Bell and Michael Dummett have investigated Frege's views on the relation with respect to differently structured sentences of natural language is beyond. tion, defended primarily by Dummett, TLP thoughts are Fregean bearers of .. have the same relation to reality as words if the latter are related to reality via. Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He is .. It should be kept in mind that Frege was employed as a mathematician, not a Frege also held that propositions had a referential relationship with their truth-value (in other words, a statement "refers" to the truth- value it takes).
Connectionist models emphasize the idea that a person's lexicon and their thoughts operate in a kind of distributed, associative network. Reductionist models attempt to explain higher-level mental processes in terms of the basic low-level neurophysiological activity of the brain. There have been a number of different perspectives on this issue, each offering a number of insights and suggestions.
Linguists Sapir and Whorf suggested that language limited the extent to which members of a "linguistic community" can think about certain subjects a hypothesis paralleled in George Orwell 's novel Nineteen Eighty-Four. Philosopher Michael Dummett is also a proponent of the "language-first" viewpoint. The "knowledge-first" position can be found, for instance, in the work of Paul Grice. According to his argument, spoken and written language derive their intentionality and meaning from an internal language encoded in the mind.
Another argument is that it is difficult to explain how signs and symbols on paper can represent anything meaningful unless some sort of meaning is infused into them by the contents of the mind.
One of the main arguments against is that such levels of language can lead to an infinite regress. Another tradition of philosophers has attempted to show that language and thought are coextensive — that there is no way of explaining one without the other.
Donald Davidson, in his essay "Thought and Talk", argued that the notion of belief could only arise as a product of public linguistic interaction. Daniel Dennett holds a similar interpretationist view of propositional attitudes. Some thinkers, like the ancient sophist Gorgiashave questioned whether or not language was capable of capturing thought at all. Hence, since the objects of sight cannot be presented to any other organ but sight, and the different sense-organs cannot give their information to one another, similarly speech cannot give any information about perceptibles.
Therefore, if anything exists and is comprehended, it is incommunicable. Some of them were performed by Lera Boroditsky. For example, English speakers tend to say things like "John broke the vase" even for accidents. However, Spanish or Japanese speakers would be more likely to say "the vase broke itself. Later everyone was asked whether they could remember who did what.
Spanish and Japanese speakers did not remember the agents of accidental events as well as did English speakers. The Pirahaa tribe in Brazilwhose language has only terms like few and many instead of numerals, are not able to keep track of exact quantities. The descriptions they gave differed in a way predicted by grammatical gender.
For example, when asked to describe a "key"—a word that is masculine in German and feminine in Spanish—the German speakers were more likely to use words like "hard," "heavy," "jagged," "metal," "serrated," and "useful," whereas Spanish speakers were more likely to say "golden," "intricate," "little," "lovely," "shiny," and "tiny.
They had to guess whether each alien was friendly or hostile, and after each response they were told if they were correct or not, helping them learn the subtle cues that distinguished friend from foe.
- Gottlob Frege
A quarter of the participants were told in advance that the friendly aliens were called "leebish" and the hostile ones "grecious", while another quarter were told the opposite. For the rest, the aliens remained nameless. It was found that participants who were given names for the aliens learned to categorize the aliens far more quickly, reaching 80 per cent accuracy in less than half the time taken by those not told the names.
By the end of the test, those told the names could correctly categorize 88 per cent of aliens, compared to just 80 per cent for the rest. It was concluded that naming objects helps us categorize and memorize them. In another series of experiments  a group of people was asked to view furniture from an IKEA catalog. Half the time they were asked to label the object — whether it was a chair or lamp, for example — while the rest of the time they had to say whether or not they liked it.
It was found that when asked to label items, people were later less likely to recall the specific details of products, such as whether a chair had arms or not.
It was concluded that labeling objects helps our minds build a prototype of the typical object in the group at the expense of individual features. Questions inevitably arise on surrounding topics. One question is, "What exactly is a convention, and how do we study it? However, this view seems to compete to some extent with the Gricean view of speaker's meaning, requiring either one or both to be weakened if both are to be taken as true.
Noam Chomsky proposed that the study of language could be done in terms of the I-Language, or internal language of persons. If this is so, then it undermines the pursuit of explanations in terms of conventions, and relegates such explanations to the domain of "meta-semantics".
Metasemantics is a term used by philosopher of language Robert Stainton to describe all those fields that attempt to explain how semantic facts arise. Etymology the study of the origins of words and stylistics philosophical argumentation over what makes "good grammar", relative to a particular language are two other examples of fields that are taken to be meta-semantic. Not surprisingly, many separate but related fields have investigated the topic of linguistic convention within their own research paradigms.
The presumptions that prop up each theoretical view are of interest to the philosopher of language. For instance, one of the major fields of sociology, symbolic interactionismis based on the insight that human social organization is based almost entirely on the use of meanings. Rhetoric is the study of the particular words that people use to achieve the proper emotional and rational effect in the listener, be it to persuade, provoke, endear, or teach.
