Collegium Logicum. Logische Grundlagen der Philosophie und der Wissenschaften

I try to reconstruct how Frege thought to reconcile the cognitive value of arithmetic with its analytical nature. There is evidence in Frege's texts that the epistemological formulation of the context principle plays a decisive role; it provides a way of obtaining concepts which are truly fruitful and whose contents cannot be grasped beforehand. Taking the definitions presented in the Begriffsschrift,I shall illustrate how this schema is intended to work.     

Lotze and frege: The dating of the ’Kernsätze’ ∗

Michael Dummett has shown that the fragment ‘17 Kernsätze zur Logik’ is evidence that Frege knew Lotze's Logik Dummett’s dating of this fragment prior to 1879, however, must be rejected.The present paper shows that there are other articles of Frege’s which bear clear traces of Lotze's LogikFirst of all, the expressions Vorstellungsverlauf from ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, and veranlassenden Ursachen, from ‘Logik’, certainly are borrowed from Lotze.Second, there are links between ‘Booles rechnende Logik und die Begriffsschrift’ and Lotze's Logik. Furthermore, it is shown that Frege’s ‘Kernsätze’, the ‘Dialog mit Pünjer über Existenz’, and his ‘Logik’ are intimately connected.All of this indicates that these texts were written in roughly the same period, namely the early 1880s.Conclusive evidence for this is that the terms Vorstellung and Vorstellungsverbindung are used indiscriminately in both a psychological and a logical sense in the ‘Begriffsschrift’, a fact which contradicts the ‘Kernsätze’     

Formality of logic and Frege’s Begriffsschrift

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’.     

Anti-Positionalism’s Regress

This paper is about the Problem of Order, which is basically the problem how to account for both the distinctness of facts like a’s preceding b and b’s preceding a, and the identity of facts like a’s preceding b and b’s succeeding a. It has been shown that the Standard View fails to account for the second part and is therefore to be replaced. One of the contenders is Anti-Positionalism. As has recently been pointed out, however, Anti-Positionalism falls prey to a regress argument which is to prove its failure. In the paper we spell out this worry, show that the worry is a serious one, and distinguish four possible strategies for Anti-Positionalism to deal with it.     

The role of all things considered judgements in practical deliberation

Suppose an agent has made a judgement of the form, ‘all things considered, it would be better for me to do a rather than b (or any range of alternatives to doing a)’ where a and b stand for particular actions. If she does not act upon her judgement in these circumstances would that be a failure of rationality on her part? In this paper I consider two different interpretations of all things considered judgements which give different answers to this question, one suggested by Donald Davidson, the other by Paul Grice and Judith Baker. I argue that neither interpretation is adequate. However, a third interpretation that combines features of the Grice/Baker view with the Davidsonian view is possible. In the final section of the paper I defend this interpretation against two objections.     

Frege’s Unification

What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature.     

Frege and the rigorization of analysis

This paper has three goals: (i) to show that the foundational program begun in theBegriffsschrift, and carried forward in theGrundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence ofintuitive reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue the goal of autonomy within the framework of the system of second-order logic of theBegriffsschrift. (iii) To address certain criticisms of Frege by Parsons and Boolos, and thereby to clarify what was and was not achieved by the development, in Part III of theBegriffsschrift, of a fragment of the theory of relations.     

I. Frege as a Realist

H. Sluga (Inquiry, Vol. 18 [1975], No. 4) has criticized me for representing Frege as a realist. He holds that, for Frege, abstract objects were not real: this rests on a mistranslation and a neglect of Frege's contextual principle. The latter has two aspects: as a thesis about sense, and as one about reference. It is only under the latter aspect that there is any tension between it and realism: Frege's later silence about the principle is due, not to his realism, but to his assimilating sentences to proper names. Contrary to what Sluga thinks, the conception of the Bedeutung of a name as its bearer is an indispensable ingredient of Frege's notion of Bedeutung, as also is the fact that it is in the stronger of two possible senses that Frege held that Sinn determines Bedeutung. The contextual principle is not to be understood as meaning that thoughts are not, in general, complex; Frege's idea that the sense of a sentence is compounded out of the senses of its component words is an essential component of his theory of sense. Frege's realism was not the most important ingredient in his philosophy: but the attempt to interpret him otherwise than as a realist leads only to misunderstanding and confusion.     

Effects of Event Probability and Animateness on Children's Comprehension of Active and Passive Sentences

Thirty-six three-, four-, and five-year-old boys and girls were asked to act out, with appropriate toys, 48 sentences presented with instructions to make the toys do what E said. Sentences were designed to test the effects on comprehension of (a) event probability, (b) sentence voice, and (c) subject/object animateness. Sentences with either an animate subject and object, or an inanimate subject and object, were considered to be reversible; however, not all reversible sentences were symmetrical with respect to event probability. All main effects were significant, and performance improved with age. The significant interactions indicated that there is a difference between animateness and inanimateness in reversible sentences. The data also suggested that (a) animateness may be an important variable in children's early comprehension of speech, and (b) the traditional definition of reversibility should be modified to unconfound the effects of event probability and animateness.     

