Definite Descriptions and the Gettier Example

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in his pocket shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it eithe

Propositions and Paradoxes.

Propositions are more than the bearers of truth and the meanings of sentences: they are also the objects of an array of attitudes including belief, desire, hope, and fear. This variety of roles leads to a variety of paradoxes, most of which have been sorely neglected. Arguing that existing work on these paradoxes is either too heavy-handed or too specific in its focus to be fully satisfactory, I develop a basic intensional logic and pursue and compare three strategies for addressing the paradoxes, one employing truth-value gaps, one restricting propositional quantification, and one restricting our ability to have attitudes like belief and desire. This results in four distinct resolutions of the paradoxes, all but one of which are novel and all of which receive novel and general implementations. While resolving the paradoxes is of course the ultimate goal, I do not here argue that any one of the resolutions is superior. These paradoxes have been so little studied that my primary goal is only to identify the most fundamental costs and benefits of the various approaches one can take to addressing them. Each resolution I develop has significant drawbacks, which I argue highlight tensions between the different roles propositions play. Past researchers have skirted these tensions, and the issues raised by these paradoxes more generally, by focusing on non-propositional paradoxes, such as the most familiar forms of the Liar paradox. At the least, then, I hope this dissertation establishes that the propositional paradoxes deserve attention not only because of their consequences for intensional logic, but also because of their consequences for our understanding of content, truth, quantification, and a host of mental attitudes.Ph.D.PhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89611/1/dtuck_1.pd

The Logic of Principia Mathematica

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1995.Includes bibliographical references (p. 181-184).by Darryl Jung.Ph.D

Ins and outs of Russell's theory of types

The thesis examines A.N. Whitehead and B. Russell’s Ramified Theory of Types (RTT). It consists of three parts. The first part is devoted to understanding the source of impredicativity implicit in the induction principle. The question I raise here is whether second-order explicit definitions are responsible for cases when impredicativity turns pathological. The second part considers the interplay between the vicious-circle principle and the no-class theory. The main goal is to give an explanation for the predicative restrictions entailed by the vicious-circle principle. The explanation is that set-existence is parasitic upon prior predicative specifications. The justification for this claim is given by employing the method of hierarchy of languages. Supposing the natural number structure and the language of Peano Arithmetic (PA) as given, I describe the construction of a set-theoretic language equipped with substitutionally interpreted quantifiers ranging over arithmetically definable sets. The third part considers the proposition-theoretic version of Russell’s antinomy. A solution to this paradox is offered on the basis of the ramified hierarchy propositions

Freedom as the basis of truth and reality in Russell's positivism and Stace's mysticism

Thesis (Ph.D.)--Boston UniversityPurpose. The central purpose of the dissertation is to localize the ultimate grounds of philosophic (and particularly metaphysical) differences, with the goal of achieving an eventual synthesis. To do this, the dissertation (1) analyzes the nature of metaphysical systems in general, (2) seeks a perspective (termed a meta-metaphysics) from which any metaphysical system can be derived, and (3) proposes to combine phenomenological and non-phenomenological methodologies. Method. First, the dissertation reviews representative attempts of philosophic synthesis. Those dealing with the general problem of synthesis, without specifying any particular one, are by Schiller, Montague, and Pepper. One specific attempt discussed consists of several syntheses of the existentialist and linguistic-analytic methods. Second, the dissertation presents an extended analysis of two antithetical philosophies: Russell's positivism and Stace's mysticism. By discovering the fundamental assumptions in each of these two conceptions of truth and reality and the values embodied and preserved by them, a comparison can be made with the view to finding the precise area of differences and agreements. Results. Russell is shown to hold that an acceptable definition prescribes and describes. He rejects coherence and warranted assertibility theories of truth, and defines truth as "logical, not epistemological, correspondence." The fundamental assumption in Russell's correspondence definition of truth is the postulation of qualitative metaphysical dualism, while the values embodied in his conception of definition and of truth are those found in the belief in the existence of an external world, including, of course, the existence of other minds. Russell, at times, conceives of reality as a "construction" (a notion first developed in his logic) of sensory perspectives, and at times as an inference from data. Fourteen assumptions are involved in the conceptions of reality. Among them we find "the universe is knowable through reason," "the given is a clue to a reality beyond," "the transcendent (in Kant's sense) use of the laws of inference is valid," and "the simple is more likely to correspond with events beyond sensations than the complex." Stace's position on mysticism is first examined as an interpretation of the mystical experience, and then as a theory of reality. The mystical experience may be characterized as either an experience of value, truth, or reality In mysticism as a theory of reality, value, truth, and reality each has a special ontological status. To understand mysticism is to know the interrelations of these terms. Since "assumption" is a logical term and mysticism is alogical, the phenomenological analysis of the mystical experience involves "priorities" (genetic, logical, phenomenological, axiological) in addition to assumptions. Among the twelve assumptions we find "naturalism and mysticism are two orders of one reality," "the mystic can legitimately choose his own meaning criterion," "extra-logical cognition is possible," "reality itself is extra-logical," and "subject-object bifurcations are not necessary." Conclusions. The ultimate ground for accepting these assumptions, priorities, and values is the possibility of choosing them freely, spontaneously, and autonomously. Russell must justify the possibility of correspondence (truth) and his metaphysical dualism (reality) on the grounds that they embody values which he has, in fact, freely chosen to accept. Stace's assumptions and priorities are likewise true and real because the values they embody are freely chosen. The dissertation constructs a meta-metaphysics that discloses positivism and mysticism (and any other empirically coherent metaphysics) as equality adequate world-views, differing only in the free commitment (Urentschluss) to these grounding assumptions and values. The exposition of this meta-metaphysics is the detailed description of its fundamental categories (the given, freedom, value, the logical and empirical refractory, and organizations of this given). Each of the above assumptions, priorities, and values is then interpreted in terms of this meta-metaphysics

