Robinson Arithmetic was named. Julia was a Tarski PhD (...) and, in recognition of a distinguished career, was elected President of the American Mathematics Society. https://en.wikipedia.org/wiki/Julia_Robinson http://www.awm-math.org/noetherbrochure/Robinson82.html. (shrink)

JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised (...) to find out that in normal first-order logic existential import is quite common: some universals “Everything that is S is P” —actually quite a few—imply their corresponding existentials “Something that is S is P”. Anyway, perhaps contrary to its title, this paper is not a cataloging of surprises in logic but rather about the mistakes that did or might have or might still lead people to think that there are no surprises in logic. The paper cataloging of surprises in logic is on our “to-do” list. -/- ► JOHN CORCORAN AND WILIAM FRANK, Surprises in logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] There are many surprises in logic. Peirce gave us a few. Russell gave Frege one. Löwenheim gave Zermelo one. Gödel gave some to Hilbert. Tarski gave us several. When we get a surprise, we are often delighted, puzzled, or skeptical. Sometimes we feel or say “Nice!”, “Wow, I didn’t know that!”, “Is that so?”, or the like. Every surprise belongs to someone. There are no disembodied surprises. Saying there are surprises in logic means that logicians experience surprises doing logic—not that among logical propositions some are intrinsically or objectively “surprising”. The expression “That isn’t surprising” often denigrates logical results. Logicians often aim for surprises. In fact, [1] argues that logic’s potential for surprises helps motivate its study and, indeed, helps justify logic’s existence as a discipline. Besides big surprises that change logicians’ perspectives, the logician’s daily life brings little surprises, e.g. that Gödel’s induction axiom alone implies Robinson’s axiom. Sometimes wild guesses succeed. Sometimes promising ideas fail. Perhaps one of the least surprising things about logic is that it is full of surprises. Against the above is Wittgenstein’s surprising conclusion : “Hence there can never be surprises in logic”. This paper unearths basic mistakes in [2] that might help to explain how Wittgenstein arrived at his false conclusion and why he never caught it. The mistakes include: unawareness that surprise is personal, confusing logicians having certainty with propositions having logical necessity, confusing definitions with criteria, and thinking that facts demonstrate truths. People demonstrate truths using their deductive know-how and their knowledge of facts: facts per se are epistemically inert. [1] JOHN CORCORAN, Hidden consequence and hidden independence. This Bulletin, vol.16, p. 443. [2] LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus, Kegan Paul, London, 1921. -/-. (shrink)

What’s wrong with begging the question? Some philosophers believe that question-begging arguments are inevitably fallacious and that their fallaciousness stems from a shared “formal” deficiency. In contrast, some philosophers, like Robinson deny that begging the question is fallacious at all. And others characterize begging the question as an “informal” fallacy of reasoning that can only be understood with the aid of epistemic notions. Sorensen joins this last camp by offering a powerful argument against both Robinson’s skepticism and fully (...) formal approaches to the phenomenon. According to Sorensen’s view, question-begging is fallacious because it compromises the rationality of the question-beggar’s position. Though his argument forces Robinson into a peculiar dialectical position, it does little to elucidate the reasons why Robinson’s position is unstable and it fails to embody Sorensen’s own conception of rationally persuasive argumentation. I utilize this conception to show how Robinson is left with no easily identifiable grounds on which to deny the fallaciousness of begging the question. By advancing the dialectic between Sorensen and Robinson, I aim to show that our argumentative practices must take the perspectives of others seriously, whether or not those perspectives are rational. (shrink)

What’s so good about John Ames? The narrator of Marilynne Robinson’s Gilead has been much admired, but it’s far from obvious why. His life is quiet and unassuming, and has for the most part been uneventful in the extreme. In this chapter I draw on Iris Murdoch’s moral philosophy to explain the moral arc of the novel, and suggest that the novel in turn can shed light on Murdoch’s key ethical ideas. What is so notable about John (...) Ames, I suggest, is his commitment to seeing the world justly and lovingly—a commitment which for Murdoch is at the heart of virtuous agency. (shrink)

This chapter argues that scientific and philosophical progress in our understanding of the living world requires that we abandon a metaphysics of things in favour of one centred on processes. We identify three main empirical motivations for adopting a process ontology in biology: metabolic turnover, life cycles, and ecological interdependence. We show how taking a processual stance in the philosophy of biology enables us to ground existing critiques of essentialism, reductionism, and mechanicism, all of which have traditionally been associated with (...) substance ontology. We illustrate the consequences of embracing an ontology of processes in biology by considering some of its implications for physiology, genetics, evolution, and medicine. And we attempt to locate the subsequent chapters of the book in relation to the position we defend. (shrink)

