Frege: Criteria for Sense Identity

The present article reviews the Polish-language edition of Gottlob Frege’s scientific correspondence. In the article, I discuss the material hitherto unpublished in Polish in relation to the remainder of Frege’s works. First of all, I inquire into the role and nature of definitions. Then, I consider Frege’s recognition criteria for sameness of thoughts. In the article’s third part, I study letters devoted to the principle of semantic compositionality, while in the fourth part I discuss Frege’s remarks concerning the context principle.

In this article, I first analyze and assess the epistemological and semantic status of canonical value-range equations in the formal language of Frege’s Grundgesetze der Arithmetik. I subsequently scrutinize the relation between (a) his informal, metalinguistic stipulation in Grundgesetze I, Section 3, and (b) its formal counterpart, which is Basic Law V. One point I argue for is that the stipulation in Section 3 was designed not only to fix the references of value-range names, but that it was probably also (...) intended to play a regulative role with an eye to Basic Law V. I further intend to shed new light on the status of Frege’s identification of the truth-values with their unit classes in Grundgesetze I, Section 10 and determine its place and importance in his overall logicist project. In a subsequent section, I first discuss the hypothetical extendability of the logical system of Grundgesetze. In what follows, I analyze the incompleteness of that system—were it not inconsistent and hence trivially complete—by focusing on the role of the definite description operator and the axiom governing it (= Basic Law VI) as well as on the role of the application operator. The latter is defined by means of the former. I further comment on the redundancy of an axiom that could be designed to supplement Basic Law VI by incorporating the second clause of Frege’s two-part elucidation of the description operator. I argue that although it seems likely that Basic Law VI could have been shown to be dispensable in Grundgesetze, Frege would probably have been reluctant to dispense with it, despite his commitment to axiomatic parsimony. In my view, the reason is that he considers it essential that every primitive function-name of his formal language be governed and grounded by a basic law that is tailored to the nature and the role of the primitive name occurring at a key point in the law. Toward the end of the article, I propose solutions to two problems with Frege’s use of “=” in the concept-script sentences that result from his definitions involving the replacement of the double stroke of definition with the judgment-stroke. I conclude the article with a summary of the main results that I have achieved. (shrink)

Frege believes that the content of declarative sentences divides into a thought and its ‘colouring’, perhaps combined with assertoric force. He further thinks it is important to separate the thought from its colouring. To do this, a criterion which determines sameness of sense between sentences must be deployed. But Frege provides three criteria for this task, each of which adjudicate on different grounds. In this article, rather than expand on criticisms levelled at two of the criteria offered, the author focuses (...) on the most promising candidate. As it stands, this criterion has problems, but not insuperable ones. He suggests an adjusted criterion that relies on the epistemic notion of triviality. He recommends this criterion as both harmonious with Frege’s broader thought and preferable to alternatives offered. The moral is that Frege individuates thoughts by deploying an epistemic concept, and this is the only suitable way for him to do so. (shrink)

