Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while consequences are treated more tolerantly. More specifically, ST is a three-valued logic with left sides of sequents understood as if in Kleene’s Strong Three Valued Logic, and right sides as if in Priest’s Logic of Paradox. Surprisingly, this hybrid validates the same sequents that classical logic does. A version of this result has been extended to meta, metameta, … (...) consequence levels in Barrio et al.. In my earlier paper Fitting I showed that the original ideas behind ST are, in fact, much more general than first appeared, and an infinite family of many valued logics have Strict/Tolerant counterparts. This family includes both Kleene’s and Priest’s logic individually, as well as first degree entailment. For instance, for both the Kleene and the Priest logic, the corresponding strict/tolerant logic is six-valued, but with differing sets of strictly and tolerantly designated truth values. The present paper extends that generalization in two directions. We examine a reverse notion, of Tolerant/Strict logics, which exist for the same structures that were investigated in Fitting. And we show that the generalization extends through the meta, metameta, … consequence levels for the same infinite family of many valued logics. Finally we close with remarks on the status of cut and related rules, which can actually be rather nuanced. Throughout, the aim is not the philosophical applications of the Strict/Tolerant idea, but the determination of how general a phenomenon it is. (shrink)

Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...) strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If (...) the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode , Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223]. (shrink)

Several justification logics have evolved, starting with the logicLP, (Artemov 2001). These can be thought of as explicit versions of modal logics, or logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. Modal logics come in various strengths. For their corresponding justification logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar (...) extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

£ The existence of a model for a logic program is generally established by lattice-theoretic arguments. We present three examples to show that metric methods can often be used instead, generally in a direct, straightforward way. One example is a game program, which is not stratified or locally stratified, but which has a unique supported model whose existence is easily established using metric methods. The second example is a program without a unique supported model, but having a part that is (...) ‘well-behaved.’ The third example is a program in which one part depends on another, illustrating how modularity might be treated metrically. Finally we use ideas from this third example to prove a general result from [3]. The intention in presenting these examples and the theorem is to stimulate interest in.. (shrink)

Participants maneuvered a rat image through a circular region on the computer screen to find a hidden target platform, blending aspects of two well-known spatial tasks. Like the Morris water maze task, participants first experienced a series of learning trials before having to navigate to the hidden target platform from different locations and orientations. Like the dot-location task, they determined the location of a position within a two-dimensional circular region. This procedure provided a way to examine how the number of (...) surrounding cues (1, 2, or 3) affects the memory for spatial location in navigation. Memory performance was better when there were more cues and when targets were close to cues, consistent with the idea that cues bolster fine-grain memory, especially in proximal regions. Early and late measures of bias in memory reflected biases in a direction toward the nearest cue, implicating a cue-based category structure of the navigational space. Collectively, results suggest cue-based spatial memory representations that have been inferred from the dot-location task generalize to a navigation task within a simple, computer-based environment, as demonstrated by the good fits of the spatial model developed for the dot-location task (Fitting, Wedell, & Allen, 2005, 2007). (shrink)

This article explores the labour behind local food in the Canadian Atlantic province of Nova Scotia. Based on surveys and interviews with farmers, migrant farmworkers, and farmers’ market consumers in the province, we suggest that the celebration of local food by government and industry is a form of “local washing.” Local washing hides key aspects of the social relations of production: in this case, it hides insufficient financial and policy supports for Nova Scotian farms and the increased reliance on migrant (...) farmworkers via the Seasonal Agricultural Worker Program and the Temporary Foreign Worker Program. Our research found that a growing reliance on migrant farmworkers was not just the case for larger, industrial farms, but also for smaller farms participating in local and alternative food initiatives, like farmers’ markets and fresh produce subscription boxes. Additionally, our surveys show that while farmers’ market shoppers expressed an interest in supporting local foods, they reported knowing little about farm workers or working conditions. Our paper contributes to the literature on local and alternative food initiatives by connecting the relations of production to consumption. Rather than focusing solely on the nature of the relationships between farmers and consumers and the values embodied in direct agricultural markets, this research explores the central role of permanently temporary migrant workers in local agriculture. (shrink)

The authors argue against direction of fit accounts of the distinction between belief and desire.

