In Freedom of the Will and the Concept of a Person, Harry Frankfurt put forward a theory that what is essential to be a person is second-order volition. The notion of second-order volition can be used as a key conceptual tool in understanding the conflict between desires. By means of the notion, this paper argues that the conflict between desires in our minds lies in the conflict between second-order volitions, other than the conflict (...) between first-order desires. Based on this claim, this paper suggests that, due to the misunderstanding of the nature of the conflict between desires, the analysis of unwilling addict and wanton addict given by Frankfurt is thus wrong, and in his follow-up articles he made wrong description of the phenomenon concerning the conflict between desires. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: Umpleby’s approach to second-order science is top-down, and as such, fails to distinguish the cognitive mechanisms that provide the direct enacted link between such science and constructivism. When the idea of “ceteris paribus” holds little meaning to the examined situation, we are in the realm of second-order science, or Science 2. Only Science 2 can deal with emergence, volition, (...) and reflexive anticipation. These three properties are how constructivism gets enacted and provide the foundation upon which Science 2 inquiries rest. (shrink)

In this article I look at some the issues, problems and self-imposed dilemmas that emerge from Harry Frankfurt’s well-known essay ‘Freedom of the Will and the Concept of a Person’. That essay has exerted a widespread influence on subsequent thinking in ethics and philosophy of mind, especially through its central idea of ‘second-order’ desires and volitions. Frankfurt’s approach promises a third-way solution to certain longstanding issues – chiefly those of free-will versus determinism and the mind/body problem – (...) that have up to now resisted the best efforts of philosophical deliverance or therapy. It looks very much like the kind of answer that would avoid the ‘high priori road’ of any Kantian or suchlike metaphysical approach by adopting a broadly naturalized conception of human moral agency while not going so far down the path toward wholesale ethical naturalism as to lose the benefits that come with the Kantian conception. However I suggest that this appearance is deceptive and that Frankfurt’s way of addressing these issues – especially his leading idea of second-order desires and volitions – lies open to a long-familiar range of objections from both a naturalist and a strong autonomist quarter. More specifically, I show that his notion of moral will as possessing a multiplex structure whereby higher-order volitions can reject or countermand the promptings of unregenerate first-order desire is one that must inherently give rise to various problems of a logical, metaphysical, and – most importantly in this context – ethical character. I conclude that a thoroughgoing naturalism is the only response that can meet the kinds of challenge increasingly mounted from various scientific quarters, notably those of neurophysiology and cognitive psychology.U ovome članku razmatram neka pitanja, probleme i, kako mi se čini, samonametnute dileme koje proizlaze iz dobro poznatog ogleda Harryja Frankfurta “Freedom of the Will and the Concept of a Person”. Taj je ogled izvršio široki utjecaj na kasnije mišljenje u etici i filozofiji uma, naročito svojom središnjom idejom želja i htijenja “drugog reda”. Frankfurtov pristup obećava rješenje u obliku trećeg puta određenih starih problema – uglavnom problema odnosa slobodne volje i determinizma te odnosa uma i tijela – koji su se dosad opirali najboljim naporima filozofskog rješavanja ili terapije. On veoma nalikuje onoj vrsti odgovora koji apriorni put bilo kakva kantovskog ili sličnog metafizičkog pristupa želi izbjeći usvajanjem u širokom smislu naturalizirane koncepcije ljudskog moralnog djelovanja, ali tako da ne ode toliko daleko u smjeru etičkog naturalizma da izgubi prednosti koje su povezane s kantovskim pristupom. Tvrdim, međutim, da takav izgled vara i da je Frankfurtov način pristupanja tim pitanjima – a naročito njegova glavna ideja želja i htijenja drugog reda – podložna odavno poznatim prigovorima koji dolaze kako od strane naturalistâ tako i od strane strogih autonomista . Konkretnije, pokazujem da njegov pojam moralne volje kao nečega što posjeduje kompleksnu strukturu, čime htijenja višeg reda mogu odbaciti ili poništiti poticaje pokvarene želje prvog reda, jest takav da inherentno mora izazvati različite logičke, metafizičke i – što je u ovome kontekstu najvažnije – etičke probleme. Zaključujem da je posvemašnji naturalizam jedini odgovor koji može izaći na kraj s izazovima koji se sve više upućuju iz različitih znanstvenih krugova, naročito iz područja neurofiziologije i kognitivne psihologije. