This develops a framework for second-order conditionalization on statements about one's own epistemic reliability. It is the generalization of the framework of "Second-Guessing" (2009) to the case where the subject is uncertain about her reliability. See also "Epistemic Self-Doubt" (2017).

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation in inquisitive semantics: (...) truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

The aim of this paper is to apply the accuracy based approach to epistemology to the case of higher order evidence: evidence that bears on the rationality of one's beliefs. I proceed in two stages. First, I show that the accuracy based framework that is standardly used to motivate rational requirements supports steadfastness—a position according to which higher order evidence should have no impact on one's doxastic attitudes towards first order propositions. The argument for this will require (...) a generalization of an important result by Greaves and Wallace for the claim that conditionalization maximizes expected accuracy. The generalization I provide will, among other things, allow us to apply the result to cases of self-locating evidence. In the second stage, I develop an alternative framework. Very roughly, what distinguishes the traditional approach from the alternative one is that, on the traditional picture, we're interested in evaluating the expected accuracy of conforming to an update procedure. On the alternative picture that I develop, instead of considering how good an update procedure is as a plan to conform to, we consider how good it is as a plan to make. I show how, given the use of strictly proper scoring rules, the alternative picture vindicates calibrationism: a view according to which higher order evidence should have a significant impact on our beliefs. I conclude with some thoughts about why higher order evidence poses a serious challenge for standard ways of thinking about rationality. (shrink)

A normative reason for a person to? is a consideration which favours?ing. A motivating reason is a reason for which or on the basis of which a person?s. This paper explores a connection between normative and motivating reasons. More specifically, it explores the idea that there are second-order normative reasons to? for or on the basis of certain first-order normative reasons. In this paper, I challenge the view that there are second-order reasons so understood. I (...) then show that prominent views in contemporary epistemology are committed to the existence of second-order reasons, specifically, views about the epistemic norms governing practical reasoning and about the role of higher-order evidence. If there are no second-order reasons, those views are mistaken. (shrink)

Is second-order logic logic? Famously Quine argued second-order logic wasn't logic but his arguments have been the subject of influential criticisms. In the early sections of this paper, I develop a deeper perspective upon Quine's philosophy of logic by exploring his positive conception of what logic is for and hence what logic is. Seen from this perspective, I argue that many of the criticisms of his case against second-order logic miss their mark. Then, in (...) the later sections, I go beyond Quine to develop a novel case that quantification into polyadic predicate position, understood as requiring quantifiers to range over relations, isn't intelligible. (shrink)

A second-order conspiracy (SOC) is a conspiracy that aims to create (and typically also disseminate) a conspiracy theory. Second-order conspiracy theories (SOCT) are theories that explain the occurrence of a given conspiracy theory by appeal to a conspiracy. In this paper I argue that SOC and SOCT are useful and coherent concepts, while also having numerous philosophically interesting upshots (in terms of epistemology, explanation, and prediction). Secondly, I appeal to the nature of two specific kinds of (...) second-order conspiracies to make the case for what has been called ‘local generalism’ (Stamatiadis-Bréhier 2023a). Specifically, I focus on so-called ‘denial industries’ to argue that the structure of these second-order conspiracies allows us to infer non-accidental generalisations about the domain of conspiracy theories. Even though it is true that there is nothing epistemically problematic with the general class of conspiracy theories, there are specific subsets of conspiracy theories that warrant immediate strong suspicion (cf. Dentith 2022). By looking at the intricate mechanisms by which these denial industries operate, we can infer that the conspiracy theories that are produced by them are epistemically unwarranted. I conclude by making some exploratory remarks about what the metaphysics of second-order conspiracies would look like. (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)

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine (...) Williamson’s primitivist approach according to which second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion. (shrink)

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.