I argue that the concept of direction of fit is best seen as picking out a certain inferential property of a psychological attitude. The property in question is one that believing shares with assuming and fantasizing and fails to share with desire. Unfortunately, the standard analysis of DOF obscures this fact because it conflates two very different properties of an attitude: that in virtue of which it displays a certain DOF, and that in virtue of which it displays certain (...) revision conditions. I claim that the latter corresponds with the aim of an attitude, not its DOF. In order to remedy this failure of the standard analysis, I offer an alternative account of DOF, which I refer to as the two-content analysis. (shrink)

The idea of direction of fit has been found appealing by many philosophers. Anscombe’s famous examples have persuaded many of us that there must be some deep difference between belief and desire that is captured by the metaphor of direction of fit. Most of the aim of the paper is to try to get clear on which intuitions Anscombe’s example taps into. My view is that there is more than one intuition in play here, and I will try (...) to show that various distinctions and points are confused in the literature on direction of fit. But I also want to argue that once the proper distinctions are made, it’s not clear that the notion of direction of fit can do any of the philosophically significant work that it was supposed to do. I first argue that the best way to unpack the notion of direction of fit would indeed be by means of the constitutive relation between truth and belief. In particular, the notion of direction of fit is best understood as different ideals, or formal ends, guiding the inference, from what I call “prima-facie” attitudes to what I call “all-out” attitudes respectively in the theoretical and practical realm. However, I’ll argue that there’s no non-circular way of making this distinction. But even if no definition of “belief” and “desire” come out of the distinction between directions of fit, it does elucidate the different natures of practical and theoretical enquiry. However, understood this way, the notion of direction of fit does not seem to capture the distinction illustrated by Anscombe’s example. I try to argue in the last section that Anscombe’s compelling example is best explained not by a distinction between directions of fit, but by a distinction between two different inferential mistakes: one from general to general or particular to general, and the other from general to particular. There’s an important asymmetry between practical and theoretical endeavours in this neighbourhood. However, noticing this asymmetry will also fail to deliver the philosophical payoffs that the notion of direction of fit was supposed to have. (shrink)

What is the difference between belief and desire? In order to explain the difference, recent philosophers have appealed to the metaphor of.

The difference between cognitive and conative mental states, such as beliefs and desires, has sometimes been held to be that they have different “directions of fit” between the mind and the world – mind-to-world for beliefs and world-to-mind for desires (see Desire). Some philosophers have pursued the idea that if this thought can be given a plausible explanation it can be used to ground Hume's claim that “reason is the slave of the passions,” i.e., that no moral or other “practical” (...) belief, e.g., about what is best or right to do, can ever by itself be enough to motivate action. A desire or desire-like state is always required (see Reason and Passion; Hume, David). This issue will be discussed below. (shrink)

According to the Humean theory of motivation, a person can only be motivated to act by a desire together with a relevantly related belief. More specifically, a person can only be motivated to ϕ by a desire to ψ together with a belief that ϕ-ing is a means to or a way of ψ-ing. In recent writings, Michael Smith gives what has become a very influential argument in favour of the Humean claim that desire is a necessary part of motivation, (...) and a great deal has been written about Smith's defence of this Humean claim. However, no one has yet identified the fundamental weakness of his defence. The fundamental weakness is that there is no single conception of directions of fit that does all the work Smith needs it to do throughout the various stages of his defence. (shrink)

In this paper, I show that we should understand the direction of fit of beliefs and desires in normative terms. After rehearsing a standard objection to Michael Smith’s analysis of direction of fit, I raise a similar problem for Lloyd Humberstone’s analysis. I go on to offer my own account, according to which the difference between beliefs and desires is determined by the normative relations such states stand in. I argue that beliefs are states which we have reason (...) to change in light of the world, whereas desires are states that give us reason to change the world. After doing this, I show how the view avoids various objections, including two from David Sobel and David Copp. The paper ends by briefly discussing the relevance of the view to the Humean theory of motivation. (shrink)

This chapter distinguishes two different modeling relations between vehicles and targets: design relation and representation relation. The relations are characterized by their different directions of fit. Three examples of modeling enterprises are discussed: a bioengineering model, called the “lung chip,” an architectural model, called the “weekend cottage,” and an engineering design model, called the “jet engine.” The two modeling relations with different directions of fit are analyzed in the three examples. The lung chip is standing in a representation relation to (...) its corresponding target and the modeling of the cottage involves a design relation to its target. With the help of these examples a basic assumption of philosophy of engineering and philosophy of technology is challenged. These examples show that it is not strictly speaking true that engineering modeling is exclusively about how things should be rather than about how things are. It is shown that a representation relation is prominently involved in the first model of the lung chip. This modeling involves reasoning about how things are rather than about how things should be. So, one modeling enterprise seems to be rather about what is than about what should be. The other two examples may be seen as confirming evidence for the basic assumption. What is common to all three models is that they involve design and representation relations. (shrink)