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Volitional Necessity and Volitional Shift:A Key to Sobriety?John Talmadge (bio)As a long-time amateur student of philosophy, I think my most effective contribution to this discussion of Dr. Rego's paper will be to discuss Harry Frankfurt's ideas from precisely the point of view of the beginner and the novice. After all, I had never experienced the pleasure of reading Frankfurt until reading Rego, so I can hardly be considered proficient (...) and conversant in analytical philosophy. To pretend to be so would be, in Frankfurt's way of thinking, to construe what I really am (a novice) as what I would ideally like to be (an expert). He calls this "the equation of the real with the ideal," and he certainly gets us thinking. He also says that our failure to mark the distinctions among our many passions (and our attitudes toward our passions) gets us into considerable confusion and trouble.Because I am most familiar with the diagnosis and treatment of addictions, I confine my comments to that domain. I have enjoyed over the years over the puzzling question of whether addiction should actually be called a "disease." This puzzle confounds us for one reason apparent to any armchair philosopher: how can we name something a disease when the removal of the offending agent banishes the problem? I have come to believe that Locke had it right when he said, "We would have a great many fewer disputes in the world if words were taken for what they are, the signs of our ideas only, and not for things themselves." (1994, 122) Addiction is not so much a disease as it is an idea. And this is where I think that Dr. Rego's insights have their most value.In his essay "The Importance of What We Care About," Frankfurt offers a particularly helpful example for those of us interested in the addictions. He observes that there are occasions when we care about something powerfully, and we care about it in such a fashion that we cannot avoid the consequences of the caring. His example from history is Martin Luther, who nailed his declaration to the door of the church with the statement, "Here I stand; I can do no other."It is clear, of course, that the impossibility to which Luther referred was a matter neither of logical nor of causal necessity. After all, he knew well enough that he was in one sense quite able to do the very thing he said he could not do; that is, he had the capacity to do it. What he was unable to muster was not the power to forbear, but the will.(Frankfurt 1988, 86)When an alcoholic finds success through Alcoholics Anonymous, he experiences what I would term a "volitional shift." No longer in the grip of alcohol itself, the alcoholic is constrained by what Frankfurt terms "volitional necessity." The alcoholic has a new constraint to which he declares he is subject, that is, "Today I will remain sober." [End Page 327]Frankfurt says that this capacity—the ability to reflect on ourselves—is precisely what separates us as uniquely human. As Frankfurt sees the world, the will of an agent is identical with the desire that motivates him (or would motivate him if he should act).1A first-order desire, such as the alcoholic's craving for a drink, may be contradicted by a second-order desire, specifically a desire not to crave a drink. The second-order desire is born of the individual's knowledge that the use of alcohol, in his case, will lead to dire consequences in terms of health, happiness, and stability. Frankfurt believes that an addict, for example, typically experiences a desire for the destructive chemical but also a desire not to use the chemical. This second-order desire is the one with which the addict identifies, and this reflects the addict's true self (Frankfurt 1988, 14).If we take Dr. Rego's point and notice how a therapist might approach a patient and define a problem, we see obvious distinctions between different schools of thought. To take three simple examples, consider the following: (a) a... (shrink)

While many profound philosophical questions arise about psychopaths, I wish to draw attention to two limitations in current debates. First, philosophers mainly deal with offender and forensic populations neglecting so-called ‘successful’ psychopaths. Second, philosophers mainly focus on the issue of empathy and responsibility, while relatively little attention is paid to volitional aspects. I address these two limitations together and argue that ‘successful’ psychopaths are volitionally constrained. In order to grasp and explore this deficiency, I argue in favour of (...) a more refined and fine-grained understanding of identifications. (shrink)