Some relevant applications of the field include the examination of propaganda and didacticismthe examination of the purposes of swearing and pejoratives especially how it influences the behavior of others, and defines relationshipsor the effects of gendered language. It can also be used to study linguistic transparency or speaking in an accessible manneras well as performative utterances and the various tasks that language can perform called "speech acts".
It also has applications to the study and interpretation of law, and helps give insight to the logical concept of the domain of discourse. Literary theory is a discipline that some literary theorists claim overlaps with the philosophy of language.
It emphasizes the methods that readers and critics use in understanding a text. This field, an outgrowth of the study of how to properly interpret messages, is unsurprisingly closely tied to the ancient discipline of hermeneutics. Language and Continental philosophy[ edit ] In Continental philosophylanguage is not studied as a separate discipline, as it is in analytic philosophy. Rather, it is an inextricable part of many other areas of thought, such as phenomenologysemioticshermeneuticsHeideggerean ontologyexistentialismstructuralismdeconstruction and critical theory.
The idea of language is often related to that of logic in its Greek sense as " logos ", meaning discourse or dialectic. Language and concepts are also seen as having been formed by history and politics, or even by historical philosophy itself. The field of hermeneutics, and the theory of interpretation in general, has played a significant role in 20th century Continental philosophy of language and ontology beginning with Martin Heidegger.
Heidegger combines phenomenology with the hermeneutics of Wilhelm Dilthey. Heidegger believed language was one of the most important concepts for Dasein. Heidegger believed that language today is worn out because of overuse of important words, and would be inadequate for in-depth study of Being Sein.
Philosophy of language - Wikipedia
For example, Sein beingthe word itself, is saturated with multiple meanings. Thus, he invented new vocabulary and linguistic stylesbased on Ancient Greek and Germanic etymological word relations, to disambiguate commonly used words.
He avoided words like consciousness, ego, human, nature, etc. With such new concepts as Being-in-the-world, Heidegger constructs his theory of language, centered on speech.
Frege, Gottlob: Language | Internet Encyclopedia of Philosophy
He believed speech talking, listening, silence was the most essential and pure form of language. Heidegger claims writing is only a supplement to speech, because even a reader constructs or contributes one's own "talk" while reading. The most important feature of language is its projectivity, the idea that language is prior to human speech. This means that when one is "thrown" into the world, his existence is characterized from the beginning by a certain pre-comprehension of the world. However, it is only after naming, or "articulation of intelligibility", can one have primary access to Dasein and Being-in-the-World.
In Truth and Method, Gadamer describes language as "the medium in which substantive understanding and agreement take place between two people.
For example, monuments and statues cannot communicate without the aid of language. Gadamer also claims that every language constitutes a world-view, because the linguistic nature of the world frees each individual from an objective environment: The world as world exists for man as for no other creature in the world.
Other philosophers who have worked in this tradition include Luigi Pareyson and Jacques Derrida. In this field, human language both natural and artificial is just one among many ways that humans and other conscious beings are able to communicate. It allows them to take advantage of and effectively manipulate the external world in order to create meaning for themselves and transmit this meaning to others. Every object, every person, every event, and every force communicates or signifies continuously.
The ringing of a telephone for example, is the telephone. The smoke that I see on the horizon is the sign that there is a fire. The things of the world, in this vision, seem to be labeled precisely for intelligent beings who only need to interpret them in the way that humans do.
True communication, including the use of human language, however, requires someone a sender who sends a message, or text, in some code to someone else a receiver. Language is studied only insofar as it is one of these forms the most sophisticated form of communication.
In modern times, its best-known figures include Umberto EcoA. Problems in the philosophy of language[ edit ] Vagueness[ edit ] One issue that has troubled philosophers of language and logic is the problem of the vagueness of words. The specific instances of vagueness that most interest philosophers of language are those where the existence of "borderline cases" makes it seemingly impossible to say whether a predicate is true or false.
Classic examples are "is tall" or "is bald", where it cannot be said that some borderline case some given person is tall or not-tall. In consequence, vagueness gives rise to the paradox of the heap. Many theorists have attempted to solve the paradox by way of n-valued logics, such as fuzzy logicwhich have radically departed from classical two-valued logics.
One might ask, for example, "When people say the word rocks, what is it that the word represents? Some have said that the expression stands for some real, abstract universal out in the world called "rocks". Thus, if Frege held a rationalist view of thought contents at this early point, his argument above for the indispensability of thought for language would still appear somewhat incomplete, and if he was an empiricist about thought content at the time but changed his view later, he should have been expected to supplement his argument at that later time in order to convince us of the necessity to study language in order to explore concepts and thoughts.