Context: The problems that are most in need of interdisciplinary collaboration are “wicked problems,” such as food crises, climate change mitigation, and sustainable development, with many relevant aspects, disagreement on what the problem is, and contradicting solutions. Such complex problems both require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order (...) science in domains where there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem, 4. rely on first-order perspectives to see themselves as perspectives, and 5. be based on other rules than first-order research. Implications: The perspectivist insights of second-order science provide a new way of understanding interdisciplinary research that leads to new polyocular methods and research designs. It also points to more reflexive ways of dealing with scientific expertise in democratic processes. The main challenge is that this is a paradigmatic shift, which demands that the involved disciplines, at least to some degree, subscribe to a perspectivist view. Constructivist content: Our perspectivist approach to science is based on the second-order cybernetics and systems theories of von Foerster, Maruyama, Maturana & Varela, and Luhmann, coupled with embodied theories of cognition and semiotics as a general theory of meaning from von Uexküll and Peirce. (shrink)

Philosophers who work on desert-adjustment within axiology often articulate the concept of desert as follows: x deserves y on the basis of z. This formulation allows for a focused examination that encompasses deservers, deservings, and desert bases. I call this first-order desert. This paper posits that axiology grounded solely in first-order desert fails to adequately capture our nuanced intuitions concerning desert. I contend that to construct an axiology that more effectively aligns with our desert-sensitive intuitions, we must incorporate (...) considerations of second-order desert. Second-order desert is defined as follows: x deserves to live a life in which x deserves y on the basis of z. Initially, I provide a definition of first-order desert, followed by an elucidation of second-order desert. Subsequently, I explore various counter-arguments against my proposition. I defend my proposal against potential counter-arguments, demonstrating that a desert-adjusted axiological theory will be significantly better-off by incorporating second-order desert considerations. (shrink)

Context: Many recent research areas such as human cognition and quantum physics call the observer-independence of traditional science into question. Also, there is a growing need for self-reflexivity in science, i.e., a science that reflects on its own outcomes and products. Problem: We introduce the concept of second-order science that is based on the operation of re-entry. Our goal is to provide an overview of this largely unexplored science domain and of potential approaches in second-order fields. (...) Method: We provide the necessary conceptual groundwork for explorations in second-order science, in which we discuss the differences between first- and second-order science and where we present a roadmap for second-order science. The article operates mainly with conceptual differentiations such as the separation between three seemingly identical concepts such as Science II, Science 2.0 and second-order science. Results: Compared with first-order science, the potential of second-order science lies in 1. higher levels of novelty and innovations, 2. higher levels of robustness and 3. wider integration as well as higher generality. As first-order science advances, second-order science, with re-entry as its basic operation, provides three vital functions for first-order science, namely a rich source of novelty and innovation, the necessary quality control and greater integration and generality. Implications: Second-order science should be viewed as a major expansion of traditional scientific fields and as a scientific breakthrough towards a new wave of innovative research. Constructivist content: Second-order science has strong ties with radical constructivism, which can be qualified as the most important root/origin of second-order science. Moreover, it will be argued that a new form of cybernetics is needed to cope with the new problems and challenges of second-order science. (shrink)

examine Nathan Salmon’s solution to the problem of trivialization, as it arises for conceptions of general term rigidity that construe it as identity of designation across possible worlds. I argue that he does not succeed in showing that some alleged general terms, such as “the colour of the sky” are non-rigid, but also that a small class of different examples that he presents, which can be construed as second order descriptions, are indeed non-rigid general terms, although for reasons (...) different from those he thought. (shrink)

In March 2016, an interdisciplinary group met for two days and two evenings to explore the implications for policy making of second-order science. The event was sponsored by SITRA, the Finnish Parliament's Innovation Fund. Their interest arose from their concern that the well-established ways, including evidence-based approaches, of policy and decision making used in government were increasingly falling short of the complexity, uncertainty, and urgency of needed decision making. There was no assumption that second-order science or (...) second-order cybernetics would reveal any practical possibilities at this early stage of enquiry. On the other hand, some members of the group are practioners in both policy and in facilitating change in sectors of society. Thus, the intellectual concepts were strongly grounded in experience. This is an account of the deliberations of that group and some reflections on what came out of the various shared contributions and ensuing dialogues. The overall conclusion of the event is that there definitely are possibilities that are worthy of further research and exploration. (shrink)