A pragmatic solution to Ostertag’s puzzle

Gary Ostertag (Philos Stud 146:249–267, 2009) has presented a new puzzle for Russellianism about belief reports. He argues that Russellians do not have the resources to solve this puzzle in terms of pragmatic phenomena. I argue to the contrary that the puzzle can be solved according to Nathan Salmon’s (Frege’s puzzle, 1986) pragmatic account of belief reports, provided that the account is properly understood. Specifically, the puzzle can be solved so long as Salmon’s guises are not identified with sentences.     

The use theory of meaning and semantic stipulation

According to Horwich’s use theory of meaning, the meaning of a word W is engendered by the underived acceptance of certain sentences containing W. Horwich applies this theory to provide an account of semantic stipulation: Semantic stipulation proceeds by deciding to accept sentences containing an as yet meaningless word W. Thereby one brings it about that W gets an underived acceptance property. Since a word’s meaning is constituted by its (basic) underived acceptance property, this decision endows the word with a meaning. The use-theoretic account of semantic stipulation contrasts with the standard view that semantic stipulation proceeds by assigning the meaning (reference) to W that makes a certain set of sentences express true propositions. In this paper I will argue that the use-theoretic account does not work. I take Frege to have already made the crucial point: "a definition does not assert anything but lays down something ["etwas festsetzt"]” (Frege 1899, 36). A semantic stipulation for W cannot be the decision to accept a sentence containing W or be explained in terms of such an acceptance. Semantic stipulation constitutes a problem for Horwich's use theory of meaning, especially his basic notion of acceptance.

A CRITIQUE OF FREGE ON COMMON NOUNS

Frege analyzed the grammatical subject‐term ‘S’ in quantified subject‐predicate sentences, ‘q S are P’, as being logically predicative. This is in contrast to Aristotelian Logic, according to which it is a logical subject‐term, like the proper name ‘a’ in ‘a is P’– albeit a plural one, designating many particulars. I show that Frege’s arguments for his analysis are unsound, and explain how he was misled to his position by the mathematical concept of function. If common nouns in this grammatical subject position are indeed logical subject‐terms, this should require a thorough reevaluation of the adequacy of Frege’s predicate calculus as a tool for the analysis of the logic and semantics of natural language.     

On a property of BCK-identities

A BCK-algebra is an algebra in which the terms are generated by a set of variables, 1, and an arrow. We mean by aBCK-identity an equation valid in all BCK-algebras. In this paper using a syntactic method we show that for two termss andt, if neithers=1 nort=1 is a BCK-identity, ands=t is a BCK-identity, then the rightmost variables of the two terms are identical.This theorem was conjectured firstly in [5], and then in [3]. As a corollary of this theorem, we derive that the BCK-algebras do not form a variety, which was originally proved algebraically by Wroski ([4]).To prove the main theorem, we use a Gentzen-type logical system for the BCK-algebras, introduced by Komori, which consists of the identity axiom, the right and the left introduction rules of the implication, the exchange rule, the weakening rule and the cut. As noted in [2], the cut-elimination theorem holds for this system.Presented byJan Zygmunt     

Beyond the Tools of the Trade: Heidegger and the Intelligibility of Everyday Things

In everyday life, we constantly encounter and deal with useful things without pausing to inquire about the sources of their intelligibility. In Div. I of Being and Time, Heidegger undertakes just such an inquiry. According to a common reading of Heidegger's analysis, the intelligibility of our everyday encounters and dealings with useful things is ultimately constituted by practical self‐understandings (such as being a gardener, shoemaker, teacher, mother, musician, or philosopher). In this paper, I argue that while such practical self‐understandings may be sufficient to constitute the intelligibility of the tools and equipment specific to many practices, these “tools of the trade” are only a small portion of the things we encounter, use, and deal with on a daily basis. Practical self‐understandings cannot similarly account for the intelligibility of the more mundane things—like toothbrushes and sidewalks—used in everyday life. I consider whether an anonymous self‐understanding as “one,” “anyone,” or “no one in particular” —das Man—might play this intelligibility‐constituting role. In examining this possibility, another type of self‐understanding comes to light: cultural identities. I show that the cultural identities into which we are “thrown,” rather than practical identities or das Man, constitute the intelligibility of the abundance of mundane things that fill our everyday lives. Finally, I spell out how this finding bears on our understanding of Heidegger's notion of authenticity.     