How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects of the theory. Because the philosophical side has radical elements, so does the physical-theory side. The philosophical side is radical, first, in proposing that the productivity or dynamism in the universe that many believe to be responsible for (...) its systematic regularities is actually itself a physical constituent of the universe, along with more familiar entities. Indeed, it proposes that instances of dynamism can themselves take part in physical interactions with other entities, this interaction then being “meta-dynamism” (a type of meta-causation). Secondly, the theory is radical, and unique, in arguing that consciousness is necessarily partly constituted of meta-dynamic auto-sensitivity, in other words it must react via meta-dynamism to its own dynamism, and also in conjecturing that some specific form of this sensitivity is sufficient for and indeed constitutive of consciousness. The article proposes a way for physical laws to be modified to accommodate meta-dynamism, via the radical step of including elements that explicitly refer to dynamism itself. Additionally, laws become, explicitly, temporally non-local in referring directly to quantity values holding at times prior to a given instant of application of the law. The approach therefore implicitly brings in considerations about what information determines states. Because of the temporal non-locality, and also because of the deep connections between dynamism and time-flow, the approach also implicitly connects to the topic of entropy insofar as this is related to time. (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of generalizations, (...) not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

I present considerations surrounding pre-reflective self-consciousness, arising in work I am conducting on a new physicalist, process-based account of [phenomenal] consciousness. The account is called the meta-causal account because it identifies consciousness with a certain type of arrangement of meta-causation. Meta-causation is causation where a cause or effect is itself an instance of causation. The proposed type of arrangement involves a sort of time-spanning, internal reflexivity of the overall meta-causation. I argue that, as a result of the account, any conscious (...) process has PRSC. Hence, PRSC does not need to be taken as a stipulation or argued for on purely phenomenological grounds or as a necessary support for reflective consciousness. I also show how it is natural to the account that PRSC is not an additional, peripheral, sort of consciousness, but is intrinsic to all consciousness, thereby fitting claims about self-intimation and co-constitution by various authors, and also being amenable to an adverbial account. As part of this, consciousness of an external object is just the form that current self-consciousness takes, the meta-causal constitution of it being inextricably modulated by the causal relationship with the object. The article also discusses how MCA helps explore issues of for-me-ness, transparency of perceptual consciousness, and possible immediacy and non-relationality of self-consciousness. (shrink)

The book is thought-provoking and informative, wide in scope while also being technically detailed, and still relevant to modem AI [at least as of 1998, the time of writing this review, but probably also at the time of posting this entry here, 2023] even though it was published in 1989. This relevance lies mainly in the book’s advocacy of distributed computation at multiple levels of description, its combining of neural networks and other techniques, its emphasis on the interplay between action (...) and perception, and its particular approach to natural language processing. The criticisms I have occasionally made above are relatively minor, and one of the major shortcomings of schema theory at least at the time of the book’s publication -- namely the lack of a detailed, preferably neural, mechanism for schema instantiation -- is one of which Arbib is well aware. The book is well produced, for the most part clearly written, and has useful summaries at the beginning of each chapter. Both general readers and AI researchers (mainly but not exclusively those working on robotics, vision and neural networks) could benefit from reading the book. (shrink)

Closure is the epistemological thesis that if S knows that P and knows that P implies Q, then if S infers that Q, S knows that Q. Fred Dretske acknowledges that closure is plausible but contends that it should be rejected because it conflicts with the plausible thesis: Conclusive reasons (CR): S knows that P only if S believes P on the basis of conclusive reasons, i.e., reasons S wouldn‘t have if it weren‘t the case that P. Dretske develops an (...) analysis of knowing that centers on CR, and argues that the requirement undermines skepticism by implying the falsity of closure. We develop a Dretske-style analysis of knowing that incorporates CR, and we argue that this analysis not only accords with closure, but also implies it. In addition, we argue that the analysis accounts for the prima facie plausibility of closure-invoking skeptical arguments, and nonetheless implies that they are fallacious. If our arguments turn out to be sound, the acceptability of Dretske‘s analysis of knowing will be significantly enhanced by the fact that, despite implying closure, it undermines closure-based skepticism. (shrink)