Both motivational internalism and externalism need to explain why sometimes moral judgments tend to motivate us. In this paper, I argue that Dreier’ second-order desire model cannot be a plausible externalist alternative to explain the connection between moral judgments and motivation. I explain that the relevant second-order desire is merely a constitutive requirement of rationality because that desire makes a set of desires more unified and coherent. As a rational agent with the relevant second-order (...) desire is disposed towards coherence, she will have some motivation to act in accordance with her moral judgments. Dreier’s second-order desire model thus collapses into a form of internalism and cannot be a plausible externalist option to explain the connection between moral judgments and motivation. (shrink)

The paper sets forth an argument against Kim's distinction between levels and orders.

Aside from the systematic theory of recognition, Honneth’s work in the last decade has also centered around a less commented-upon theme: the critical social theoretic diagnosis of social pathologies. This paper claims first that his diverse diagnoses of specific social pathologies can be productively united through the conceptual structure evinced by second-order disorders, where there are substantial disconnects, of various kinds, between first-order contents and second-order reflexive understandings of those contents. The second major claim (...) of the paper is that once we understand social pathologies as second-order disorders, it becomes apparent that critical social theory must do more than accurately identify and explicate these disorders at the phenomenological and action-theoretic levels. It must further engage in insightful sociological explanations of the social causes of those pathologies in order to further the prognostic and therapeutic tasks implied by the aim of developing a social theory with emancipatory intent. The paper argues that the identificatory and explicative components of diagnostic social theory have been fulfilled by Honneth to a much greater degree than the latter components of explanation, prognosis and therapy. (shrink)

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as (...) being either extensional or intensional—and whether either is more appropriate for this approach to the foundations of set theory. Although there seems to be a case for the extensional interpretation resulting from modal considerations, I show how there is no obstacle to starting with an intensional second-order logic. I do so by showing how the $\varepsilon$ operator can have the effect of “extensionalizing” intensional second-order entities. (shrink)

A number of widely discussed court decisions on cases of insults against religious feelings in Russia, such as the relatively recent “Pokemon Go” case of blogger Ruslan Sokolovsky or the lawsuit filed against an Orthodox priest by Nikolai Ryabchevsky in Yekaterinburg for comparing Lenin with Hitler, make pertinent the question of why toleration becomes so difficult in matters concerning religion. In this paper, I revise the classical liberal concept of toleration (David Heyd, Peter Nicholson, and John Horton), arguing that it (...) is challenged by contemporary philosophers, who see no room for applying this concept in the “domain of identities”. The most prominent case of “primordial” identity, that is, the notion of identity as a given, is the claim of devoted believers for recognition. Should we replace the principle of toleration by the principle of recognition since the latter better corresponds to identity claims? To address this question, in the first part of the article I describe the mechanism of tolerant attitude (Nicholson, Heyd) and in the second part, I analyze the debates about the possibility or impossibility of inner religious toleration (Avishai Margalit, Cary Nederman, and Maxim Khomyakov) and further compare toleration and recognition as normative principles. In the light of the debates I took part in the conference hosted by the University of Southern Denmark in October 2019 as part of the project “Religious Majority/Minority in Public Space in Russia and Northern Europe: Historical-Cultural Analysis”, I come to the conclusion that the principle of toleration is preferable to the principle of recognition because the “second-order” arguments for toleration in a secular state will be universally acceptable (pragmatic argument) and, therefore, the principle of toleration is more logical (analytical argument). Following Peter John’s thesis about minimal recognition embedded in toleration, it may also be concluded that we need a normatively charged idea of citizenship, which could provide us with universal “second-order” foundation. (shrink)

Here's the thing: when you look at it from just the right angle, it's entirely obvious how semantics for second-order relevant logics ought to go. Or at least, if you've understood how semantics for first-order relevant logics ought to go, there are perspectives like this. What's more is that from any such angle, the metatheory that needs doing can be summed up in one line: everything is just as in the first-order case, but with more indices. (...) Of course, it's no small matter finding the magical angle from which everything becomes obvious. And even having found this perspective, one cannot assume one's audience will find things as obvious as oneself. All that to say this: if the results in the paper below strike you as obvious, pay attention to the perspective that makes that possible. And if they don't, feel free to ignore this preamble in its entirety. (shrink)