So let us take a closer look both at Frege's views of the nature of thought content and at plausible rationalist motivations for the philosophical study of language based on the idea that language is necessary for human thought. Let us first get back to Frege's apparent view — in his piece — that basic forms of sense perception and memory are possible without prior possession of non-sensual thought contents. This view appears to contradict his own later remarks on perception in, for instance, 's "Thought".
There he emphasizes that: Sense impressions alone do not reveal the external world to us. Perhaps there is a being that has only sense impressions without seeing or touching things Having visual impressions is certainly necessary for seeing things, but not sufficient.
Philosophy of language
What must still be added is not anything sensible. And yet this is just what opens up the external world for us; for without this non-sensible something everyone would remain shut up in his inner world.
So perhaps, since the decisive factor lies in the non-sensible, something non-sensible, even without the cooperation of sense impressions, could also lead us out of the inner world and enable us to grasp thoughts For Frege, forming a thought about the external world -- even the kind of thought involved in the mere perception of an object -- requires more than sense impressions that are available to the human mind.
In addition, something non-sensible has to be assumed in order to account for the possibility of perception. The aim of "Thought" was to show that this something is the thought itself -- an entity that, as Frege argues here, belongs neither to the inner world of subjective ideas nor to the world of spatio-temporal, perceivable objects, but rather to a third realm of objective but non-physical things.
Indeed, as we read in an earlier passage of the piece, "although the thought does not belong with the contents of the thinker's consciousness, there must be something in his consciousness that is aimed at the thought. But this should not be confused with the thought itself" ibid.: In this last passage, Frege clearly distinguishes between a conscious act of thinking — which must be in a certain way "aimed at" an abstract, objective thought — and the thought itself at which it is aimed.
In addition, Frege explicitly rejects the idea that sense impressions alone could enable our minds to grasp such an objective, non-sensible thought -- rather, what is required is again something "non-sensible. For according to that remark, language — as a means for grasping thoughts — presupposes reason at least as an independent potential. Reason, then, is a likely candidate for the "something non-sensible" that may be required, according to Frege in"to lead us out of the inner world and enable us to grasp thoughts.
However, Frege does not make use of the term "reason" in his piece but speaks more concretely of a "special mental capacity, the power of thinking", which is supposed to explain our ability to grasp a thought ibid.: In any case, these remarks provide clear evidence that Frege in conceived of thoughts as existing independently of both physical and empirically psychological reality — thereby ruling out an empiricist account of their constitution.
They do not provide conclusive evidence that Frege endorsed a rationalist or transcendentalist view of the origin or nature of conceptual entities, if by this we understand a view according to which either a special faculty of reason — or pure understanding — or alternatively a certain normative value or principle that is constitutive of rationality in general serve to provide the conceptual content of our thought episodes.
Rather, Frege's remarks would just as well be compatible with a naive Platonist view about thought contents, according to which their objective existence is a brute fact, that is, not accountable or explainable in terms of anything else.
It seems obvious, however, that Frege favored a broadly rationalist or transcendentalist account of the origin of conceptual entities both in his first monograph Conceptual Notation and in his second, The Foundations of Arithmetic Those judgments, by contrast, which "at first glance seem to be possible only on the grounds of some intuition" presumably are those of arithmetic, which Kant had believed to be grounded on the pure intuition of time.
This metaphor of pure thought as grounding arithmetical judgments by way of "the content that arises from its own nature" not only appears inconsistent with Frege's seeming slip into psychologism about mental content, but at the same time suggests a rationalist or transcendental approach to the nature of at least some of the contents of our judgments.
This is so if we conceive of "pure thought" as referring to a capacity or principle that is constitutive of the rational mind, which is how this expression, and similar ones, had been used by LeibnizKantand their successors. In other passages of Foundations, Frege presents objectivity itself as being constituted by reason, and numbers as its nearest kin: I understand objective to mean what is independent of our sensations, intuition and imagination, and of all construction of mental pictures out of memories of earlier sensations, but not what is independent of the reason, - for what are things independent of the reason?
On this view of numbers the charm of work on arithmetic and analysis is, it seems to me, easily accounted for.
We might say, indeed, almost in the well-known words: The reason's proper study is itself. In arithmetic we are not concerned with objects which we come to know as something alien from without through the medium of the senses, but with objects given directly to our reason and, as its nearest kin, utterly transparent to it. And yet, or rather for that very reason, these objects are not subjective fantasies.
These latter constitute part of the transcendental as opposed to the subjective, psychological aspect of the mind according to Kant. Scholars who tend to read Frege from the perspective of Neo-Kantianism have therefore taken passages like those above as strong evidence for the thesis that his notion of objectivity was not dogmatically metaphysical but epistemological in the tradition of transcendental philosophy cf. Indeed, as we saw, Frege had initiated this argument with observations about the effect of sense-impressions on our attention.