Reasoning about mental states and processes is important in various subareas of the legal domain. A trial lawyer might need to reason and the beliefs, reasoning and other mental states and processes of members of a jury; a police officer might need to reason about the conjectured beliefs and reasoning of perpetrators; a judge may need to consider a defendant's mental states and processes for the purposes of sentencing and so on. Further, the mental states in question may themselves be (...) about the mental states and processes of other people. Therefore, if AI systems are to assist with reasoning tasks in law, they may need to be able to reason about mental states and processes. Such reasoning is riddled with uncertainty, and this is true in particular in the legal domain. The article discusses how various different types of uncertainty arise, and shows how they greatly complicate the task of reasoning about mental states and processes. The article concentrates on the special case of states of belief and processes of reasoning, and sketches an implemented, prototype computer program (ATT-Meta) that copes with the various types of uncertainty in reasoning about beliefs and reasoning. In particular, the article outlines the system's facilities for handling conflict between different lines of argument, especially when these lie within the reasoning of different people. The system's approach is illustrated by application to a real-life mugging example. [NB: The date on the archived preprint avail via this Phil* page has an incorrect date, 2011, on it. The correct date is 2001.]. (shrink)

Although Paul Churchland and Jerry Fodor both subscribe to the so-called theory-theory– the theory that folk psychology (FP) is an empirical theory of behavior – they disagree strongly about FP’s fate. Churchland contends that FP is a fundamentally flawed view analogous to folk biology, and he argues that recent advances in computational neuroscience and connectionist AI point toward development of a scientifically respectable replacement theory that will give rise to a new common-sense psychology. Fodor, however, wagers that FP will be (...) largely preserved and vindicated by scientific investigations of behavior. Recent findings by developmental psychologists, I argue, will push both Churchlandians and Fodorians toward the pessimistic view that FP is a misguided theory that will never be displaced, because it is, so to speak, built into our cognitive systems. I explore the possibility of preserving optimism by rejecting the theory-theory and adopting the simulation theory, a competing view developed by Robert Gordon, Alvin Goldman, and Jane Heal. According to simulationists, common-sense interpretation of behavior is accomplished by means of pretense-like operations that deploy the cognitive system’s own reasoning capabilities in a disengaged manner. Since on this view no theory-like set of principles would be needed, the simulation theory seems to enjoy a simplicity advantage over the theory-theory. Steven Stich and Shawn Nichols, however, contend that as the cognitive system would require special mechanisms for disengaged operation, the simplicity question cannot be resolved until suitable computational models are developed. I describe a set of models I have constructed to meet this need, and I discuss the contribution such models can make to determining FP’s fate. (shrink)

The representation of propositional attitudes (beliefs, desires, etc.) and the analysis of natural-language, propositional-attitude reports presents difficult problems for cognitive science and artificial intelligence. In particular, various representational approaches to attitudes involve the incorrect “imputation,” to cognitive agents, of the use of artificial theory-laden notions. Interesting cases of this problem are shown to occur in several approaches to attitudes. The imputation problem is shown to arise from the way that representational approaches explicate properties and relationships, and in particular from the (...) way they explicate propositional attitudes themselves. Another factor contributing to imputation is the compositional nature of typical semantic approaches to propositional-attitude reports. Some strategies for avoiding undesirable imputation are examined. One of the main conclusions is that the importance of imputations that arise in a representation scheme depends strongly on the use to which the scheme is put -- on whether, for instance, the scheme is used as part of a formal, objective account of natural language, or is used rather as a representational tool within an agent. (shrink)

We consider the varieties and directions of influence that the source and target domains involved in a conceptual metaphor can have on each other during the course of understanding metaphorical utterances based on the metaphor. Previous studies have been restricted both as to direction of influence and as to type of influence. They have been largely confined to the “forward” (source to target) direction of influence, and they have concentrated on the transfer of features or propositions and (to some extent) (...) the highlighting of aspects of a domain. By contrast, this article stresses the importance both of other varieties of influence (e.g., transfer of queries and uncertainty effects) and of “reverse” influence (target to source). We seek to curb the natural tendency to think that, because metaphor involves an overall move from source to target, therefore all inter-domain influences in the course of understanding go in that direction. The bulk of the article explores the theoretical issues involved. These issues have arisen out of a reasoning-based approach to metaphor, seeking to make best use of information from metaphorical utterance, context, source and target domains, and known metaphorical mappings, by applying a complex overall reasoning process. The article briefly explains the thorough implementation of reverse influence in a computer program for metaphorical reasoning called ATT-Meta, although the theoretical considerations are relevant to all disciplines concerned with metaphor. We make some suggestions for further computational and psychological research on metaphor. (shrink)