Classical Liberalism is a view that the only justifiable restraints on the actions and choices of individuals in political orders are ones necessary to preserve individual liberty. Central to this view of liberty is the individual being left free from coercive interference from other individuals and society as a whole. This view presumes the idea that the individual is, firstly, able to choose his ends and actions, and secondly, that the individual is the best judge of these. Thus, the individualism (...) of classical liberalism presupposes a view of human consciousness that is volitional: capable of engaging in choice and individual self-direction. If this view of human consciousness is in conflict with the physical casual and evolutionary accounts of the world, then classical liberalism would seem to have serious problem. Therefore, I argue that the correct conception of volitional consciousness is consistent with the physical causal and evolutionary accounts of the world. Presenting a conception of volitional consciousness that makes the best sense of our introspective experience and knowledge of the world, I then show how such a volitional consciousness is consistent with causality and biological evolution. (shrink)

In § 6 of his General Psychopathology (1st edition 1913) Jaspers distinguished between drives, wants and volitions as three different and irreducible kinds of motivational phenomena which are involved in human decision making and which may lead to successful actions. He has characterized the qualitative differences between volitions in comparison with basic vital drives and emotional wants such as being (a.) intentional, (b.) content-specific and (b.) directed towards concrete objects and actions as goals. Furthermore, Jaspers has presented and (...) discussed three kinds of pathological problems about motivation and willing. (1.) The first kind is impulsive action or impulsive behaviour, as e.g. in psychoses or personality disorders, which he compares with instinctive action which are both without any previous hesitation, deliberation and reflection of any presumable consequences, but still very different with respect to their motivational content. (2.) The second kind of pathological problems about motivation and willing are the inhibitions of the will and Jaspers is discussing two major kinds of them: (a.) the energetic or motivational inhibition of the will which is an inability of willing due to the mere lack of any drives and motives, as in the case of any severe and pathological depression; (b.) the cognitive inhibition of the will which is due to the pathological inability to be aware of and understand properly the complexity and difficulty of real life situations in order to solve some given tasks by appropriate decision making, as e.g. in some cases of schizophrenia. (3.) The third kind is a pathological weakness of the will which is extraordinary and not familiar to normal human adults. This pathological kind of weakness of the will consist in the complete causal ineffectiveness of the subjectively felt impulse of willing which is not leading to any inward and outward observable action, such as e.g. as a movement of the limbs or some verbal utterance. This pathological weakness of the will is a complete ineffectiveness of the volitional impulse and therefore different from what philosophers discuss under the heading of weakness of the will which presuppose some evaluation of the intended resp. realized action as ethically, morally or religiously right or wrong. Finally, there are three kinds of normal or non-pathological weakness of the will, as discussed by philosophers: (A.) ethical weakness of the will as in Aristotle’s disagreement about akrasia with the Platonic Socrates; (B) moral weakness of the will as in Kant’s analysis of the absence or failure of any specific moral reasoning by pure practical reason as opposed to mere strategic and pragmatic reason or as the occurrence of a self-deceptive “dialectics of the exception“; (C.) religious weakness of the will as in Pauls personal insight about the incoherence between his high spiritual aspirations and his factual ethical achievements. (shrink)

This essay considers how the Zhuangzi 莊子 sheds light on a new direction to the contemporary discussion of desires. Harry Frankfurt proposes an account of personhood based on a hierarchy of desires. He defines a wanton as a being that does not have second-order volitions, the desires that a certain desire of action becomes her will. J. David Velleman proposes, in the context of the Zhuangzi, that when a Daoist sage performs her skills she can be regarded (...) as a “higher” wanton because her actions are spontaneous flows of skillful actions. In this essay, I propose along the line of Velleman a constructive interpretation of the Zhuangzian way to deal with desires from my reading of the Zhuangzi. I argue that there are two roles a Daoist sage can play: the observer and the performer. A Daoist sage can be an observer at a certain time and a performer at other times. Although a performer can be regarded as a higher wanton, it is inappropriate to regard an observer as a wanton. Also, I propose that observation is a means to transform desires—once the practitioner achieves high spirituality, one does not need to possess second-order volitions because one’s first-order desires are transformed such that they are in accordance with the Dao 道. (shrink)