The idea that there are representations with a double direction of fit has acquired a pride of place in contemporary debates on the ontology of institutions. This paper will argue against the very idea of anything at all having both directions of fit. There is a simple problem which has thus far gone unnoticed. The suggestion that there are representations with both directions of fit amounts to a suggestion that, in cases of discrepancy between a representation and the world, (...) both should change—the representation and the world. But that would merely amount to another discrepancy, and so both should change again, ad infinitum. The paper will first elucidate the notion of a “direction of fit” and clarify how the criticism to be presented here differs from earlier criticisms (Section 1).The next section sheds some light on why and how acts and attitudes with both directions of fit have seemed to play a part in explaining the existence of institutional reality (Section 2). The next sections present the argument against any representations with both directions of fit, relying on a normative understanding of the distinction. The argument will have three steps (Sections 3, 4, and 5). The section that follows shows that the criticism also applies to the dispositional understanding of the notion of a direction of fit (Section 6), and then the paper asks whether a third kind of reading would be available (Section 7) and whether the infallibility of the relevant representations would be of help (Section 8). Finally, the paper assesses briefly the consequences of dropping the notion of two directions of fit (Section 9). (shrink)

Proponents of Humean belief-desire psychology often appeal to the metaphor of direction of fit. Roughly, the distinction between belief and desire boils down to the differing relationship between the attitude, its content, and the way the world is. Belief in P will tend to go out of existence when confronted with the introduced (perception-like) state of not P. The desire that p will, by contrast, persist in face of the introduced state that not P. The world is to be (...) aligned to match it. Two problems threaten the direction of fit strategy. The first is a worrying lack of clarity in the notion of an introduced state. On Smith’s view, this state looks and functions like a belief; this saddles the direction of fit strategy with vicious circularity. Second, David Copp and David Sobel argue that whether the metaphor iscashed out in descriptive or normative terms, the direction of fit metaphor is fatally flawed. This gloomy prognosis is premature: the Humean should adopt a normative interpretation, since doing so would yield salvage the metaphor. The cost of the salvage, however, might be higher than Humeans want, since the normative view can be happily accepted by Kantians. (shrink)

We standardly attribute beliefs to both individuals and organised groups, such as governments, corporations and universities. Just as we might say that an individual believes something, for instance that oil prices are rising, so we might say that a government or corporation does. If groups are to genuinely have beliefs, then they need states with the characteristic features of beliefs. One feature standardly taken to characterise beliefs is their mind to world direction of fit: they should fit the way (...) the world is. By contrast, desires are standardly taken to have a world to mind direction of fit: they aim for the world to be a certain way and are satisfied when the world fits them. Recently, Lackey ( 2021 ) has appealed to direction of fit to argue against certain nonsummative accounts of group belief. Here, I argue that on deeper inspection, belief’s mind to world direction of fit is difficult to accommodate on summative accounts of group belief including Lackey’s own neo-summative account. Further, I argue that direction of fit considerations in fact motivate the main non-summative approaches to belief, namely functionalism and interpretationism. Along the way, we see how addressing the issue of the direction of fit of group beliefs raises important questions about how to understand group evidence and its relationship to the evidence of members. (shrink)

Direction of fit theories usually claim that beliefs are such that they “aim at truth” or “ought to fit” the world and desires are such that they “aim at realization” or the world “ought to fit” them. This essay argues that no theory of direction of fit is correct. The two directions of fit are supposed to be determinations of one and the same determinable two-place relation, differing only in the ordering of favored terms. But there is no (...) such determinable because of ineliminable asymmetries between the way that beliefs “aim at truth” and the way that desires “aim at realization.” This essay traces the ills of direction of fit theory to a misunderstanding of Anscombe and proposes a cure that distinguishes theoretical and practical thought by appeal to a distinction between thought in the form of a state and thought in the form of an event. (shrink)

The classic thought experiments for Content Externalism have been motivated by consideration of intentional states with a mind-to-world direction of fit. In this paper, I argue that when these experiments are run on intentional states with a world-to-mind direction of fit, the thought experiments actually support Content Internalism. Because of this, I argue that the classic thought experiments alone cannot properly motivate Content Externalism. I do not show that Content Externalism is false in this paper, just that it (...) cannot be motivated by the classic thought experiments alone. I discuss various externalist responses to the argument I raise and show that they all fail. (shrink)