This article arises indirectly out of the development of a particular approach, called ATT-Meta, to the understanding of some types of metaphorical utterance. However, the specifics of the approach are not the focus of the present article, which concentrates on some general issues that have informed, or arisen from, the development of the approach. The article connects those issues to the questions of metaphorical meaning and truth. -/- A large part of the exploration of metaphor in fields such as Cognitive (...) Linguistics and natural language Pragmatics takes metaphor to rest on complex mappings between a target subject matter and a source subject matter (see, e.g., Lakoff 1993, 2008). This is one main way in which some aspects of the source, generally including some structural aspects, can have parallels in the target. It is typical for much, and perhaps the whole, of the meaning of a metaphorical expression to be explained by means of these parallels. We will talk about “parallelism” rather than “isomorphism,” or even “analogy,” because “isomorphism” implies a strict one-to-one correspondence between items in the source scenario and items in the target scenario, and analogy theorists often hold that analogy rests on isomorphism. We wish not to prejudge the question of whether looser, messier forms of parallelism are sometimes needed. Also, we will talk about parallels rather than mappings, because our discussion will embrace the question of parallelism that may be discernible, albeit implicitly, in accounts of metaphor that are not presented as being based on mappings. Three main cases of such accounts are Relevance Theory (RT: e.g., Sperber & Wilson 2008, Wilson & Carston 2006), the categorization-based or "class-inclusion“ approach (Glucksberg 2008), and Ritchie’s (2006) CLST account (Context-Limited Simulation Theory). -/- One main issue we will address is that of substantial non-parallelism that can exist between source and target subject-matters in metaphor: more precisely, the issue that there may be source aspects that are exploited by the utterance and have a deep effect on metaphorical interpretation but that do not themselves have a natural parallel in the target subject-matter (although we will point out that artificial parallels can generally be created). This is part of a broader point that the content of metaphorical discourse should often be seen as being derived in a rather holistic way from several metaphorical bits of the discourse, which conspire to describe some source-domain scenario, rather than being derived by putting together metaphorical meanings of each metaphorical bit (even if each bit could in principle be assigned its own separate metaphorical meaning). As a result, we suggest that it is misguided to think of the propositions making up the content (or, if you like, "meaning“) about the target scenario that is being described is a matter of metaphorical meaning of specific grammatical units such as sentences, clauses or other constituents that a traditional semantic theory would assign propositional meaning to. Rather, grammatical units (that are to be taken metaphorically) have meanings in source-domain terms; content in target-domain terms is derived from the source-domain scenario depicted by those units and fleshed out through inference; and the target-domain content is only (in general) fuzzily relatable to particular grammatical units. This view is on a spectrum at whose extreme point we could place Davidson’s (1984) view that metaphors only have literal (i.e., source-domain) meanings, with other effects on the understander not being a matter of propositional content. However, on our view it is proper to take metaphorical discourse as having non-literal meaning, couched as a collection of propositions, among other things possibly; it is just that the propositions are not to be thought of (in general) as meaning of specific sentences, clauses or other grammatical units rather than of a possibly only fuzzily delineated piece of discourse. -/- A second main concern of the article is the question of how much, and what types of, inference are involved in the derivation of metaphorical meaning. While our own ATT-Meta approach accords with, amongst other accounts, Relevance Theory (RT) as to the centrality of inference in metaphor interpretation, we disagree with RT on its claim that metaphor interpretation is a matter of (a relatively high degree of) concept "broadening“ and (often) "narrowing“. We argue that almost all inference can in fact be theoretically re-described as concept broadening and/or narrowing, and what is left over should be included in the metaphor interpretation process anyway. Thus, the RT claim about broadening and narrowing really just says that inference, of unrestricted type, is involved in metaphor understanding, in accord with what ATT-Meta claims. (shrink)