'God needs no instruments to act', Malebranche writes in Search 6.2.3; 'it suffices that He wills in order that a thing be, because it is a contradiction that He should will and that what He wills should not happen. Therefore, His power is His will' (450). After nearly identical language in Treatise 1.12, Malebranche writes that '[God's] wills are necessarily efficacious ... [H]is power differs not at all from [H]is will' (116). God's causal power, here, clearly traces only to (...) His volitions - not merely to the fact that He wills, but specifically to the content of His volitions ('"what" He wills'). Yet despite the obviously key role the ordinary notion of volitional content plays for Malebranche, recent writers have paid surprisingly little attention either to it or its exegetical implications. I hope to rectify this situation here. The plan of this paper is this: first, to borrow current work in the philosophy of mind to sketch the notion of an incomplete volition, i.e. one whose content is 'incomplete' in a sense to be explained; second, to show that Malebranche clearly allows and uses something like this notion; third, to apply the notion to Malebranche's doctrine of human freedom. In so doing, I believe, we can understand this doctrine in a new way, and one which: (i) is clearly consistent with his texts, and (ii) unlike other interpretations makes coherent sense out of the conflicting streams in his heroic attempt to reconcile his occasionalism - the doctrine that no finite substances have genuine causal powers - with our freedom; fourth, Contrast my interpretation with those of two recent writers: Sleigh et al. (1998) and Schmaltz (1996); and Fifth, Summarize the major results. (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)

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)

A rich literature has discussed what it is to respond to a reason, e.g., to believe or act on the basis of some consideration or another. In comparison, what it would be to respond to a second-order reason has been underexplored. Yet formulating an account of this is vital for maintaining the existence of second-order reasons in both the practical and epistemic domains. And indeed, there are reasons to doubt this is possible. For example, responding to (...) second-order reasons is meant to be different from simply coming to believe or act for a more richly described first-order reason but it's not clear what this would look like. This paper introduces an account of the second-order basing relation which meets these concerns. It therefore both develops our picture of second-order reasons and helps to defend their existence. (shrink)

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably (...) construed, in accordance with an abundant or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational. (shrink)

We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As (...) a corollary we obtain a semantic argument that the quantifier V is not definable in IPC² from ⊥, V, ^, →. (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)

Intuitionistic dependence logic was introduced by Abramsky and Väänänen [1] as a variant of dependence logic under a general construction of Hodges’ (trump) team semantics. It was proven that there is a translation from intuitionistic dependence logic sentences into second order logic sentences. In this paper, we prove that the other direction is also true, therefore intuitionistic dependence logic is equivalent to second order logic on the level of sentences.

In this paper, I shall provide a defence of second-order logic in the context of its use in the philosophy of mathematics. This shall be done by considering three problems that have been recently posed against this logic: (1) According to Resnik [1988], by adopting second-order quantifiers, we become ontologically committed to classes. (2) As opposed to what is claimed by defenders of second-order logic (such as Shapiro [1985]), the existence of non-standard models of (...) first-order theories does not establish the inadequacy of first—order axiomatisations (Melia [1995]). (3) In contrast with Shapiro’s suggestion (in his [1985]), second-order logic does not help us to establish referential access to mathematical objects (Azzouni [1994]). As I shall argue, each of these problems can be neatly solved by the second-order theorist. As a result, a case for second-order logic can be made. The first two problems will beconsidered rather briefly in the next section. The rest of the paper is dedicate to a discussion of the third. (shrink)