In this he simply followed Leibniz, who — although a rationalist about the origin of thought — had granted that the senses are required to make the mind attentive to truths and to direct it towards some truths rather than others. For this reason, according to Leibniz, even though intellectual ideas and the truths arising from them do not "originate in the senses", without the senses we would never think of them ibid.
Given such presuppositions about the causal role sensation plays in the generation of actual processes of conscious thought, Frege can still make his case for the necessity of language for thinking by arguing as follows: Without sensible symbols, which — due to their intimate connection to reason perhaps in the form of a set of innate ideas — are able to draw our attention away from other sensory input and toward conceptual thought, our entire mental life would be largely dictated by the nature of our immediate sensations.
Therefore, we would be psychologically unable to rise to higher forms of conscious awareness and contemplation than those provided by immediate sense perception and the fleeting memory images arising from it. This way of arguing would not commit him to the view that concepts or conceptual thought contents themselves depend for their existence on symbols or on any other sensible images. Rather, the dependence of human thought on language could itself be thought of as merely causal Baker and Hacker As we saw before, Frege apparently sympathized with Leibniz's view that what is innate may need to be learned in order for us to become consciously aware of it.
But if we need to learn about truths and concepts that have been in our understanding all along — as Leibniz saw it — then this is compatible with the claim that in order to learn them we need to use language. Indeed, in a much later piece written and submitted for publication shortly before his death "Sources of Knowledge of Mathematics and the Mathematical Natural Sciences"Frege finally comes to explicitly commit himself to the view that language is necessary not for the existence of thought contents themselves, but only for our conscious awareness of them, that is, for our acts of thinking.
In this context, he speaks of a "logical source of knowledge" and a "logical disposition" in us that must be at work in the formation of language, where he made use in of the ambiguous word "reason" and in of the expression "power of thinking" to denote a special mental capacity: The senses present us with something external and because of this it is easier to comprehend how mistakes can occur than it is in the case of the logical source of knowledge which is wholly inside us and thus appears to be more proof against contamination.
But appearances are deceptive. For our thinking is closely bound up with language and thereby with the world of the senses. Perhaps our thinking is at first a form of speaking which then becomes an imaging of speech. Silent thinking would in that case be speech that has become noiseless, taking place in the imagination.
Now we may of course also think in mathematical signs; yet even then thinking is tied up with what is perceptible to the senses. To be sure, we distinguish the sentence as the expression of a thought from the thought itself. We know we can have various expressions for the same thought. The connection of a thought with one particular sentence is not a necessary one; but that a thought of which we are conscious is connected in our mind with some sentence or other is for us humans necessary.
But that does not lie in the nature of the thought but in our own nature. There is no contradiction in supposing there to exist beings that can grasp the same thought as we do without needing to clad it in a form that can be perceived by the senses.
But still, for us humans there is this necessity. Language is a human creation; and so humans had, it would appear, the capacity to shape it in conformity with the logical disposition alive in them. Certainly the logical disposition of humans was at work in the formation of language but equally alongside this many other dispositions — such as the poetic disposition. And so language is not constructed from a logical "blueprint" Here, Frege explains how it comes about that language in a certain sense "contaminates" the logical source of knowledge — that is, the faculty in us that enables us to have knowledge about logical structures and relations.
As he sees it here, this logical disposition in us is not identical to the ability to speak a language, although it is required for the development and acquisition of a language.
As he points out in a later passage, If we disregard how thinking occurs in the consciousness of an individual, and attend instead to the true nature of thinking, we shall not be able to equate it with speaking. In that case we shall not derive thinking from speaking; thinking will then emerge as that which has priority and we shall not be able to blame thinking for the logical defects we have noted in language" ibid.: Accordingly, thoughts are not to be identified with their linguistic expressions, and they do not in principle require any language in order to be accessible to rationally ideal beings that are capable of grasping them in an entirely non-sensible way.
Presumably, these beings would possess a logical source of knowledge that is so powerful that it doesn't require language at all in order to produce acts of thought. They do not require language precisely because their attention is not distracted or dominated by the continuous impact of sense impressions. As opposed to this, Frege points out human beings require language in order to become conscious of a thought. And this, together with the fact that ordinary language — the kind of language in which human beings normally learn to think — is shaped also by other, less rational aspects of human nature, explains for Frege why actual human thought as opposed to the bare content of pure thought, or that at which an act of thinking, as part of human consciousness, has to aim in order to be a thought at all is prone to impurity through the influence of the language in which it is normally clad.
However, according to Dummett, it simply becomes the question of how we refer to, that is, succeed in talking about, numbers. And as Dummett understands this question, it is answered simply by Frege's account of the meanings of conventionally introduced expressions. The problem with this interpretation is that, presumably, for Frege any complete account of how expressions can possess meaning at all would have to involve a complete account of how we can grasp and understand pure thoughts — and it does not appear that he thought this question could be sufficiently answered with recourse to language simply because for Frege language itself presupposes certain rational capacities in order to be capable of expressing thoughts.
