This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski's theory of truth. Philosophers do not agree on how Tarski's theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science.In this paper I argue that Tarski's chief concern was the following question. Suppose a (...) language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? (shrink)

Widespread deflationistic readings of Quine misrepresent his view of disquotation’s significance and the truth predicate’s utility. I demonstrate this by answering a question that philosophers have not directly addressed: how does Quine understand the philosophical problem of truth? A primary thesis of this paper is that we can answer this question only by working from within Quine’s naturalistic framework. Drawing on neglected texts from Quine's corpus, I defend the view that, for Quine, the problem of truth emerges from the development (...) of science, in particular, from logical theorizing. I show that disquotation itself, from this Quinean point of view, is the problematic phenomenon calling for philosophical reflection. I conclude by arguing that Quine does not envisage the kind of explanatory role for disquotation taken up by contemporary deflationists, and he shows no interest in the task that animates deflationism, namely, to show that concerns with truth’s nature are fundamentally confused. (shrink)

In the paper the problem of definability and undefinability of the concept of satisfaction and truth is considered. Connections between satisfaction and truth on the one hand and consistency of certain systems of omega-logic and transfinite induction on the other are indicated.

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints (...) of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)

Minimalism is currently the received deflationary theory of truth. On minimalism, truth is a transparent concept and a deflated property of truth bearers. In this paper, I situate minimalism within current deflationary debate about truth by contrasting it with its main alternative―the redundancy theory of truth. I also outline three of the primary challenges facing minimalism, its formulation, explanatory adequacy and stability, and draw some lessons for the soundness of its conception of truth.

From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...) in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (shrink)

Tarski’s pioneering work on truth has been thought by some to motivate a robust, correspondence-style theory of truth, and by others to motivate a deflationary attitude toward truth. I argue that Tarski’s work suggests neither; if it motivates any contemporary theory of truth, it motivates conceptual primitivism, the view that truth is a fundamental, indefinable concept. After outlining conceptual primitivism and Tarski’s theory of truth, I show how the two approaches to truth share much in common. While Tarski does not (...) explicitly accept primitivism, the view is open to him, and fits better with his formal work on truth than do correspondence or deflationary theories. Primitivists, in turn, may rely on Tarski’s insights in motivating their own perspective on truth. I conclude by showing how viewing Tarski through the primitivist lens provides a fresh response to some familiar charges from Putnam and Etchemendy. (shrink)

Tarski's analysis of the concept of truth gives rise to a hierarchy of languages. Does this fragment the concept all the way to philosophical unacceptability? I argue it doesn't, drawing on a modification of Kaplan's theory of indexicals.