Sellars [1960, ‘Grammar and existence: A preface to ontology’] argues that the truth of a second-order sentence does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come (...) to understand sentences of a second-order language wherein the truth of second-order existential sentences do not require there to be abstract entities. In addition to this, as Sellars [1979, Naturalism and Ontology] notes, a formal account of quantification is required that does not make use of the apparatus of sequences. Both such a translation of and a formal account of quantification are provided in this article. (shrink)

Open peer commentary on the article “Second-Order Cybernetics as a Fundamental Revolution in Science” by Stuart A. Umpleby. Upshot: Connecting Umpleby’s article with Piaget and García’s genetic epistemology, I will argue that the revolution the former discerns is more comprehensive. Additionally, since the latter differ from cybernetic and radical traditions in their philosophical assumptions about society and its conditioning on knowledge, I will suggest that these assumptions must be considered to explain each constructivist program’s achievements and challenges.

A second-order preference is a preference over preferences. This paper addresses the role that second-order preferences play in a theory of instrumental rationality. I argue that second-order preferences have no role to play in the prescription or evaluation of actions aimed at ordinary ends. Instead, second-order preferences are relevant to prescribing or evaluating actions only insofar as those actions have a role in changing or maintaining first-order preferences. I establish these claims (...) by examining and rejecting the view that second-order preferences trump first-order preferences. I also examine and reject the view that second-order preferences give additional normative force to an agent’s preferred first-order preferences. I conclude by arguing that second-order preferences should be integrated into an agent’s object-level preference ordering, and by explaining how best to make sense of this integration. (shrink)

When laypersons are presented with scientific information which seeks to modify their way of life, they are expected to believe, suspend belief, or reject it. Second-order assessment of scientific experts helps laypersons to make an informed decision in such situations. This is an assessment of the trustworthiness of the person making the scientific claim. In this paper I challenge the optimistic view of Anderson, regarding the ease with which laypersons can perform second-order assessment of experts, by (...) pointing out some of the obstacles that may prevent laypersons from arriving at an informed decision through this means. By showing that laypersons cannot easily perform second-order assessment of experts, I make a case for sharing epistemic burdens in science communication by using Lackey's concept of dualism in the epistemology of testimony and Irzik and Kurtulmus’ work on public epistemic trust in science, as a guide. I invite experts to bear a greater share of the epistemic burden when communicating with laypersons because of their privileged epistemic condition vis-à-vis laypersons. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: Second-order science requires a specific methodology. It thereby reverses the classical observer-observed relation in favor of the observed - i.e., the first-order observers - if the principle of autopoiesis is acknowledged.

This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking (...) coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators. (shrink)

The logic of paradox, LP, is a first-order, three-valued logic that has been advocated by Graham Priest as an appropriate way to represent the possibility of acceptable contradictory statements. Second-order LP is that logic augmented with quantification over predicates. As with classical second-order logic, there are different ways to give the semantic interpretation of sentences of the logic. The different ways give rise to different logical advantages and disadvantages, and we canvass several of these, concluding (...) that it will be extremely difficult to appeal to second-order LP for the purposes that its proponents advocate, until some deep, intricate, and hitherto unarticulated metaphysical advances are made. (shrink)

We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory (...) and second-order logic are not radically different: the latter is a major fragment of the former. (shrink)

Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a (...) logic, but rather must be presupposed. I call this the logic-metalogic link. There are two facets to the logic-metalogic link. First, when a logic is entangled with a substantive issue, the same position on that issue should be taken at the meta- level as at the object level; and second, if an expression has a clear meaning in natural language, then the corresponding concept can equally well be deployed in a formal language. The determinate nature of the power set operation is one such substantive issue in set theory. Whether there is a determinate power set of an infinite set can only be presupposed in set theory, not proved, so the use of second-order logic cannot be ruled out by virtue of presupposing one answer to this question. Moreover, the legitimacy of presupposing in the background logic that the power set of an infinite set is determinate is guaranteed by the clarity and definiteness of the notions of all and of subset. This is also exactly what is required for the same presupposition to be legitimately made in an axiomatic set theory, so the use of second-order logic in set theory rather than first-order logic does not require any new metatheoretic commitments. (shrink)