This seems to be precisely why Frege repeatedly takes refuge in various metaphors to indicate the existence of certain rational faculties that enable us to grasp a thought, like the mysterious "power of thinking" that he talks about in "Thought".
Indeed, in a draft dating from he explicitly describes the act of thinking as "perhaps the most mysterious of all", and adds that he regards the question of how it is possible as "still far from being grasped in all its difficulty" At the same time, he explicitly denies that this question could ever be answered in terms of empirical psychology or in terms of logic. Certainly, then, he could not seriously hold that specifying a relation between expressions and what they designate, or between sentences and their truth-values, could ever fully replace the question of how it is possible that we can think of anything at all.
Consequently, this also means that a philosophy of language in Frege's view could never be more than a fragment of a complete philosophy of human thought, albeit an important one. Dummett is aware that in this sense, Frege's philosophical account of thought and understanding is still incomplete; however, it is doubtful that Frege would have agreed that it could be completed by reflecting further on the uses and functions of language — which is Dummett's own proposal In fact, whether the question of what thoughts consist in and what their preconditions are could be completely settled within the philosophy of language or not has been one of the major — and most interesting — issues of dispute in 20th century analytic philosophy.
For detailed discussions of Dummett's interpretation of Frege see Dummett and Lotterchap. The Formal Language Approach We now begin to understand why language was a serious matter to Frege, even though he did not consider it his primary object of interest. His interest in the philosophy of language was based on his firm belief that language is necessary for human thought, and it was triggered in particular by his investigations into the foundations of mathematics, in which he faced a serious problem concerning the symbolic tools that were available at the time for such investigations.
In his "Notes for Ludwig Darmstaedter," he describes the problem that first led him to investigate language as follows: I started out from mathematics.
The most pressing need, it seemed to me, was to provide this science with a better foundation. I soon realized that number is not a heap, a series of things, nor a property of a heap either, but that in stating a number that we have arrived at as the result of counting we are making a statement about a concept.
The logical imperfections of language stood in the way of such investigations. I tried to overcome these obstacles with my concept-script. In this way I was led from mathematics to logic" Frege Points out that the logical imperfections of language — by which he means the natural language of everyday life, or the "language of life", as he sometimes calls it — had proven to be an obstacle for his investigations into the ontology of numbers and the epistemology of mathematics, especially arithmetic.
He was trying to find out whether all arithmetic formulas could be proven on the basis of logical axioms and definitions alone, and whether numbers could therefore be construed as logical objects — a view that later came to be called "logicism.
However, the formula language of arithmetic, in which numbers and their relations are expressed, did not contain expressions for specifically logical relations; and ordinary language proved to be insufficiently transparent with regard to the discovery of logical relations — especially logical consequence — to serve Frege's purposes well. Therefore, Frege decided to create what he regarded as a logically superior notational system for arithmetic — a notational system that was supposed to be as transparent as possible with respect to the logical structure of thought in that area, and one that contained symbols not only for arithmetical entities but also for specifically logical relations and concepts.
Moreover, each term contained or introduced into this notational system should be given a precise and fixed meaning by way of definitions in terms of small number of primitive terms.
Although "Begriffsschrift" is usually translated as "concept script" or "conceptual notation", it is sometimes translated differently; in Fregefor example, it is translated as "ideography". He gives two independent reasons for the choice of this terminology: First — as he explains in the preface to Conceptual Notation — because in it all and only that part of the content of natural language expressions is to be represented that is of significance for logical inference; and this is what Frege called the "conceptual content" of an expression Secondly — as we learn again from his piece mentioned earlier — Frege means by "Begriffsschrift" a symbolic system in which, contrary to natural language, the written symbols come to express their subject matter directly, that is, without the intervention of speech In this way, expressions of conceptual content could be radically abbreviated; for instance, a simple statement could be accommodated in one line as a formula of the concept script.
Frege also decided to represent complex statements of propositional logic — statements linking two or more simple statements — in a two-dimensional manner for reasons of perspicuity. Historically, the idea of a concept script derives from the Leibnizian project of developing a so-called "universal characteristic" characteristica universalis: A universal symbolic system in which every complex concept is completely defined based on a set of primitive concepts and logical rules of inference and definition, and which thus enables us to make the conceptual structure of our universe explicit.
Such a symbolic system would also contain a logical calculus calculus ratiocinator consisting of purely syntactic inference rules based on the types of symbols used within the formal language.
However, according to the Leibnizian conception, logic itself is not merely a calculus but expressible in an ideal language, that is, in the universal characteristic.
Frege certainly adopted this view of logic from Leibniz; his main source of his understanding of Leibniz's conception very likely was again Trendelenburg's essay Slugach. However, 20th and 21st century mainstream analytic philosophy has somewhat misleadingly characterized Frege as regarding logic itself as a universal language rather than a calculus for example, van Heijenoort, The latter characterization is misleading for two reasons. The first is that, as we have seen, Frege did not regard language as the source of thought contents; he did regard logic, however, as consisting of true thought contents though this has been recently disputed for the Frege of the Conceptual Notation period in Linnebo Hence, he could not have regarded logic as being identical with any language.