عنوان المقالة: الثقافة بين الأنا والآخر-مقاربات للتفكير.. الاسم الكامل: الصديق الصادقي العماري... .جامعة سيدي محمد بن عبد الله، فاس، المغرب.... ....التخصص: علم الاجتماع...... ...ملخص: .... لكل أمة ثقافة تعبر عن كينونتها، وتعكس طبيعتها، وتسجل إنتاجاتها المتراكمة عبر التاريخ، فتخلق منها أمة ذات تفردات تميزها عن غيرها من الأمم. وكذلك هي الثقافة في تميزها عن الثقافات السائدة، سواء في الزمن الواحد، أو في أزمنة متطاولة، وإن كانت تأخذ عنها، وتقتبس منها، وتتلاقح معها، فتتقارب، وتتحاور، وتتفاعل بطرق متباينة، فتكتسب قوة في المناعة، (...) وقدرة على التناغم مع البيئة، وعلى التكيف مع المحيط الإنساني العام، وتلك هي طبيعة الثقافة لدى أي أمة من الأمم، وفي كل عصر من العصور. كما أن لكل ثقافة هوية، ولكل هوية جوهر تعبر عنه خصوصيات معينة، وتنبثق عنه قيم سامية ومثل عليا، هي عنوان الأصالة والعراقة اللتين تعتبران القواعد الراسخة للثقافة. غير أنه من الصعب الحديث عن عمليات تبادل وحوار ثقافي بين ثقافتين غير متكافئتين، لأن التفاعل يتم من خلال الاعتراف أولا بثقافة الآخر، وإعطائها القيمة والمكانة التي تستحقها إلى جانب نظيرتها، كما أن الحوار واحترام الاختلاف يجب أن يكون من الطرفين معا، لهم الرغبة المتبادلة بعيدا عن الإكراه والاستغلال. إذ أن تبادل أشكال وعناصر الثقافة بين الشعوب والأمم لا ينبع من الإعجاب والرغبة في التوظيف الإيجابي لصالح ثقافة الأصل، وإنما يخضع لاعتبارات سياسية وأيديولوجية بالدرجة الأولى، حيث أن هذه الأشكال تتصارع فيما بينها وتخضع لاعتبارات حاسمة. فالصورة السلبية والقدحية التي أصبحت الميزة الحقيقية للمثاقفة في العصر الحالي، من خلال اعتماد الثقافة كآلية وأسلوب للتحكم والسيطرة على المستضعفين، ولد لدى الشعوب والأمم، خاصة العربية منها، خوفا على الهوية العربية الإسلامية من الضياع، مما دفع بالكثيرين إلى السعي نحو التعريف بالتراث والثقافة الخاصة وإبراز أهم مكوناتها، غير أن مسألة الرجوع للتراث العربي الإسلامي اختلفت حسب نوع التوجه والقناعة، ونوع المرجعية التي تؤطر كل فئة ولو من داخل نفس الشعب. مما نتج عن ذلك اختلافات وتشعبات في قراءة هذا التراث، حيث استند البعض على الأصولية الحادة، أما البعض الآخر اشتغل من داخل الاتجاه اليساري أو اللبرالي. من أجل تحليل وتفتيت هذا الإشكال بخصوص محورية الثقافة بين الأنا والآخر المختلف، تسعى هذه المقالة إلى الوقوف عند مفهوم الثقافة من داخل الأنثروبولوجيا وعلم الاجتماع، وإبراز العلاقة التلازمية بين الثقافة والهوية وطريقة تشكلهما، ثم التطرق لظاهرة المثاقفة والتثاقف وأهم الوظائف المميزة لهما، وأخيرا إبراز وتحليل الأسس التي تنبني عليها العلاقة بين الثقافة العربية وثقافة الآخر المختلف، وأهم الجوانب التي تحكمهما. ............. Each nation has a culture that expresses its identity, reflects its nature and records its accumulated productions throughout history, creating a nation unique in relation to other nations. Culture is also distinct from traditional cultures, both in time and in extended periods, although it takes, quotes and insinuates with them, converges, interacts and interacts in different ways, gaining the strength of immunity, the ability to align with the environment, the ability to adapt to the human environment in general, and that’s the nature of the culture of every nation and nation. (shrink)

In this paper, I revisit Frege's theory of sense and reference in the constructive setting of the meaning explanations of type theory, extending and sharpening a program–value analysis of sense and reference proposed by Martin-Löf building on previous work of Dummett. I propose a computational identity criterion for senses and argue that it validates what I see as the most plausible interpretation of Frege's equipollence principle for both sentences and singular terms. Before doing so, I examine Frege's implementation of his (...) theory of sense and reference in the logical framework of Grundgesetze, his doctrine of truth values, and views on sameness of sense as equipollence of assertions. (shrink)

According to Frege, we need a criterion for recognising when different sentences express the same thought to make progress in logic. He himself hedged his own equipollence criterion with a number of provisos. In the literature on Frege, little attention has been paid to the problems these provisos raise. In this paper, I will argue that Fregeans have ignored these provisos at their peril. For without these provisos, Frege’s criterion yields wrong results; but with the provisos in place, it is (...) of no use for Frege’s purposes. This is connected to what Frege took to be the ‘greatest difficulty for philosophy’: natural language sentences don’t just express thoughts; they convey evaluations and communicative hints. Because of this, Frege’s recognition criterion for thoughts cannot be applied to them and we cannot make logical progress by ‘recognising a thought in different linguistic guises’. (shrink)

According to a criterion of difference for thoughts derived from Frege, two thoughts are different if it is at the same time possible for a rational subject to take conflicting epistemic attitudes toward them. But applying this criterion to perception-based demonstrative thoughts seems to slice thoughts too finely and lead to their proliferation which makes the criterion implausible. I argue that such a proliferation of thoughts is blocked by transforming this criterion into a related one that is shown to be (...) essential in individuating thoughts as they are conceived of in this paper. This has to do with the fact that what makes demonstrative sense synchronically or diachronically the same is the subject’s unreflective taking-for-granted that the object that she is perceiving is a single object that does not require her to keep track of it in the sense supposed by Evans and Campbell. (shrink)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