The notion of Simulative Reasoning in the study of propositional attitudes within Artificial Intelligence (AI) is strongly related to the Simulation Theory of mental ascription in Philosophy. Roughly speaking, when an AI system engages in Simulative Reasoning about a target agent, it reasons with that agent’s beliefs as temporary hypotheses of its own, thereby coming to conclusions about what the agent might conclude or might have concluded. The contrast is with non-simulative meta-reasoning, where the AI system reasons within a detailed (...) theory about the agent’s (conjectured) reasoning acts. The motive within AI for preferring Simulative Reasoning is that it is more convenient and efficient, because of a simplification of the representations and reasoning processes. The chapter discusses this advantage in detail. It also sketches the use of Simulative Reasoning in an AI natural language processing system, ATT-Meta, that is currently being implemented. This system is directed at the understanding of propositional attitude reports. In ATT-Meta, Simulative Reasoning is yoked to a somewhat independent set of ideas about how attitude reports should be treated. Central here are the claims that (a) speakers often employ commonsense (and largely metaphorical) models of mind in describing agents’ attitudes, (b) the listener accordingly needs often to reason within the terms of such models, rather than on the basis of any objectively justifiable characterization of the mind, and (c) the commonsense models filter the suggestions that Simulative Reasoning comes up with concerning target agents’ reasoning conclusions. There is a yet tighter connection between the commonsense models and the Simulative Reasoning. It turns out that Simulative Reasoning can be rationally reconstructed in terms of a more general type of reasoning about the possibly-counterfactual “world” that the target agent believes in, together with an assumption that that agent has a faithful representation of the world. In the ATT-Meta approach, the reasoner adopts that assumption when it views the target agent through a particular commonsense model (called IDEAS-AS-MODELS). (shrink)

The science of the mind, and of consciousness in particular, needs carefully to consider people's common-sense views of the mind, not just what the mind really is. Such views are themselves an aspect of the nature of (conscious) mind, and therefore part of the object of study for a science of mind. Also, since the common-sense views allow broadly successful social interaction, it is reasonable to look to the common-sense views for some rough guidance as to the real nature of (...) the mind. On the other hand, to the extent that common-sense views are inaccurate, and perhaps even in gross conflict with the true nature of the mind, one interesting scientific question is: why do we hold such views, given our access to our own minds? Why should introspection be limited in a way that allows inaccurate views to hold sway? Now, common-sense views of the mind are revealed in natural language discourse that describes mental states, and such descriptions are largely metaphorical. The metaphors are used within thinking about the mind as well as in language. Therefore the study of metaphor is central to the study of mind. The present article is a preliminary study of the importance of metaphor in the scientific study of consciousness. It concentrates on analysing the nature of a range of important metaphors of mind, briefly discussing the extent to which they can be used to describe or qualify states of consciousness, and pointing to important questions about the nature of consciousness that the study of the metaphors raises. The article further conjectures that the reason people use metaphors in describing themselves is often not (just) that they have intellectually worked out some structural analogy --- e.g., between interactions of physical objects in physical space and interactions of ideas in the mind --- but rather that they {\it feel} their own minds to be as described by the metaphor --- e.g., they feel that the ideas in their minds are interacting physical entities. This matter of how a mind feels to itself is an aspect of the central issue of consciousness, namely its phenomenal quality. -/- (NB: The archived file is a preprint. However, it is substantially the same as the published version.). (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.

In 1937 Joan Robinson proposed that “when capitalism is rightly understood, the rate of interest will be set at zero and the major evils of capitalism will disappear”. A permanent zero rate would abolish capitalist profit except in limited cases, leaving nearly all output to be claimed by labour as wages. It would allow capital to be allocated on the basis of prospective social benefit rather than short-term profitability and a collateral basis that favours the wealthy. It would remove (...) some of the economic pressure to use resources unsustainably. So why not do this? I argue that the few available philosophical arguments for positive interest rates are unsatisfactory. Those who want a just and sustainable form of capitalism should target net zero for the interest rate. (shrink)

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and validates (...) the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

The social welfare functional approach to social choice theory fails to distinguish a genuine change in individual well-beings from a merely representational change due to the use of different measurement scales. A generalization of the concept of a social welfare functional is introduced that explicitly takes account of the scales that are used to measure well-beings so as to distinguish between these two kinds of changes. This generalization of the standard theoretical framework results in a more satisfactory formulation of welfarism, (...) the doctrine that social alternatives are evaluated and socially ranked solely in terms of the well-beings of the relevant individuals. This scale-dependent form of welfarism is axiomatized using this framework. The implications of this approach for characterizing classes of social welfare orderings are also considered. (shrink)

In a recent very interesting and important challenge to tracking theories of knowledge, Williams & Sinhababu claim to have devised a counter-example to tracking theories of knowledge of a sort that escapes the defense of those theories by Adams & Clarke. In this paper we will explain why this is not true. Tracking theories are not undermined by the example of the backward clock, as interesting as the case is.