Secondly, Frege did not actually attempt to develop his concept script as a universal language in Leibniz's sense though he agrees that logic itself contains universally applicable laws of thought. Rather, he held the more cautious belief that if such a language could be developed at all, its development would have to proceed gradually, in a step-by-step manner: The concept script offered here adds a new one to these — indeed, the one located in the middle, adjoining all the others.
From here, with the greatest prospect of success, one can then proceed to fill in the gaps in the existing formula languages, connect their hitherto separate fields into the domain of a single formula language and extend it to fields that have hitherto lacked such a language" Thus, Frege intended his concept script primarily for the expression of logical relations within the realm of arithmetic — the field that he saw as located in the middle of all other areas of possible inquiry.
He did seem optimistic that his concept-script could be successfully applied "wherever a special value has to be placed on the validity of proof" ibid.
He also expressed — in the piece mentioned earlier — the belief that in principle the concept-script could be applied wherever logical relations pertain, and that therefore philosophers as well should pay attention to it.
However, he was never ambitious or even interested in examining how it could be applied to areas that were remote from arithmetic. Frege's revival of the idea of a universal, logically ideal language for the analysis and advancement of science and human knowledge subsequently became extremely influential especially through the writings of Russell and the early Wittgenstein and it contributed to the development of Logical Positivism in the first half of the 20th century.
Rudolf Carnap and other members of the Vienna Circle actually worked on the establishment of a universal formal language of science in which not only every scientific theory could be expressed in a unified way, but also every meaningful philosophical problem would be soluble by way of logical reconstruction Carnap a and b.
Still in the fifties and sixties of the last century, after attempts at establishing a universal formal language of science had eventually proven unsuccessful, Nelson Goodman practiced and endorsed an axiomatic approach -- based on the idea of multiple formal reconstructions of certain areas of philosophical inquiry -- for investigating the conceptual relation between universals and particulars and between the world of phenomenal experience and that of physical objects Goodman Frege, by contrast, never applied his concept-script to fields other than logic and mathematics, choosing an informal, argumentative rather than formal and "constructivist" approach to dealing with philosophical issues arising from — or underlying — his logicist project.
Some remarks in the preface to Conceptual Notation might give us a clue as to why he did not go so far as Carnap and Goodman in his adherence to formula language in philosophical inquiry.
There, Frege uses the analogy of the microscope and the eye in order to explain the relation between ordinary language or the "language of life", as Frege calls it and concept-script: The latter that is, the eyebecause of the range of its applicability and because of the ease with which it can adapt itself to the most varied circumstances, has a great superiority over the microscope. Of course, viewed as an optical instrument it reveals many imperfections, which usually remain unnoticed only because of its intimate connection with mental life.
But as soon as scientific purposes place strong requirements upon sharpness of resolution, the eye proves to be inadequate. On the other hand, the microscope is perfectly suited for just such purposes; but, for this very reason, it is useless for all others" According to Frege, the concept-script is not to replace ordinary language in all its uses; on the contrary, he regards it as "useless" in all contexts but "scientific" ones. Given this belief, it remains undecided whether Frege regarded philosophy itself as an entirely scientific discipline or whether he thought that there are areas of philosophy in which the concept-script would be useless in principle.
That he never even considered formalizing his claims about perception, meaning, the nature of thought, or the basis of objectivity may be taken as some evidence for the latter, although it would not be conclusive. The Logical Imperfections of Ordinary Language What all of these "formal language" approaches have in common is not merely the insight that ordinary language lacks a certain amount of transparency when it comes to exploring the meanings and logical relations between words and sentences.
It is moreover the assumption that an artificial formula language is in principle able to capture the logical structure of thought — or even of the world itself as it is reflected in thought — better than any natural language that characterizes the approach to language taken by Frege — and after him Russell, the early Wittgenstein, and the Logical Positivists.
The following is a brief survey of what Frege considered the most prominent logical impurities of natural language that stood in the way of his logical investigations into the foundations of arithmetic, and how Frege thought them to be eliminated in a logically perfect language like his concept-script.
Gottlob Frege: Language
Non-Observance of the Difference Between Concept and Object According to Frege, the difference between concept and object is not generally well observed in natural languages. Often, the same word serves to designate both a concept and an object that falls under it. The word "horse", for instance, sometimes serves to denote a concept, as in "This is a horse", other times a single object, as in "This horse is black", and sometimes also an entire biological species, as in "The horse is an herbivorous animal" Even though we could read the second sentence above as "There is exactly one x at location y such that x is a horse and x is black", thereby maintaining the same logical category for "horse" as in the first sentence, this syntactical structure is not transparent in ordinary language.