Frege's mature writings apparently contain two different criteria of sense identity. While in "Über Sinn und Bedeutung" (1892) and in "Kurze Übersicht meiner logischen Lehren" (1906?) he seems to advocate a psychological criterion, his letter to Husserl of December 12, 1906 offers a thoroughly logical criterion of sense identity. It is argued that the latter proposal is not a "momentary aberration", but rather Frege's official criterion; his psychological criteria only serve as a way of illustrating questions of sense identity by (...) appealing to the thoughts of completely rational thinkers. (shrink)

While it is highly controversial whether Frege's criterion of sameness and difference for sense is true, it is relatively uncontroversial that that principle is inconsistent with Millian–Russellian views of content. I argue that this should not be uncontroversial. The reason is that it is surprisingly difficult to come up with an interpretation of Frege's criterion which implies anything substantial about the sameness or difference of content of anything.

This paper develops a criterion for sameness of Fregean senses. I consider three criteria: logical equivalence, intensional isomorphism, and epistemic equipollence. I reject the first two and argue for a version of the third.

The paper analyses Frege's approach to the identity conditions for the entity labelled by him as Sinn. It starts with a brief characterization of the main principles of Frege's semantics and lists his remarks on the identity conditions for Sinn. They are subject to a detailed scrutiny, and it is shown that, with the exception of the criterion of intersubstitutability in oratio obliqua, all other criteria have to be discarded. Finally, by comparing Frege's views on Sinn with Carnap's method of (...) extension and intension and the method of intensional isomorphism, it is proved that these methods do not provide a criterion for the identity of Frege's Sinn, even for extensional contexts, that the concept of intension does not coincide, as stated by Carnap, in these contexts, with Frege's concept of Sinn, and that Carnap's claim that in oratio obliqua Frege's semantics leads to an infinite hierarchy of Sinn entities can be questioned at least hypothetically in the light of certain new historical facts. (shrink)

In §1 of this paper I will present the two criteria, which I will call respectively the coextensionality and the recognitional criteria of synonymy. An established tendency in the literature is to ascribe to Frege only the recognitional criterion, discounting the coextensionality criterion as inconsistent with some of his other views. My aim in the paper will be to contribute to the reversal of this tendency. First, I wish to show that the recognitional criterion is flawed in a way that (...) makes it unacceptable as a criterion of synonymy and that Frege was aware of this. I will argue, second, that in Frege’s writings a modified version of the coextensionality criterion finds better support than the recognitional criterion. And I will suggest, third, that although there is an inconsistency between some of Frege’s views and the coextensionality criterion, this inconsistency can be explained as a prominent feature of his philosophy, a tension inherent in his goals and views. Finally, in a brief appendix, I will focus on the way in which Frege applied the two criteria in the practice of linguistic analysis, and I will argue that, contrary to the accepted wisdom, within this practice the two criteria are compatible with each other. (shrink)

One particular topic in the literature on Frege’s conception of sense relates to two apparently contradictory theses held by Frege: the isomorphism of thought and language on one hand and the expressibility of a thought by different sentences on the other. I will divide the paper into five sections. In (1) I introduce the problem of the tension in Frege’s thought. In (2) I discuss the main attempts to resolve the conflict between Frege’s two contradictory claims, showing what is wrong (...) with some of them. In (3), I analyze where, in Frege’s writings and discussions on sense identity, one can find grounds for two different conceptions of sense. In (4) I show how the two contradictory theses held by Frege are connected with different concerns, compelling Frege to a constant oscillation in terminology. In (5) I summarize two further reasons that prevented Frege from making the distinction between two conceptions of sense clear: (i) the antipsychologism problem and (ii) the overlap of traditions in German literature contemporary to Frege about the concept of value. I conclude with a hint for a reconstruction of the Fregean notion of ‘thought’ which resolves the contradiction between his two theses. (shrink)

In this paper, I will discuss a well-known oscillation in Frege’s conception of sense. My point is only partially concerned with his two different criteria of sense identity, and touches upon a more specific point: what happens if we apply Frege’s intuitive criterion for the difference of thoughts to logically equivalent sentences? I will try to make a schematic argument here that will preempt any endeavor to make Frege more coherent than he really is. In sections A and B, I (...) will present two alternative Fregean ways to treat the sense of logically equivalent sentences. Frege really oscillated between two alternative conceptions of sense, and his inability to detect the contrast between the two alternative conceptions is partly due to his strong conception of rationality. To apply the criterion of difference of thoughts to logical matters, we may also use a weak notion of rationality, or at least a notion of rationality of human agents, with limited computational resources. The distinctions towards which Frege was striving are better understood nowadays from the point of view of the treatment of limited rationality, which imposes itself even in logical matters. (shrink)

It is easy to think of Frege as having offered two unintentionally discordant criteria for the identity of senses—one tied to the truth conditions of sentences, and one meant to capture relations of cognitive discriminability. This reading, however, is doubly mistaken; the discord between these two ways of thinking of senses has a Fregean resolution, but neither the resolution nor either of the original two pictures affords a genuine criterion for the identity of senses.