Harry Frankfurt had insightfully pointed out that an agent acts freely when he acts in accord with the mental states with which he identifies. The concept of identification rightly captures the ownership condition (something being one’s really own), which plays a significant role in the issues of freedom and moral responsibility. For Frankfurt, identification consists of one’s forming second-order volitions, endorsing first-order desires, and issuing in his actions wholeheartedly. An agent not only wants to φ but (...) also fully embraces his desire to φ (and φ). Frankfurt’s official theory above encounters some serious problems, especially since it is believed that his concept of wholehearted identification is too strong to be necessary for freedom. In this paper, I propose that we can uncouple identification from wholeheartedness and thus get two different senses of identification: weak identification and strong identification. Then, I argue that this distinction does a better job than Frankfurt’s official theory. On the one hand, weak identification is enough for ownership and freedom and thus more promising than strong identification; on the other hand, this distinction has an attractive implication that it fits well with our intuition about the degree of freedom and responsibility. (shrink)

On Frankfurt's view of free will, in its simplest form, an agent is free just in case her second-order volitions -- those second-order desires she wishes to be effective -- are in accord with her first-order volitions -- those first-order desires that one actually acts upon. That is, an agent has free will just in case she has the desires she wants to have and they are the desires she acts upon. But (...) now consider an agent who lacks free will because her first-order volitions and second-order volitions conflict. Suppose also that, with enough therapy, she could alter her first-order volitions to be in accord with her second-order volitions. So it is true that she can alter her first-order volitions. Still, there is the question of what she should she do. A natural response that a real self theorist might make is that the agent should change her first-order volitions in order to reflect her second-order volitions. But this is not, in principle, the only option available to our agent. Instead of changing her first-order volitions to reflect her second-order volitions, she might also consider simply revising her second-order volitions to fit with her first-order volitions. In fact, since second-order volitions are arguably more reasons responsive, it could turn out for our agent that changing her second-order volitions is actually the most rational option to take. This applies to even the most recent developments of real self, hierarchical, reasons responsive, and even intention embedded accounts of free will. Indeed, there is empirical evidence that people change their conceptions of themselves quite readily in the face of cognitive dissonance of the kind faced by desire conflicts. But this way of attaining free will does not seem to comport with our conception of a free agent. Free will seems too easy to obtain if all that is required is that our second-order volitions are in accord with our first-order volitions, and I see no particularly principled way of arguing that we shouldn't consider changing our second-order volitions instead of changing our first-order volitions. Secondly, this conception of free will is also subject to other counter examples. A person, for instance, may not be able to respect hierarchies due to some personality trait or other, but she might also be the kind of person for whom even were this trait lacking, still would not want to respect hierarchies. Here we have case in which a person's first order volitions and second order volitions coincide, but we do not want to call her free either. Additional evidence that this cannot be the right conception of free will comes from ideas put forth in the literature on practical rationality: I can be in situations in which the only rational action for me to take is to change my desires (MacIntosh), but if we cannot make irrational decisions, and these are understood as decisions to act in ways that go against our current desires, then being in a situation in which I choose to change my current desires should not be possible, thereby challenging any conception of free will that requires the changing of desires, whether first-order or second-order. I conclude, then, that any compatibilist conception of free will of the kind mentioned will be ultimately unsatisfying. (shrink)

We try to answer the question which is the “right” foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first order theory, we have to rephrase the question. We formulate what we call the second order view and a competing set theory view, and then discuss the merits of both views. On the surface these two views seem to be (...) in manifest conflict with each other. However, our conclusion is that it is very difficult to see any real difference between the two. We analyze a phenomenon we call internal categoricity which extends the familiar categoricity results of second order logic to Henkin models and show that set theory enjoys the same kind of internal categoricity. Thus the existence of non-standard models, which is usually taken as a property of first order set theory, and categoricity, which is usually taken as a property of second order axiomatizations, can coherently coexist when put into their proper context. We also take a fresh look at complete second order axiomatizations and give a hierarchy result for second order characterizable structures. Finally we consider the problem of existence in mathematics from both points of view and find that second order logic depends on what we call large domain assumptions, which come quite close to the meaning of the axioms of set theory. (shrink)