In a logically ideal language, by contrast, every word or complex expression would have to stand for exactly one object, concept, or relation, and it would have to be clear from the syntax of the language -- that is, from the syntactical categories of the expressions themselves -- to which of those ontological categories the entity designated belongs.
Thus, the logical syntax of the language would reflect the logical structure within the realm of entities to which it is applied. The main rationale for Frege's strict distinction between concepts and objects, as well as their corresponding syntactic categories, appears to lie in his understanding of logical unity.
In his "Notes for Ludwig Darmstaedter" Frege points out that: The sharp separation of what is in need of supplementation from what is saturated is very important" Rather, in order to account for the possibility of logically complex units at all, we have to assume that they are composed of a combination of two types of logical components; saturated, complete, self-subsisting ones, on the one hand, and unsaturated, incomplete ones — ones that essentially are in need of supplementation — on the other.
On the level of ontology, Frege calls every unsaturated entity a "concept" or "relation", and every saturated one an "object". Up until the very last phase of his intellectual career, he included in the latter category not only physical things, and psychological events, but also abstract entities like sets, numbers, truth values, and even entire thoughts in his specific sense of that which is grasped in an act of thinking.
On the syntactic level, the contrast between saturated and unsaturated entities is reflected in the distinction between proper names, on the one hand, and predicates which Frege calls "concept-words" on the other. In this sense, we can say that in Frege, syntactic distinctions as well as relations are not only presupposed in the creation of any meaningful linguistic unit but they already have a meaning in themselves. Thus, the mere combination of a proper name with a predicate in a logically ideal language as such already expresses something — namely, it expresses that an object falls under a concept which was for Frege the most basic logical relation one can think of.
A proper name in Frege's sense is any singular expression, that is, a proper name is any expression that serves to designate one and only one particular object; a predicate, by contrast, designates a concept or a relation. Thus, the class of Fregean proper names in ordinary language comprises not only names in the narrow sense like "Aristotle" but also any other expression that is used to refer to one particular object.
Notoriously, since at least from onwards Frege conceives of truth values as objects and of sentences as referring to truth values ahe regards complete sentences of ordinary language as proper names as well — unlike assertions or asserted judgments, which are represented in the concept script by means of an assertion sign a; Empty Proper Names Besides its lack of exact correspondence between syntactical and ontological categories, another problem of ordinary language — which Frege encountered not only in fictional but also in scientific contexts — is that of empty proper names.
These are grammatically well-formed singular expressions that do not happen to denote anything, or that apply to more than one thing and therefore do not actually fulfill their function as singular terms. One example that Frege cites is the syntactically well-formed expression "the celestial body most distant from the Earth"; it is doubtful whether this expression denotes anything at all.
This is even more obvious with expressions like "the least rapidly convergent series", which are just as void of an object of designation as is the name "Odysseus" a; In a logically perfect language, by contrast, "every expression grammatically well constructed as a proper name out of signs already introduced shall in fact designate an object, and In addition Frege suggested that, if need be, an artificial significance could be stipulated for all those proper names that turn out to lack reference to an actually existing object ibid.
The Vagueness of Predicates According to Frege, while proper names serve to designate objects, concept-words serve to designate concepts, which as such belong to an entirely separate logical category This is also reflected in the use of concept-words, which -- in contrast to proper names -- can refer even if no object falls under the concept they designate Nonetheless, a concept-word lacks significance just like an empty proper name if it does not clearly express under which conditions an object falls under the designated concept and under which it doesn't.
For Frege, the logic of pure thought cannot acknowledge concepts with undetermined boundaries a, b. It seems obvious that most, if not all, concept-words in natural language lack the kind of semantic precision that Frege expects of a logically perfect language. If not then — barring the remote possibility that there really is a sharp boundary of which we are more or less ignorant — most if not all ordinary language concept-words have vague meanings in Frege's sense. Hence, strictly speaking most, if not all, concept-words in ordinary language would lack significance, according to Frege's logic.
In a logically perfect language — as Frege conceived of it — the vagueness of predicates could be eliminated through their arrangement in an axiomatic system, through logical analysis, as well as informal elucidations and clarification of the primitive terms by way of examples.
Frege strictly distinguishes definitions from illustrative examples. The latter, together with other forms of elucidation, merely serve to clarify the meanings of primitive signs signs whose meanings cannot be analyzed further into logical components. Theoretically, one would never be able to fully clarify the meaning of such an expression by way of examples; however, according to Frege "we do manage to come to an understanding about the meanings of words" in practice.
Definitions in the proper sense are constructive, in that they introduce a new sign to abbreviate a more complex expression that we have constructed out of its logical components. Frege distinguishes from these purely stipulative definitions cases of what were in his time called "analytic definitions". These display a logical analysis of the sense of a sign that has long been in use before by identifying its sense with that of a complex expression; this sense then is a function of the senses of the latter's logical parts.