Anselm's argument for the existence of God in Proslogion Chap.II starts from the contention that `lq when a Fool hears `something-than-which-nothing-greater-can-be-thought', he understands what he hears, and what he understands is in his mind. This is a special feature of the Pros.II argument which distinguishes the argument from other ontological arguments set up by, for example, Descartes and Leibniz. This is also the context which makes semantics necessary for evaluation of the argument. It is quite natural to ask `lq What (...) is understood by the Fool, and what is in his mind? It is essential for a proper consideration of the argument to identify the object which is understood by the Fool, and so, is in his mind. A semantics gives answers to the questions of `lq What the Fool understands? and `lq What is in the Fool's mind? If we choose a semantics as a meta-theory to interpret the Pros.II argument, it makes an effective guide to identify the object. It is a necessary condition for a proper evaluation of the Pros.II argument to fix our universe of discourse, especially since, in the argument, we are involved in such talk about existing objects as Anselm's contention that `when a Fool hears `something-than-which-nothing-greater-can-be-thought', he understands what he hears, and what he understands is in his mind. The ontology to which a semantic theory commits us will be accepted as our scope of objects when we introduce our semantic theory to interpret the Pros.II argument, and this ontological boundary constrains us to identify the object in a certain way. Consistent application of an ontology, most of all, is needed for the evaluation of the logical validity of an argument. If we take Frege's three-level semantics, we are ontologically committed to intensional entities, like meaning, as well as extensional entities. Sluga contends that Frege's anti-psychologism for meanings should not be interpreted as vindicating reification of intensional entities in relation to Frege's contextualism, that Frege's anti-psychologism with his contextualism is nothing but a linguistic version of Kantian philosophy for the transcendental unity of a judgement. There is, however, another possible interpretation of Frege's contextualism. According to Dummett, the significance of Frege's contextualism must be understood as a way of explanation for a word's having meaning. If Dummett's view is cogent, we could say that Frege's contextualism does not prevent our interpreting his semantics as being committed to intensional entities. We need not worry that Frege's over all semantics, especially with his contextualism, would internally deny the ontological interpretation of his theory. We see Anselm's argument for the existence of God in Pros.II is an invalid argument if we introduce Frege's three-level semantics, i.e. if we acknowledge meanings of words as entities in our universe of discourse. We can also employ extensional semantics for the interpretation of the Pros.II argument. According to extensionalists, like Quine and Kripke, we need not assume intensional entities, like meaning, to be part of our ontological domain. They argue that we can employ our language well enough without assuming intensional entities. If we choose extensional semantics as a meta-theory to interpret the Pros.II argument, it commits us only to extensional entities as objects in the Universe of our interpretation. In Sections 1.4 and 1.5, I show that extensional semantics makes the Pros.II argument a valid argument for the existence of God. `lq Necessary existence is the central concept of Anselm's argument for the existence of God in Proslogion Chap.III. It has been said that, even if the argument is formally valid, it cannot stand as a valid argument for the existence of God, since `lq necessary existence is an absurd concept like `lq round square. And further that even if there is a meaningful combination of concepts for `lq necessary existence, it cannot quality as a subject of an a priori argument. As objections to the interpretations which make the Pros.III argument valid, it has been argued that even if there is a concept of `lq necessary existence which is meaningful and there is another concept of `lq necessary existence which is suitable as a subject of an a priori argument, there is no concept of `lq necessary existence which is meaningful and at the same time suitable as a subject of an a priori argument. In Chap.2 and Chap.3, I try to show that there can be concepts of `lq necessary existence which are proof against these objections. Anselm's arguments for the existence of God in Proslogian Chap.II and Chap.III are logically valid arguments on some logical principles. Some fideists, K. Barth, for example, argue that Anselm's arguments for the existence of God in Proslogion are not proofs for the existence of God even if they are logically valid arguments. I raise the question how this attitude could be possible, in Chap.4 and Chap.5. Barth's fideistic interpretation of Anselm's Proslogion arguments does not find any flaw in the validity of the arguments, and it accepts the meaningfulness and truth of the premises even to the fool in Proslogion. If this is the case, i.e. if Barth's interpretation accepts the validity of the arguments and the truth of the premises, I raise the question, how can the arguments not be interpreted as proofs for the existence of God? How is it possible that the function of the arguments is not that of proving the existence of God? According to Wittgensteinian fideism, premises in the arguments should not be intelligible to those who do not believe in God's existence already, and so the real function of the arguments is the elucidation, the understanding of believer's belief, rather than proving articles of belief to unbelievers. Barth's fideistic interpretation of the arguments, however, fully recognizes the meaningfulness and truth of the premises in the arguments as well as the validity of the arguments. I argue that there could be a justification for the Barthian fideism. As Malcolm notices, there are still atheists who understand Anselm's arguments as valid, but the only possibility for the people who recognize the validity of Anselm's arguments still to remain atheists has been thought to be to challenge the truth of premises employed in the arguments. Now, of the atheistic possibility, we can change the direction of our attention, that is, to the question about the function of a logically valid argument itself. What has not been thought of in relation to Anselm's arguments is the significance of logical truth or the logical validity of an argument. We have not asked such questions as `lq What does a logical truth say? and `lq What does a logically valid argument guarantee with true premises? Let us assume that even the premises are accepted by atheists. Do they all convert to theism? If that were so, the disagreement between atheist and believer over the ontological arguments should turn only on the truth of premises. If that is not so, there is some point in raising this other question. If there are people who, recognizing the premises and validity of an argument, are still reluctant to accept the conclusion, we have reason to question the function of a valid argument. I argue that there is a way of being consistently reasonable while accepting the premises and the validity of the ontological arguments and yet remaining an atheist or an agnostic. (shrink)