Thinking about multiple identities boosts children’s flexible thinking

Studies of children's developing social identification often focus on individual forms of identity. Yet, everyone has multiple potential identities. Here we investigated whether making children aware of their multifaceted identities—effectively seeing themselves from multiple angles—would promote their flexible thinking. In Experiment 1, 6‐ to 7‐year‐old children (N = 48) were assigned to either a Multiple‐Identities condition where they were led to consider their multiple identities (e.g. friend, neighbor) or to a Physical‐Traits condition where they considered their multiple physical attributes (e.g. legs, arms). Children in the Multiple‐Identity condition subsequently expressed greater flexibility at problem‐solving and categorization than children in the Physical‐Traits condition. Experiment 2 (N = 72) replicated these findings with a new sample of 6‐ to 7‐year‐old children and demonstrated that a Multiple‐Identity mindset must be self‐relevant. Children who were led to think about another child's multiple identities did not express as much subsequent creative thinking as did children who thought about their own multiple identities. Experiment 3 (N = 76) showed that a Mmultiple‐Identity framework may be particularly effective when the identities are presented via generic language suggesting that they are enduring traits (in this case, identities depicted as noun phrases rather than verbal phrases). These findings illustrate that something as simple as thinking about one's identity from multiple angles could serve as a tool to help reduce rigid thinking, which might increase open‐mindedness in a society that is becoming increasingly diverse.     

The motivations for Walter Burley’s theory of the proposition

Walter Burley (born c. 1275; died. c. 1344) claims throughout his career that the mind can make a statement (propositio) out of things. Since things include entities that exist outside of the mind, Burley appears to be claiming that the mind can form a statement out of things that exist outside of it. Most scholars of Burley offer a deflationary reading of this claim, arguing that it confuses two distinct but closely related philosophical issues: the nature of propositional content, on the one hand, and the role of facts in a compelling account of truth, on the other. But I argue that Burley means exactly what he says: that the mind can, quite literally, form statements out of things that exist outside of it. In Burley’s account, statements of this sort function as the propositional contents of our thoughts and written or uttered sentences. This account of propositional content is motivated by three more fundamental theses to which Burley is committed: referentialism, compositionality, and a claim about truth-conditionality I call intellectualism.     

Consequences of enactment and concealment for felt authenticity: Understanding the effects of stigma through self-distancing and motive fulfillment

Grounded in Motivated Identity Construction Theory and Self-Determination Theory, two studies examined the consequences of identity enactment and concealment for motive fulfillment and explored how these mediate the negative effects of stigmatized identities on felt authenticity. Participants (Ns = 343 and 344) reported the extent to which they had enacted and/or concealed 8 to 12 of their identities in the past 3 days and evaluated their motive fulfillment and felt authenticity. Using multilevel modeling, we found that identity enactment positively predicted felt authenticity via motive satisfaction, while concealment negatively predicted authenticity via thwarted motive satisfaction. Identities were coded with respect to stigmatization in Study 2 and stigmatized identities felt relatively less authentic, with effects mediated through suppressed enactment, heightened concealment, and thwarted motives. Thus, stigmatized identities do not inherently feel less authentic, rather it is individuals’ self-distancing behaviors that impair feelings of authenticity for a stigmatized identity.     

Local pragmatics in a Gricean framework

The pragmatic framework developed by H.P. Grice in “Logic and Conversation” explains how a speaker can mean something more than, or different from, the conventional meaning of the sentence she utters. But it has been argued that the framework cannot give a similar explanation for cases where these pragmatic effects impact the understood content of an embedded clause, such as the antecedent of a conditional, a clausal disjunct, or the clausal complement of a verb. In this paper, I show that such an explanation is available. One of the central arguments of the paper (Section 2) is that in a significant subset of cases, local pragmatic effects are a consequence of a global (utterance-level) pragmatic requirement. In these cases, local pragmatic effects are a consequence of ‘acting locally’ to resolve a potential global pragmatic violation. These cases do not require us to posit application of pragmatic principles (Maxims of Conversation) to the contents of embedded clauses. The account does, though, require the assumption that interpreters can identify and reason about the contents of unasserted sub-parts of sentences, an assumption that I motivate in section 3. Building on this, in section 4 of the paper, I argue that once we have recognized that interpreters can, and do, reason independently about the contents of non-asserted clauses, it becomes unproblematic to assume that in some cases, Gricean conversational principles do apply directly to these contents, providing an alternative route to account for local pragmatic effects. In revisiting the ideas of this paper in my response to the commentaries, I consider in more detail the revisions to Grice’s broader program that are necessitated by these moves, in particular acknowledging the problematicity of Grice’s notion of what is said. I argue that the starting point for Gricean reconstructions should instead be merely what is expressed, which carries no pragmatic commitments regarding what is speaker meant.