Leibniz and the rationality of the infinite

Part 1 Historically the term 'infinite' has had two apparently contrary meanings. On the one hand, it was taken by metaphysicians like Plotinus to mean that which " ... has never known measure and stands outside number, and so is under no limit either in regard to anything external or internal ... " (Branford 1949, V.5.11). 'Infinite' in this sense means 'irrevocably complete'. On the other hand, Aristotle defined it in this way: "A quantity is infinite if it is such that we can always take a part outside what has already been taken." (Hardie and Gaye 1941, 207a, 5-10) 'Infinite', in this second sense means, 'irrevocably incomplete'. Leibniz is someone who uses both these meanings. In particular, he identifies the irrevocably complete with God and the irrevocably incomplete with the world (as we know it). Given, firstly, that what is irrevocably complete includes everything and, secondly, that it excludes anything incomplete, the following conclusion can be drawn: Leibniz's philosophy of the infinite makes of the-world-as-we-know-it something that is logically dependent on God, but also something that exists in contradiction to 'him'. Leibniz cannot escape a kind of contradiction in what he says about God and the world but this is not a straightforward case of self-refutation. The reason turns on the consideration that to divorce the concept of the irrevocably complete from its object is to deprive this concept of its sense, specifically of its sense of completeness. For if the two are distinct, then there is something beyond the irrevocably complete, namely, how this is independently of its concept. It follows that to deny the irrevocably complete is, in the same breath, to affirm that very thing. Yet if we cannot quite deny the irrevocable complete, neither can we as human beings quite affirm it either-for the human mind is, we do not doubt, a limited one. Thus the irrevocably complete can neither be affirmed nor denied without contradiction. There is a strong resemblance between this paradox and the paradox of the liar: in both cases there is a thesis that says of itself that it is untrue and, in both cases, thesis and antithesis tum out to be equivalent. Part 2 Kant offers some powerful reasons to think that the paradox discussed in Part 1 involves no real contradiction. The critical philosophy suggests that the apparent contradiction is real, only if, per impossibile, we have some way to positively employ the concept of the world as it is independently of our conceptions of it. Kant's view of the infinite shares with Leibniz's the vice (if it is one) that it is paradoxical: both philosophers make use of a concept that cannot, strictly speaking, be possessed by the human mind. However each view has the significant virtue that it shows the difference between the irrevocably complete and the irrevocably incomplete to be not simply a logical difference. My overall conclusion is based on a synthesis of the Leibnizian and the Kantian philosophies of the infinite. According to Leibniz, neither the irrevocably complete, nor the irrevocably incomplete, can be eliminated from philosophy. According to Kant, infinity is-from a human perspective at least-something prior to conception; putting Leibniz and Kant together, I conclude that these modes of infinity combine to produce finitude, that they are the joint conditions under which difference, and therefore finitude, is possible. In particular, I argue that the irrevocably complete is the infinity of fullness, and that the irrevocably incomplete is the infinity of emptiness, and that logic is blind to any difference there might be between these, since both are, by definition, undifferentiated. Given that ethics, as well as logic, is dependent on finitude, I conclude, finally, that the perennial ambition to eliminate either the irrevocably complete or the irrevocably incomplete from philosophy is, not merely unrealisable, but potentially dangerous

The cybernetics of language

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.As a complement to the philosophy of language, the cybernetics of language-is to synthesise a picture of language as a whole; and runs into-(descriptive) difficulties where (at any one time) we can only speak about bounded portions of the world (Wittgenstein). This same difficulty permeates the short history of cybernetics in the concern for wholistic representation, and thus the concern of the cybernetics of language leads to (or arises in) the concern for the language of cybernetics. It becomes resolvable in the context of Second order cybernetics (i.e. the cybernetics of' describing as well as described systems (von Foerster)). The difficulty and the possibility of its resolution are introduced in terms of differences between Russell and Wittgenstein; in terms of the second order cybernetic discussions of the black box (seen as capturing Wittgenstein's silence and, in general, interpretation) and distinctions (G. S. Brown); and in terms of the distinction between natural and artificial languages and the problem of describing description (self-reference). Here the cybernetics of language concerns the nature of inquiry into our descriptive abilities and activities, and determines what we can and what we cannot (objectively) speak about. The notions of 'the function of language' and 'the existence of language' (presupposed in a first order description) are shown to be mutually interdependent, giving rise to a paradox of means (and giving rise to the question of the 'origin of language'). This paradox is resolved where a language is seen as constructed (for a particular purpose), and thus the circularity is unfolded, considering that (i) in terms of a constructive function of language, there is no language (something is in the process of being constructed); (ii) in terms of a communicative function of language, such a construction is in the process of being accepted (something is being negotiated); (iii) in terms of an argumentative-function of language, a language (accepted, eg. having, been negotiated) is used to negotiate things distinct from-this language. Language is seen as comprising the interaction between these activities. The cybernetics of language is developed in terms of the requirements for an observer to construct, communicate and argue: a language is constructed for the description of these processes in terms of the; complementarity between description and interpretation (underlying the process of construction) and the complementarity between saying and doing (enabling an observer to explore, eg. question, test and explain his construction and distinguish another observer; and enabling two or more observers to negotiate and accept relations and argue by distinguishing both a language and the things this is used to describe)

The essential nature of trueness

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