I propose a characterization of the dialectical dimension of argumentation by considering the activity of arguing as involving a “second order intersubjectivity”. I argue that argumentative communication enables this kind of intersubjectivity as a matter of the recursive nature of acts of arguing—both as justificatory and as persuasive devices. Calling attention to this feature is a way to underline that argumentative discourses represent the explicit part of a dynamic activity, “a mechanism of rational validation”, as Rescher showed, which (...) is a practice that presupposes the possibility of attaining objectivity. (shrink)

It seems natural to think of an unwilling addict as having a pattern of preferences that she does not endorse—preferences that, in some sense, she does not ‘identify’ with. Following Frankfurt (1971), Jeffrey (1974) proposed a way of modeling those features of an agent’s preferences by appealing to preferences among preferences.Th„e addict’s preferences are preferences she does not prefer to have. I argue that this modeling suggestion will not do, for it follows from plausible assumptions that a minimally rational agent (...) must prefer those first-order preferences she actually has. I close by considering two different but related ways to think about the initial phenomenon. (shrink)

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol (...) Logic 45:464–482, 1980 ). Therefore, it is not clear how this logic should be interpreted. (3) Second-order logic also has strong ontological commitments: (a) it is ontologically committed to classes (Resnik, J Phil 85:75–87, 1988 ), and (b) according to Quine (Philosophy of logic, Prentice-Hall: Englewood Cliffs, 1970 ), it is nothing more than “set theory in sheep’s clothing”. (4) It is also not better than its first-order counterpart, in the following sense: if first-order logic does not characterize adequately mathematical systems, given the existence of non - isomorphic first-order interpretations, second-order logic does not characterize them either, given the existence of different interpretations of second-order theories (Melia, Analysis 55:127–134, 1995 ). (5) Finally, as opposed to what is claimed by defenders of second-order logic [such as Shapiro (J Symbol Logic 50:714–742, 1985 )], this logic does not solve the problem of referential access to mathematical objects (Azzouni, Metaphysical myths, mathematical practice: the logic and epistemology of the exact sciences, Cambridge University Press, Cambridge, 1994 ). In this paper, I argue that the second-order theorist can solve each of these difficulties. As a result, second-order logic provides the benefits of a rich framework without the associated costs. (shrink)

This paper investigates whether there is an acceptable version of Functionalism that avoids commitment to second-order properties. I argue that the answer is "no". I consider two reductionist versions of Functionalism, and argue that both are compatible with multiple realization as such. There is a more specific type of multiple realization that poses difficulties for these views, however. The only apparent Functionalist solution is to accept second-order properties.

Pure second-order logic is second-order logic without functional or first-order variables. In "Pure Second-Order Logic," Denyer shows that pure second-order logic is compact and that its notion of logical truth is decidable. However, his argument does not extend to pure second-order logic with second-order identity. We give a more general argument, based on elimination of quantifiers, which shows that any formula of pure second-order logic with (...) second-order identity is equivalent to a member of a circumscribed class of formulas. As a corollary, pure second-order logic with second-order identity is compact, its notion of logical truth is decidable, and it satisfies a pure second-order analogue of model completeness. We end by mentioning an extension to n th-order pure logics. (shrink)