Epistocracy and populism are usually seen as opposites. The first finds error in democracy’s reliance on the sub-optimal decisions by the supposedly incompetent masses, and argues that political decisions should be tied to epistemic merit, not popularity. The populist critique of democracy, contrarily, finds that there is not enough political confrontation in standard representative democracies where the ‘real people’ are not properly embodied, and thus pits an imagined direct will of the unified and virtuous people against a self-serving establishment. This (...) article demonstrates that these ideologies have surprising underlying similarities concerning their categorization, political ontology, epistemology and a conception of political authority. Firstly, they both are second-order political ideologies that are not directly tied with substantive political content but rather with the interpretation of how to govern assuming disagreement concerning first-order political ideologies. Secondly, their political ontology divides citizens into two constitutively differing parts, one of which they (partly) exclude from political membership. Thirdly, their political epistemology assumes the existence of political truths which makes their conception of authority anti-proceduralist, either instrumentalist or moralist. Fourthly, they downplay the value of pluralism, deliberation and dissent. Uncovering these commonalities helps us detect and understand the dynamics of some anti-democratic tendencies better. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

These comments, on the paper by Branden Thornhill-Miller and Peter Millican, and on the critique of that paper by Janusz Salamon, divide into four sections. In the first two sections, I briefly sketch some of the major themes from the paper by Thornhill-Miller and Millican, and then from the critique by Salamon. In the final two sections, I provide some critical thoughts on Salamon’s objections to Thornhill-Miller and Millican, and then on the leading claims made by Thornhill-Miller and Millican. I (...) find much to commend, but also some things to dispute, in both papers. As is so often the way, I shall focus on areas of disagreement. (shrink)

The target article proposes that people perceive social robots as depictions rather than as genuine social agents. We suggest that people might instead view social robots as social agents, albeit agents with more restricted capacities and moral rights than humans. We discuss why social robots, unlike other kinds of depictions, present a special challenge for testing the depiction hypothesis.

Egan argues against Lewis’s view that properties are sets of actual and possible individuals and in favour of the view that they are functions from worlds to extensions (sets of individuals). Egan argues that Lewis’s view implies that 2nd order properties are never possessed contingently by their (1st order) bearers, an implication to which there are numerous counter-examples. And Egan argues that his account of properties is more commensurable with the role they play as the semantic values of (...) predicates than is Lewis’s. (shrink)

Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.

This paper proposes the feasibility of a second-order approach in cosmology. It is intended to encourage cosmologists to rethink standard ideas in their field, leading to a broader concept of self-organization and of science itself. It is argued, from a cognitive epistemology perspective, that a first-order approach is inadequate for cosmology; study of the universe as a whole must include study of the scientific observer and the process of theorizing. Otherwise, concepts of self-organization at the cosmological scale (...) remain constrained by unacknowledged assumptions and biases. Examples of limiting notions are discussed in the context of alternatives. To include the role of the theorist does not mean reducing science to subjective or sociological terms. On the contrary, second-order science would provide a more complete portrait of nature. The work of cosmologist Lee Smolin is discussed as a candidate example of second-order cosmology. (shrink)

A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal (...) representations of belief: they cannot be both fully accurate and maximally specific. (shrink)

We extend Barbanera and Berardi's symmetric lambda calculus [2] to second-order classical propositional logic and prove its strong normalization.

Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I argue that radical constructivism poses a series of deep methodological constraints on educational research. We focus on the work of Ulrich et al. to illustrate the practical implications of these constraints.