The so-called ‘Humean’ view of motivation is pretty standard in the Philosophy of Mind. Its most prominent contemporary defender, Michael Smith, calls it a ‘dogma’. Humeans believe in a strict divide between beliefs and desires. Beliefs have no intrinsic motivating force: I may believe anything at all, but only with the contribution of a separate desire will I be motivated to act. This claim should be broadened out to include all cognitive states (belief, knowledge…). The Humean claim is that cognitive (...) states are wholly lacking in conative power. If some beliefs seem to us to motivate action, that can only be due to a contingent association with a separate conative state. (shrink)

Those working within the tradition of Humean psychology tend to mark a clear distinction between beliefs and desires. One prominent way of elucidating this distinction is to describe them as having different “directions of fit” with respect to the world. After first giving a brief overview of the various attempts to carry out this strategy along with their flaws, I argue that the direction of fit metaphor is misleading and ought to be abandoned. It fails to take into account (...) the actual complexity of the roles played by belief and desire and forces us to look for a single, fundamental contrast between these two that is unlikely to be found. (shrink)

An important argument for the belief-desire thesis is based on the idea that an agent can be motivated to act only if her mental states include one which aims at changing the world, that is, one with a “world-to-mind”, or “telic”, direction of fit. Some cognitivists accept this claim, but argue that some beliefs, notably moral ones, have not only a “mind-to-world”, or “thetic”, direction of fit, but also a telic one. The paper first argues that this cognitivist (...) reply is deficient, for only the “dominant” direction of fit of an attitude is responsible for its character and function. Further, it seems that the dominant direction of fit of an attitude is determined by its psychological mode, and so all beliefs seem to have a dominant thetic direction of fit, and to be motivationally inert. The main part of this paper, however, is devoted to explaining how it is that attitudes, like moral attitudes, can truly have two directions of fit in a way which enables them to be both cognitive and motivational. Reflection on the nature of beliefs suggests that the claim that the dominant direction of fit of an attitude is determined by its psychological mode should be qualified. The reasons beliefs provide draw their authority for the agent – their demanding nature – from the objects represented by these beliefs, and so, it is the beliefs’ content which determine their dominant direction of fit, as far as their role in practical reasoning is concerned. Thus, in the sense relevant to practical reasoning a belief with a normative content does have a dominant telic direction of fit. At the same time, in the sense relevant to its satisfaction conditions a moral belief has a dominant thetic direction of fit, which underlies its classification as a cognitive attitude. Cognitivists, then, can have it both ways. (shrink)

Although predictive coding may offer a computational principle that unifies perception and action, states with different directions of fit are involved (with indicative and imperative contents, respectively). Predictive states are adjusted to fit the world in the course of perception, but in the case of action, the corresponding states act as a fixed target towards which the agent adjusts the world. This well-recognised distinction helps side-step some problems discussed in the target article.

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap’s four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result provides (...) a natural semantics for distributed logic programs, including those involving confidence factors. The classical two-valued and the Kripke/Kleene three-valued semantics become special cases, since the logics involved are natural sublogics of Belnap’s logic, the logic given by the simplest bilattice. (shrink)

A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.

Darwin’s claim about natural selection is reconstructed as an empirical claim about a causal connection leading from the match of the physiology of an individual and its environment to leaving surviving progeny. Variations in this match, Darwin claims, cause differences in the survival of the progeny. Modern concepts of fitness focus the survival side of this chain. Therefore, the assumption that evolutionary theory wants to explain reproductive success in terms of a modern concept of fitness has given rise to the (...) so-called tautology problem. It is shown that the tautology problem reappears in the treatment of fitness proxies in today’s experimental evolutionary biology when these proxies are considered to indicate fitness only. Taking Darwin’s empirical claim seriously suggests, by contrast, that fitness proxies are first of all measures of the match between organism and environment, which I call the organism’s ‘fittedness’. At the same time, they are indeed related to reproductive success. Thus looking in both directions, at fitness and at fittedness, they are janiform. Acknowledging this situation not only allows for rejection of the tautology objection, but also for integration of Darwin’s argument into current evolutionary biology. It is suggested that this helps reframe and alleviate the dispute between the Modern Synthesis and the Extended Evolutionary Synthesis. (shrink)

While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. Thus, with (...) little more work, the theory is extended to a broad class of settings. Indeed, a result like Theorem 6.2 would not even be possible to state without the interlaced bilattice machinery. We hope the notion of interlaced bilattice will make apparent further such connections. (shrink)

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established.

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences.

In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an Mkrtychev semantics. Motivation and intuition (...) for FOLP can be found in Artemov and Yavorskaya [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with. (shrink)