Background Frege PHIL 2060 Wittgenstein Recap Logical Atomism

Background: Frege PHIL 2060 Wittgenstein

Recap: Logical Atomism

Russell’s Logical Atomism: Central Tenets • The world is real: it has nonmind dependent aspects • The world is complex and it is constituted of simple parts: the logical atoms • Anything that can’t be analyzed is a logical atom: for example, redness

Russell’s Logical Atomism: Linguistic Turn • There is a correspondence between how our language represents the world and how the world is • The world is made out of particulars and universals & relations going together in facts • These are represented by proper names, predicates, and sentences, respectively

Russell’s Logical Atomism: Goal Develop a logically perfect language where every logical atom has exactly one representation and every complex entity (fact) is analyzed into its simple parts.

Russell’s Logical Atomism: Big Picture Russell thought the only particulars we could properly name were sense data and universals. Thus atomism will analyze all other facts (about other “things”) into complex propositions about sense data and universals (“this red patch here, ” etc. ).

Logical Atomism: Conclusion

The New Empiricism Hume was also a British empiricist engaged in a project of analysis. For Hume, the objects of analysis were complex ideas which were analyzed into simple ideas. In his empiricism, Russell replaces ideas with propositions. The project becomes logical rather than psychological.

Russell’s Private Language According to Russell, you are not acquainted with ordinary objects like tables and chairs, rather you know them “by description. ” That is a particular table will not be given a proper name in theory, but a definition in terms of other logical atoms.

The Demise of Analysis “A tiger is a large carnivorous quadrupedal feline, tawny yellow in color with blackish transverse stripes and white belly. ”

Naming the New Philosophy • Analytic • Anglo-Austrian • Anglophone • ? ? ?

Frege & Analytic Philosophy

Gottlob Frege (1848 -1925) • German mathematician, logician, and philosopher • Descendant of one of the founders of Lutheranism, Philipp Melanchthon • Instructor at various levels (sometimes paid, sometimes not) at University of Jena • Dissertation on Geometry

Frege: Work & Reception • Published his Begriffschrift (1879) • “[T]he book was not well-reviewed by Frege's contemporaries, who apparently found its two-dimensional logical notation difficult to comprehend, and failed to see its advantages over previous approaches, such as that of Boole. ” [IEP]

Frege: Work & Reception • Tried to publish a more popular outline of his project (1884): Die Grundlagen der Arithmetik (“The Foundations of Arithmetic”) • “However, this work seems to have been virtually ignored by most of Frege's contemporaries. ” [IEP]

Frege: Work & Reception • Self-published (1893): Grundgesetze der Arithmetik ("Basic Laws of Arithmetic"), volume I. • “Again, however, Frege's work was unfavorably reviewed by his contemporaries. ” [IEP]

Frege: Work & Reception After the first volume of the Grundgesetze was published, during the printing of the second, Frege received a letter from Russell that left him “thunderstruck”: it showed a contradiction in his system (Russell’s paradox) that would lead him to give up.

The Analytic Triangle

Frege: Logicism: (Some of) mathematics was logical in nature: the mathematical truths were consequences of the logical ones, with no extra assumptions. Frege: logicist about arithmetic Russell: logicist about all math

Immanuel Kant (1724 -1804) • German philosopher • Idealist (!!!) • Thought that mathematics was synthetic a priori.

Synthetic A Priori An analytic (!!!) truth is one that is “true in virtue of meaning” or, for Kant….

Synthetic A Priori “In all judgments in which the relation of a subject to the predicate is thought… this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case, I call the judgment analytic, in the second synthetic. ” [Critique of Pure Reason]

Synthetic A Priori Examples: • All bachelors are unmarried. • Pork is the meat of pigs. • Sows are female pigs. Etc. An synthetic truth is one that is not analytic.

A Priori vs. A Posteriori “A priori” and “a posteriori” are epistemological categories having to do with how it’s possible to know something. A priori: can be known without experience A posteriori: not a priori

Synthetic A Priori Kant thought that certain truths were synthetic (not just true from meaning) but also a priori, knowable independent of experience. This included things like: • Everything has a cause. • 5 + 7 = 12

Frege-Analyticity There is something a little wrong with Kant’s notion of “analytic”. Consider: • Sows are pigs OR snow is green.

Frege: Logicism Frege’s proposed replacement: something is analytic if it follows from logic + definitions. Hence Frege’s logicist project: derive all of arithmetic from logic + definitions.

Frege: Philosophy of Language

The Unity Problems Unity of the fact: how does the pen go together with redness to make a red pen? Unity of the proposition: how does the pen go together with redness IN THOUGHT to make a red pen?

Concept and Object For Frege, the pen is an “object” and there is an essentially predicative “concept” of redness that the pen “falls under. ”

Concept and Object An object for Frege was like a particular from Russell’s theory: 2, 27, -53. 4, etc. Frege had two additional objects “The True” and “The False. ”

Concept and Object A concept was not an object but instead a function of a special type: e t

Concept and Object There are other types of functions beyond concepts: e e (e t) t

Draw on the Board Time

Frege: Comparison Quotes

Frege on Analysis “One cannot require that everything be defined, any more than one can require that a chemist decompose every substance. What is simple cannot be decomposed, and what is logically simple cannot have a proper definition… On the introduction of a name for something logically simple, a definition is not possible. ”

Frege on Correspondence “[I say that] the singular definite article always indicates an object, whereas the indefinite article accompanies a concept word. Kerry holds that no logical rules can be based on linguistic distinctions; …”

Frege on Correspondence “[B]ut my own way of doing this is something that nobody can avoid who lays down such rules at all, for we cannot understand one another without language, and so in the end we must always rely on other people's understanding words, inflexions, and sentence-construction in essentially the same way as ourselves… It is here very much to my advantage that there is such good accord between the linguistic distinction and the real one. ”

Frege on Correspondence “[A] concept is the Bedeutung of a predicate; an object is something that can never be the whole Bedeutung of a predicate, but can be the Bedeutung of a subject. ”

Study Questions

Easy Ones! 1. What did you have most trouble understanding in the reading? 2. Describe a parallel between Wittgenstein and Russell’s views. 3. What part of the reading did you find really agreeable (or disagreeable)? Why?