In this case the meaning equation is not a mere matter of arbitrary stipulation but can only be recognized by "an immediate insight. Grammatical versus Logical Categories For Frege, the logician's main goal in her struggle with language is to "separate the logical from the psychological;" that is, the logician's main goal in her struggle with language is to isolate the logically relevant aspects of grammar and meaning from those that are not.
Frege defines "logically relevant aspects of grammar" as only those aspects of language that have a bearing on logical inference Accordingly, as philosophers interested in pure thought we "have to turn our backs on" any grammatical distinctions and elements of meaning that are not relevant for logical inferences, or that may even obscure them.
This includes, but is not limited to, the grammatical distinction between the subject and the predicate of a sentence, which Frege contends misled logicians for centuries.
Grammatically speaking, the subject of a sentence is the expression that signifies what the sentence is "about", or as Frege puts it, the subject of the sentence is "the concept with which the judgment is chiefly concerned" The predicate, by contrast, would then be the expression that signifies what is being said about the subject or, alternatively, the concept that is applied to the subject. So, for instance, in the sentence "Archimedes perished at the conquest of Syracuse," the word "Archimedes" appears to be the subject; and "…perished at the conquest of Syracuse, "the predicate.
According to Frege, however, the grammatical distinction between subject and predicate, which used to be the model for traditional logic, does not match the logical structure of that part of the content of sentences that is relevant for logic.
More precisely, Frege thought the distinction between subject and predicate to be neither necessary nor sufficient to describe the logical structure of thought.
It is not necessary because it yields distinctions between sentences that appear to have the same logical power of inference. For instance, the following two sentences obviously are grammatically distinct: Yet from a logical point of view the two sentences have the same conceptual content, and therefore do not need to be distinguished in a logically perfect language ibid.: The second reason why Frege thought the grammatical distinction between subject and predicate is unnecessary for the expression of, or distinction between, conceptual contents and their components is that, logically speaking, the linguistic expression of a judgment or assertion can always be rephrased as a combination of a nominal phrase, which contains the entire conceptual content, and a grammatical predicate like "is a fact" or "is true", which does not add anything to that content.
Hence, as Frege points out, "we can imagine a language in which the proposition "Archimedes perished at the conquest of Syracuse" would be expressed in the following way: In such a case the grammatical subject contains the whole content of the judgment and the predicate serves only to present this content as a judgment; hence, strictly speaking, nothing at the level of conceptual content -- at the level of what is relevant to logical inference -- corresponds to the predicate here.
Because Frege conceives of such contents as identical to the contents of nominal phrases and thus all complete expressions in his system are names or "terms" in Russellian terminologyhis sentential logic today is sometimes called "term logic" for example, Zalta as opposed to standard propositional logic, in which propositions or sentences are regarded as a logical category distinct from both predicates and terms.
Furthermore, even for cases when we do seem to be able to use the distinction between predicate and subject to analyze judgable contents into their components, Frege thought the grammatical opposition of subject and predicate to be insufficient for capturing important logical distinctions that apply to the contents of sentences in a logically ideal language.
In particular, it does not appear to suffice for an analysis of the differences between singular, particular, and general propositions. Singular propositions, according to Frege, are those in which an object is subsumed or falls under a concept; this is what he regarded as the fundamental relation in logic to which all others can be reduced Nevertheless, for the purposes of understanding the structure and logical impact of general and existential propositions, Frege distinguishes two other structural relations within conceptual contents: First, that of subordination or bringing something under something else, which pertains between two concepts of the same logical order; and second, that of a concept's falling within a concept of higher order.
In a proposition like "All whales are mammals", for instance, the expression "all whales" again appears as grammatical subject, but "all whales" does not seem to denote a particular object, hence it cannot be construed as a proper name. Instead, what we actually mean is this: This indicates that what the sentence actually is about is a relation between two concepts, that of a whale and that of a mammal.
What the sentence says about these concepts is that whatever falls under the first also falls under the second; it thereby subordinates the first under the second concept However, the second concept is not a property of the first; being a mammal is not a property of the concept of being a whale but rather of the objects falling under that concept, just as being a whale itself is.
Hence, the two concepts are of the same logical order — they both apply to objects. This is different in statements that concern the existence of things of a certain kind. If one says "Mammals exist", or "Some mammals are elephants" then one is not talking about about any particular mammal or elephant but rather about the concepts of a mammal or an elephant; and what one means is that these concepts are satisfied in at least one case.
Frege, therefore, regards existence as a concept of the second order. A concept of the second order is one that applies to concepts of the first order; that is, a concept of the second order does not apply to objects but to concepts of the first order, and it is concepts of the first order, not concepts of the second order, that apply directly to objects.
By contrast, we could meaningfully say, "There is one man named 'Caesar;'" but in this case one is again ascribing existence to a concept; that is, one is ascribing existence to the concept of being named "Caesar".