In metaphor research there is usually some notion of transfer of aspects of the source domain to the target domain. More rarely, transfers in the opposite direction are countenanced, affecting one’s perception of source as well as target. This paper argues that, even without this aim, transfers from target to source should happen. One radical claim here is that it is often better to translate information from literal sentences into prevailing metaphorical terms than to translate the information from metaphorical sentences (...) into literal terms. The issues have been obscured by confusion between intuitive directions of static source/target mappings, directions of individual transfer actions, and direction of main intended information flow. Relevance to an implemented AI system for metaphorical reasoning, ATT-Meta, and to Blending Theory are briefly mentioned. Asymmetry of metaphor is also addressed. (shrink)

Joint attention is a social-cognitive phenomenon in which two or more agents direct their attention together towards the same object. Definitions range from this rather broad conception to more specific definitions which require that, in addition, attention be directed to the same aspect of that object and that agents need to be mutually aware of their jointly attending. Joint attention is an important coordination mechanism in joint action. The capacity for engaging in joint attention, in particular in the sense of (...) this narrower definition, is frequently taken to indicate the presence of theory of mind in the participating agents, and is also implicated in the development of theory of mind. However, the prominence of sensorimotor components in establishing and sustaining episodes of joint attention — e.g., eye and head movements, pointing and vocalizations — suggests that sensorimotor approaches to social interaction may be well-placed to account for important parts of joint attention without invoking theory-of-mind abilities, and may therefore provide a valuable alternative to approaches emphasizing theory of mind. In particular, sensorimotor accounts may explain aspects of joint attention through the dynamics and regularities in the sensorimotor processes that coordinate the activities of the agents. (shrink)

The traditional use of conventional media by businesses for audience targeting has shifted with the rise of influencer marketing, notably on platforms like TikTok, posing challenges in content adaptation and technological adaptation. Albert Bandura's Social Cognitive Theory examines factors shaping purchasing behavior, particularly relevant for young professionals. A quantitative correlational study focused on young professionals engaging with TikTok and influenced by Filipino TikTok creators, revealing education level as a key determinant of purchasing behavior. Extended TikTok engagement positively correlates with increased (...) purchasing likelihood. Filipino TikTok influencers significantly impact young professionals' purchasing decisions, emphasizing the need for tailored marketing strategies targeting this demographic. Recommendations were provided for effective influencer and digital marketing strategies targeting young professionals. (shrink)

Personal AI assistants are now nearly ubiquitous. Every leading smartphone operating system comes with a personal AI assistant that promises to help you with basic cognitive tasks: searching, planning, messaging, scheduling and so on. Usage of such devices is effectively a form of algorithmic outsourcing: getting a smart algorithm to do something on your behalf. Many have expressed concerns about this algorithmic outsourcing. They claim that it is dehumanising, leads to cognitive degeneration, and robs us of our freedom and autonomy. (...) Some people have a more subtle view, arguing that it is problematic in those cases where its use may degrade important interpersonal virtues. In this article, I assess these objections to the use of AI assistants. I will argue that the ethics of their use is complex. There are no quick fixes or knockdown objections to the practice, but there are some legitimate concerns. By carefully analysing and evaluating the objections that have been lodged to date, we can begin to articulate an ethics of personal AI use that navigates those concerns. In the process, we can locate some paradoxes in our thinking about outsourcing and technological dependence, and we can think more clearly about what it means to live a good life in the age of smart machines. (shrink)

In “Beat the (Backward) Clock,” we argued that John Williams and Neil Sinhababu’s Backward Clock Case fails to be a counterexample to Robert Nozick’s or Fred Dretske’s Theories of Knowledge. Williams’ reply to our paper, “There’s Nothing to Beat a Backward Clock: A Rejoinder to Adams, Barker and Clarke,” is a further attempt to defend their counterexample against a range of objections. In this paper, we argue that, despite the number and length of footnotes, Williams is still wrong.