In his Grundgesetze, §32, Frege launched the idea that the meaning of a sentence is given by its truth condition, or, in his particular version, the condition under which it will be a name of the True. This, indeed, was only one of the many roles in which truth has to serve within the Fregean system. In particular, truth is an absolute notion in the sense that bivalence holds: every Gedanke is either true or false, in complete independence of any (...) conative activity, whether by God or man. Thus various epistemological notions, such as the correctness of an assertion made, or judgement passed, are reducible to this absolute notion of truth: an assertion made through the utterance of a declarative sentence is correct when the proposition expressed by the sentence in question is true. Given this absolute status of truth it is not surprising that Frege is of the opinion that truth is a sui generis notion which has to be left unanalyzed and, indeed, which is indefinable. (shrink)

This dissertation is an inquiry into the identity conditions for propositions, with a view to determining whether a proposition can be conceived of as composed, in different ways, of several different combinations of ultimate constituents or whether the identity conditions for propositions require them each to have a single ultimate analysis. The inquiry is prompted by there being many instances of translation that seem to entail the expression of a single proposition by differently structured sentences. If these sentences reflect alternative (...) ultimate structures of the propositions they express, then some interesting consequences may follow. For example, propositions may not involve ontological presuppositions in the way that they do if they have unique structures. Conversely, grasping a particular proposition may require, not possessing a particular conceptual apparatus, but possessing any one of several. Hence the motivation for inquiring what sort of structure propositions are required to have by their identity conditions. ;Frege's remark that a proposition can be carved up in more than one way suggests that a Fregean criterion for propositional identity would allow propositions to have multiple ultimate structures, and that it might even illuminate the relationship among the structures that a proposition can have. The dissertation accordingly seeks to reconstruct a Fregean criterion for propositional identity, beginning with a Fregean criterion for expressing the same proposition. Most of the conclusions concern the latter kind of criterion, for work on it takes up a large part of the dissertation. It is concluded that Frege provides no criterion that is both noncircular and compatible with a proposition's having more than one ultimate structure. Additional results are a Fregean treatment of indexicals, the discovery that logical equivalence plays a central role in Frege's thinking about propositional identity, and the concomitant discovery that the idea of a criterion of propositional identity based on logical equivalence leads to substantial difficulties. (shrink)

Frege's writings on meaning are often interpreted within the framework of possible worlds semantics. The resulting theories rely on contingency to account for a variety of linguistic phenomena, such as the behavior of expressions in propositional attitude contexts, or the idea that a definition might fix the reference of an expression without establishing its meaning. In this thesis, I interpret Frege's ideas within a different framework, to provide a semantic theory that is able to account for some of these same (...) phenomena as they occur in a certain non-contingent language , where the possible worlds approach breaks down. ;The first part of the thesis is a detailed study of Frege's writings on sense identity, as well as some of the more modern literature on synonymy. I argue that instead of searching for a single relation of meaning equivalence among expressions, we should expect to find several different relations of meaning congruence. I claim that Frege was committed to this more flexible approach as well. To support my claim, I show that his standards for sense identity were strongly psychological; and then, relying on certain parallels between traditional ideas of definition and concept formation, I describe a problem about the senses of expressions introduced into a language through stipulative definitions. In the second part of the thesis, I develop a simple model of senses as procedures. I then use this model to deal with the problem about the senses of defined expressions set out earlier, and to deal also with the clash between Frege's compositional idea that the sense of a complete expression is assembled from the senses of its parts, and his decompositional idea that we can understand certain incomplete expressions only by first understanding complete expressions in which they occur. (shrink)

Frege had not one but two different notions of sense, namely, that of ?Über Sinn und Bedeutung? and one implicit in a letter to Husserl of 1906 and elsewhere. This last one originates in Frege's notion of conceptual content. The distinction is used to clarify some obscurities in Frege's thought. In the last section a sort of ?explicans? of Frege's notion of conceptual content is introduced and applied to the semantic analysis of mathematics.