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal semantics from an (...) ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use. (shrink)

This paper puts forward three critiques of pardo’s second-order proof rules thesis. The first criticism states that these rules are not suitable to guide the interpretation of standards of proof rules because they confuse matters of legal interpretation with matters of epistemology. The second criticism states that second-order proof rules are affected by the same indeterminacy problems they are designed to resolve, thereby rendering them unsuitable for the task they are purposely designed for. The third (...) criticism renders pardo’s proposal redundant. a reconceptualization of second-order proof rules is offered. (shrink)

Heidegger tries to explain our emotional life applying three schemes: causal explanation, mental internalisation of emotions and metaphorical expression. None of the three schemes explains emotion though. Either because the causal nexus does not always occur or because objects and people in the external world are carriers of emotional agents or because language is already on a metaphorical level. Moreover, how is it possible that there are presently emotions constituting our life without our being aware of their existence? From the (...) analysis of boredom in its three varieties (“bored by X”, “get oneself bored”, and “it is boring”) we will get to the depth where emotions lie, trying to rouse them and to keep them awake. Although it surfaces with the force and energy of the present, every emotion has its past and future constitution. How can we understand the future of a present emotion along with its past? (shrink)

A famous passage in Section 64 of Frege’s Grundlagen may be seen as a justification for the truth of abstraction principles. The justification is grounded in the procedureofcontent recarvingwhich Frege describes in the passage. In this paper I argue that Frege’sprocedure of content recarving while possibly correct in the case of first-order equivalencerelations is insufficient to grant the truth of second-order abstractions. Moreover, I propose apossible way of justifying second-order abstractions by referring to the operation (...) of contentrecarving and I show that the proposal relies to a certain extent on the Basic Law V. Therefore,if we are to justify the truth of second-order abstractions by invoking the content recarvingprocedure we are committed to a special status of some instances of the Basic Law V and thusto a special status of extensions of concepts as abstract objects. (shrink)

Beginning with a survey of the shortcoming of theories of organology/media-as-externalization of mind/body—a philosophical-anthropological tradition that stretches from Plato through Ernst Kapp and finds its contemporary proponent in Bernard Stiegler—I propose that the phenomenological treatment of media as an outpouching and extension of mind qua intentionality is not sufficient to counter the ̳black-box‘ mystification of today‘s deep learning‘s algorithms. Focusing on a close study of Simondon‘s On the Existence of Technical Objectsand Individuation, I argue that the process-philosophical work of Gilbert (...) Simondon, with its critique of Norbert Wiener‘s first-order cybernetics, offers a precursor to the conception of second-order cybernetics (as endorsed byFrancisco Varela, Humberto Maturana, and Ricardo B. Uribe) and, specifically, its autopoietic treatment of information. It has been argued by those such as Frank Pasquale that neuro-inferential deep learning systems premised on predictive patterning, suchas AlphaGo Zero, have a veiled logic and, thus, are ̳black boxes‘. In detailing a philosophical-historical approach to demystify predictive patterning/processing and the logic of such deep learning algorithms, this paper attempts to shine a light on such systems and their inner workingsàla Simondon. (shrink)

In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the (...) second-order domain in terms of definability, can serve a neo-logicist's purposes. The problem, in both cases, is similar: neither Wright nor Hale is sufficiently sensitive to the demands that impredicativity imposes. Finally, I defend my own earlier attempt to finesse this issue, in "A Logic for Frege's Theorem", from Hale's criticisms. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the (...) evidence calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

This paper argues that, given the representational theory of mind, one cannot know a priori that one knows that p as opposed to being incapable of having any knowledge states; but one can know a priori that one knows that p as opposed to some other proposition q.