This paper connects recent findings from experimental epistemology to several major themes in classical Indian epistemology. First, current evidence supports a specific account of the ordinary knowledge concept in contemporary anglophone American culture. According to this account, known as abilism, knowledge is a true representation produced by cognitive ability. I present evidence that abilism closely approximates Nyāya epistemology’s theory of knowledge, especially that found in the Nyāya-sūtra. Second, Americans are more willing to attribute knowledge of positive facts than of negative (...) facts, especially when such facts are inferred and even when the positive and negative “facts” are logically equivalent. Similar suspicions about knowledge of negative facts seemingly occur in classical Indian epistemology, suggesting that the asymmetry might not be an American quirk but instead reflect a cross-culturally robust tendency in knowledge attributions. Each of these themes—abilism and the positive/negative asymmetry—presents an exciting opportunity for further research in experimental cross-cultural epistemology. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...) Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

It is proposed that our memory is made up of individual, unconnected Records, to each of which is attached a Heading. Retrieval of a Record can only be accomplished by addressing the attached Heading, the contents of which cannot itself be retrieved. Each Heading is made up of a mixture of content in more or less literal form and context, the latter including specification of environment and of internal states (e.g. drug states and mood). This view of memory allows an (...) easy account of a number of natural memory phenomena as well as a variety of laboratory findings such as the differences between recall and recognition. The theory further proposes that Headed Records can neither be deleted nor modified. Data apparently against such a hypothesis can be accounted for in terms of the retrieval process. (shrink)

In this paper, we aim to show that the framework of embedded, distributed, or extended cognition offers new perspectives on social cognition by applying it to one specific domain: the psychology of memory. In making our case, first we specify some key social dimensions of cognitive distribution and some basic distinctions between memory cases, and then describe stronger and weaker versions of distributed remembering in the general distributed cognition framework. Next, we examine studies of social influences on memory in cognitive (...) psychology, and identify the valuable concepts and methods to be extended and embedded in our framework; we focus in particular on three related paradigms: transactive memory, collaborative recall, and social contagion. Finally, we sketch our own early studies of individual and group memory developed within our framework of distributed cognition, on social contagion of autobiographical memories, collaborative flashbulb memories, and memories of high school at a high school reunion. We see two reciprocal benefits of this conceptual and empirical framework to social memory phenomena: that ideas about distributed cognition can be honed against and tested with the help of sophisticated methods in the social cognitive psychology of memory; and conversely, that a range of social memory phenomena that are as yet poorly understood can be approached afresh with theoretically motivated extensions of existing empirical paradigms. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...) of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (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)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...) that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

This compilation of references includes all references for the knowledge-how chapters included in Bengson & Moffett's edited volume. The volume and the compilation of references may serve as a good starting point for people who are unfamiliar with the philosophical literature on knowledge-how.

This paper questions the idea that theism can function as an explanatory hypothesis to account for the nature and origins of the cosmos. Invoking God cannot dissolve the mystery of existence, and the characteristic religious response here is one of awe and humility. I then address David E. Cooper’s challenge of showing how a ”doctrine of mystery’ can have any discursible content. It is argued that certain aspects of our human experience afford us glimpses of the divine nature -- intimations (...) of the transcendent, which shine through from the ineffable source of our being to the human world we inhabit. (shrink)

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner’s conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner’s original thought experiment was central to the development of QBist thinking. The (...) focus of this paper concerns two very instructive modifications to Wigner’s puzzle: One, a recent no-go theorem by Frauchiger and Renner, and the other a thought experiment by Baumann and Brukner. We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner’s action on his friend then becomes, from the friend’s perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner’s original paper, neither agent should be considered as in “suspended animation.” In this light, QBism brings an entirely new perspective to understanding Wigner’s friend thought experiments. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

Our modern egalitarian and individualistic age is suspicious of authority, and in recent times there have been almost daily reports in the press of cases where trust in various authorities, including financial, governmental, political and religious, has been found to have been abused or misplaced. Such disappointments seem to bolster the case for withholding trust in external authority and falling back on one’s own resources. But if the lessons from Linda Zagzebski’s groundbreaking work are accepted, 1 self- reliance turns out (...) to be a confused and probably incoherent ideal ; and the rational and self-reflective person is committed to believing and acting on authority. In the second half of this short discussion paper I shall raise some possible concerns about Zagzebski’s positive case for reliance on authority, focussing on the moral and religious spheres. First however, let me say something about the negative part of Zagzebski’s work, her critique of self-reliance. Since I find this wholly convincing, I shall confine myself to some supplementary observations, mainly to do with the historical context in which her critique is located. (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)