Context: The term “second-order cybernetics” was introduced by von Foerster in 1974 as the “cybernetics of observing systems,” both the act of observing systems and systems that observe. Since then, the term has been used by many authors in articles and books and has been the subject of many conference panels and symposia. Problem: The term is still not widely known outside the fields of cybernetics and systems science and the importance and implications of the work associated with (...) second-order cybernetics is not yet widely discussed. I claim that the transition from cybernetics to second-order cybernetics is a fundamental scientific revolution that is not restricted to cybernetics or systems science. Second-order cybernetics can be regarded as a scientific revolution for the general methodology of science and for many disciplines as well. Method: I first review the history of cybernetics and second-order cybernetics. Then I analyze the major contents of von Foerster’s fundamental revolution in science and present it as a general model for an alternative methodology of science. Subsequently, I present an example of practicing second-order socio-cybernetics from within. I describe some consequences of doing science from within, and I suggest some new horizons for second-order cybernetics. Results: Second-order cybernetics leads to a new foundation for conducting science and offers important contributions for a new way of organizing science. It expands the conception of science so that it can more adequately deal with living systems. Implications: Second-order cybernetics extends the traditional scientific approach by bringing scientists within the domain of what is described and analyzed. It provides models of research processes for when the scientist is within the system being studied. In this way it offers a new foundation for research in the social sciences, in management science, and in other fields such as the environmental sciences or the life sciences. Keywords: Epistemology, general scientific methodology, cybernetics, social sciences, action research, Heinz von Foerster. (shrink)

Büchi, J. R. The monadic second order theory of [omega symbol]₁.--Büchi, J. R. and Siefkes, D. Axiomatization of the monadic second order theory of [omega symbol]₁.

Clarke and Beck argue that the ANS doesn't represent non-numerical magnitudes because of its second-order character. A sensory integration mechanism can explain this character as well, provided the dumbbell studies involve interference from systems that segment by objects such as the Object Tracking System. Although currently equal hypotheses, I point to several ways the two can be distinguished.

We introduce a second-order system V1-Horn of bounded arithmetic formalizing polynomial-time reasoning, based on Grädel's 35) second-order Horn characterization of P. Our system has comprehension over P predicates , and only finitely many function symbols. Other systems of polynomial-time reasoning either allow induction on NP predicates , and hence are more powerful than our system , or use Cobham's theorem to introduce function symbols for all polynomial-time functions . We prove that our system is equivalent to (...) QPV and Zambella's P-def. Using our techniques, we also show that V1-Horn is finitely axiomatizable, and, as a corollary, that the class of Σ1b consequences of S21 is finitely axiomatizable as well, thus answering an open question. (shrink)

Resumen En una serie de escritos Timothy Williamson ha argumentado a favor del necesitismo, esto es, la tesis de que es necesario que todo exista necesariamente. Este trabajo discute el necesitismo de segundo orden, esto es, la tesis de que es necesario que toda propiedad exista necesariamente, considerando líneas de argumentación semejantes a las desplegadas en primer orden. Se examinan tres de estos argumentos: el carácter necesario de ser una propiedad, la aparición de las propiedades en proposiciones, y los compromisos (...) ontológicos del metalenguaje en el que se formula la semántica. Se argumenta que ninguno de ellos es realmente convincente. La justificación del necesitismo de segundo orden parece requerir más metafísica sustantiva que resultados formales, al menos si es que los resultados formales de que se trata son aquellos discutidos aquí.In a series of writings Timothy Williamson has argued for necessitism, i. e. the thesis that it is necessary that everything exists necessarily. This work discusses second-order necessitism, i. e. the thesis that it is necessary that every property exists necessarily, considering lines of argument similar to those displayed on first-order. Three of those arguments are examined. the necessary character ofbeing a property, the occurrence of properties in propositions, and the ontological commitments of the metalanguage where the semantics is formulated. It is argued that none of them are compelling. The justification for second-order necessitism seems to require more substantive metaphysics than formal results, at least if the formal results in view are those discussed here. (shrink)

According to Pylyshyn, depictive representations can be explanatory only if a certain kind of first-order isomorphism exists between the mental representations and real-world displays. What about a system with second-order isomorphism (similarities between different mental representations corresponding with similarities between different real-world displays)? Such a system may help to address whether “depictive” representations contribute to the visual nature of imagery.