Purpose – This study aims to examine the observer’s role in “infant psychophysics”. Infant psychophysics was developed because the diagnosis of perceptual deficits should be done as early in a patient’s life as possible, to provide efficacious treatment and thereby reduce potential long-term costs. Infants, however, cannot report their perceptions. Hence, the intensity of a stimulus at which the infant can detect it, the “threshold”, must be inferred from the infant’s behavior, as judged by observers (watchers). But whose abilities are (...) actually being inferred? The answer affects all behavior-based conclusions about infants’ perceptions, including the well-proselytized notion that auditory stimulus-detection thresholds improve rapidly during infancy. Design/methodology/approach – In total, 55 years of infant psychophysics is scrutinized, starting with seminal studies in infant vision, followed by the studies that they inspired in infant hearing. Findings – The inferred stimulus-detection thresholds are those of the infant-plus-watcher and, more broadly, the entire laboratory. The thresholds are therefore tenuous, because infants’ actions may differ with stimulus intensity; expressiveness may differ between infants; different watchers may judge infants differently; etc. Particularly, the watcher’s ability to “read” the infant may improve with the infant’s age, confounding any interpretation of perceptual maturation. Further, the infant’s gaze duration, an assumed cue to stimulus detection, may lengthen or shorten nonlinearly with infant age. Research limitations/implications – Infant psychophysics investigators have neglected the role of the observer, resulting in an accumulation of data that requires substantial re-interpretation. Altogether, infant psychophysics has proven far too resilient for its own good. Originality/value – Infant psychophysics is examined for the first time through second-order cybernetics. The approach reveals serious unresolved issues. (shrink)

Abstract : The main goal in this work to find the general solution for some kind of linear second order homogenous differential equations with variable coefficients which have the general form , by using the substitution ,which transform form the above equation to Riccati equation .

In this paper, a horizontally moving suspended mass pendulum base is designed and controlled using robust control theory. H  optimal loop shaping with first and second order desired loop shaping function controllers are used to improve the performance of the system using Matlab/Simulink Toolbox. Comparison of the H  optimal loop shaping with first and second order desired loop shaping function controllers for the proposed system have been done to track the desired angular position of (...) the pendulum using step and sine wave input signals and a promising result has been obtained succesfully. (shrink)

Constructivism is a philosophical current that manifests itself greatly within the realm of contemporary epistemology. Its bases come from the idea that knowledge is not only actively constructed by the observer but also provides a lens through which reality can be interpreted as a result of experiences. This paper traces a brief interdisciplinary curve that outlines some of the most important philosophical approaches that contributed to the consolidation of this school of thought for more than twenty-five centuries.

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a (...) proposition that represents a proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

First-order evidence is evidence which bears on whether a proposition is true. Higher-order evidence is evidence which bears on whether a person is able to assess her evidence for or against a proposition. A widespread view is that higher-order evidence makes a difference to whether it is rational for a person to believe a proposition. In this paper, I consider in what way higher-order evidence might do this. More specifically, I consider whether and how higher-order (...) evidence plays a role in determining what it is rational to believe distinct from that which first-order evidence plays. To do this, I turn to the theory of reasons, and try to situate higher-order evidence within it. The only place I find for it there, distinct from that which first-order evidence already occupies, is as a practical reason, that is, as a reason for desire or action. One might take this to show either that the theory of reasons is inadequate as it stands or that higher-order evidence makes no distinctive difference to what it is rational to believe. I tentatively endorse the second option. (shrink)

Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved. Second, a further such debate, the tropes versus universals dispute, is taken to be resolved. In this paper I first argue that higher- (...) class='Hi'>order realism does not in fact resolve the tropes versus universals dispute. In a constructive spirit, I then develop higher-order realism in a way that leads to a dissolution, rather than a resolution, of this dispute too. (shrink)

I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled (...) way of knowing when to stop second-guessing oneself. Peer disagreement is treated as a special case where one doubts oneself because of news that an intellectual equal disagrees. This framework, and variants of it, imply that the typically stated belief that an equally reliably peer disagrees is incoherent, and thus that pure rationality constraints without further substantive information cannot give an answer as to what to do. The framework also shows that treating both ourselves and others as thermometers in the disagreement situation does not imply the Equal Weight view. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology (...) of disagreement. Third, the answer is not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

In this paper, we give a new argument for the existence of moral luck. The argument is based on a manipulation case in which two agents both lack second-order control over their actions, but one of them has first-order control. Our argument is, we argue, in several respects stronger than standard arguments for moral luck. Five possible objections to the argument are considered, and its general significance for the debate on moral luck is briefly discussed.