Excerpts and paraphrases of this memoir appeared in 2008 and 2009. I posted it in full here in happy memory of Peter Hare and my joyful years with him. -/- 2008. Remembering Peter Hare 1935–2008. Philosophy Now. Co-authors: T. Madigan and A. Razin. Issue 66 March/April 2008. Pages 50–2. PDF -/- 2009. Remembering My Life with Peter Hare. Remembering Peter Hare 1935–2008. Ed. J. Campbell. Society for the Advancement of American Philosophy. pp. 9–16. http://american-philosophy.org/documents/RememberingPeterHare_final.pdf -/- Peter H. Hare, Distinguished Professor (...) Emeritus of Philosophy at the University of Buffalo (SUNY at Buffalo), died peacefully in his sleep on Thursday, January 3, 2008. I would like to share my memories of my life with him. Others have eulogized him, enumerated his virtues and accomplishments, and written his obituaries. I am revisiting my personal relationship with him. These memories are as much about me as about him. (shrink)

This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. Polygons are plane or two-dimensional; the simplest are triangles. Polyhedra [or polyhedrons] are solid or three-dimensional; the simplest are tetrahedra [or triangular pyramids, made of four triangles]. -/- A regular polygon has equal sides and equal angles. A polyhedron having congruent faces and congruent [polyhedral] angles is not called regular, as some might expect; rather they are said to be subregular—a word coined for (...) this lecture. To repeat, a subregular polyhedron has congruent faces and congruent [polyhedral] angles. A subregular polyhedron whose faces are all regular polygons is regular—using standard terminology. -/- Geometers before Euclid showed that there are “essentially” only five regular polyhedra: every regular polyhedron is a tetrahedron (4 faces), a hexahedron or cube (6 faces), an octahedron (8 faces), a dodecahedron (12 faces), or an icosahedron (20 faces). -/- The first question is whether there are subregular polyhedra that are not regular. For example, are there tetrahedra having congruent angles and congruent triangular faces but whose faces are not equilateral triangles? -/- Another question is the classification of subregular polyhedra if they exist. For example, considering the fact that the regular tetrahedra all have equilateral triangles as faces, we ask which triangles other than equilaterals are faces of subregular tetrahedra. Similarly, considering the fact that the regular hexahedra all have squares as faces, we ask which quadrangles other than squares are faces of subregular hexahedra. -/- After introductory remarks that include historical and philosophical points, we concentrate on tetrahedra. A triangle that is congruent to each of the four faces of a tetrahedron is called a generator of the tetrahedron. The main result proved is that every acute triangle is a generator of a subregular tetrahedron. The proof includes an algorithm –implementable with scissors and paper –that constructs from any given acute triangle a subregular tetrahedron whose faces are congruent to the given triangle. -/- Algorithm: Given any acute triangle. Construct a similar triangle whose sides are double the sides of the given triangle. Draw the three lines connecting the three midpoints of the sides (making four triangles congruent to the given triangle—a central triangle surrounded by three peripheral triangles). Make three “hinges” along the lines connecting the midpoints. “Fold” the peripheral triangles together (into a tetrahedron). [LIGHTLY EDITED VERSION OF PRINTED ABSTRACT] Acknowledgements: William Lawvere, Colin McLarty, Irvin Miller, Frango Nabrasa, Lawrence Spector, Roberto Torretti, and Richard Vesley. -/- . (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...) weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself.Em sua forma mais forte e geral, o princípio da referência universalista afirma que toda proposição refere-se ao universo completo do discurso propriamente dito, independentemente de quão limitados sejam os referentes de seus termos não-lógicos ou com conteúdo. Embora Boole mudasse de um modelo monístico de universo-fixo nos seus trabalhos iniciais de 1847 e 1848 para um modelo pluralista de universo-múltiplo no seu tratado maduro de 1854, ele nunca hesitou em sua aceitação franca do princípio da referência universalista, possivelmente em uma forma ligeiramente mais fraca. De fato, ele considerou este princípio como um acompanhamento essencial para a sua teoria de formação de conceitos e de proposições. Visões semelhantes são encontradas em lógicos posteriores, e algumas das mais recentes formulações da lógica clássica de primeira ordem parecem estar de acordo com uma forma deste, se é que elas não implicam, de fato, o próprio princípio. (shrink)