This thesis studies Judea Pearl’s logic of counterfactuals derived from the causal modeling framework, in comparison to the influential Stanlnaker-Lewis counterfactual logics. My study focuses on a characteristic principle in Pearl’s logic, named reversibility. The principle, as Pearl pointed out, goes beyond Lewis’s logic. Indeed, it also goes beyond the stronger logic of Stanlnaker, which is more analogous to Pearl’s logic. The first result of this thesis is an extension of Stanlnaker’s logic incorporating reversibility. It will be observed that the (...) translation of reversibility from Pearl’s language to the standard language for conditional logic deserves some attention. In particular, a straightforward translation following Pearl’s suggestion would render reversibility incompatible with Stanlnaker’s logic. A new translation of reversibility will be proposed, and an extension of Stanlnaker’s logic with the inclusion of the translated reversibility will be investigated. More importantly, it will be shown that the extended Stanlnaker’s logic is sound and complete with respect to a modified Stanlnaker’s semantics. The extension of Stanlnaker’s logic has an interesting implication. Zhang, Lam, and de Clercq have shown that special case of reversibility, despite its name, actually states an important kind of irreversibility: counterfactual dependence between distinct events is irreversible. In other words, reversibility entails that there is no cycle of counterfactual dependence altogether generalizations of reversibility. However, as shown in Zhang et al., Pearls’ logic does not rule out cycles of counterfactual dependence altogether. It in fact allows cycles that involve three or more distinct events. This is peculiar because the status of cyclic counterfactual dependence seems no more metaphysically secure than that of mutual counterfactual dependence. This consideration leads to an exploration of logics that rule out all cycles of counterfactual dependence. A surprising result is that the extension of Stanlnaker’s logic is precisely a logic of this sort. (shrink)

This article focuses on defective conditionals ? namely indicative conditionals whose antecedents are false and whose truth-values therefore cannot be determined. The problem is to decide which formal connective can adequately represent this usage. Classical logic renders defective conditionals true whereas traditional mathematics dismisses them as irrelevant. This difference in treatment entails that, at the propositional level, classical logic validates some sentences that are intuitively false in plane geometry. With two proofs, I show that the same flaw is shared by (...) a family of trivalent logics. I go on to examine the strict conditional and its derivatives. This family is the only one to avoid the faulty inference but it does so without addressing the status of the truth-value assigned to defective conditionals. (shrink)

Previous research into the formalisation of statute law identified a number of uses of language which posed problems for formalisation. A previous paper argued that these uses establish the requirement that a formalisation be isomorphic, but noted that this has odd consequences. This paper expands on what these consequences are and argues that they undermine the very idea of formalisation. Therefore, the whole argument constitutes a reductio ad absurdum of the idea of formalising statute law. The paper provides reasons why (...) this activity is impossible and places the conclusion in the context of the development of modem logic, in which context it appears uncontroversial. (shrink)

The aim of this paper is to discuss a basic assumption tacitly shared by many philosophers of mind and language: that whatever can be meant, can be said. It specifically targets John Searle's account of this idea, focusing on his Principle of Expressibility . In the first part of the paper, PE is exposed underlining its analyticity and its relevance for the philosophy of language , mind , society and action . In the critical part, the notion of Background is (...) taken into account in order to re-evaluate two basic distinctions: the one between sentence and utterance meanings , and the one between native and type speakers . PE is reconsidered in the light of the previous arguments as a methodological strategy that does not prevent uses of language from eventual semantic excesses and deficits , and a complementary Principle of Expression Fallibility is finally proposed. (shrink)

Quine's argument for a naturalized epistemology is routinely perceived as an argument from despair: traditional epistemology must be abandoned because all attempts to deduce our scientific theories from sense experience have failed. In this paper, I will show that this picture is historically inaccurate and that Quine's argument against first philosophy is considerably stronger and subtler than the standard conception suggests. For Quine, the first philosopher's quest for foundations is inherently incoherent; the very idea of a self-sufficient sense datum language (...) is a mistake, there is no science-independent perspective from which to validate science. I will argue that a great deal of the confusion surrounding Quine's argument is prompted by certain phrases in his seminal ‘Epistemology Naturalized’. Scrutinizing Quine's work both before and after the latter paper provides a better key to understanding his remarkable views about the epistemological relation between theory and evidence. (shrink)

The text consists of two parts. Part one puts the works of Hans Blumenberg, as far as they tackle the problem of rhetoric, into their historical context. Relevant here in particular is the tradition of topological philosophies of the Renaissance and their different types of revival in the 20th century. Part two analyses three main ‘absolute metaphors’ or ‘topoi’ Hans Blumenberg has investigated, the metaphors of ‘light’, ‘shipwreck’, and ‘book of nature’, in order to add to the philosophical perspective taken (...) by Blumenberg a hidden philological perspective, which shows the shortcomings of conceptualizing rhetorical techne (how does a metaphor work), which does not always account for philological techne (how do we write texts). (shrink)

This paper is an exercise in intellectual history, an attempt to understand how a specific term—”informal logic”— came to be interpreted in so many different ways. I trace the emergence and development of “informal logic” to help explain the many different meanings, how they emerged and how they are related. This paper is also, to some degree, an account of a movement that developed outside the mainstream of philosophy, whose origins lie in a desire to make logic useful (echoing Dewey).

Quine's holistic empiricist account of scientific inquiry can be characterized by three constitutive principles: *noncontradiction*, *universal revisability* and *pragmatic ordering*. We show that these constitutive principles cannot be regarded as statements within a holistic empiricist's scientific theory of the world. This claim is a corollary of our refutation of Katz's [1998, 2002] argument that holistic empiricism suffers from what he calls the Revisability Paradox. According to Katz, Quine's empiricism is incoherent because its constitutive principles cannot themselves be rationally revised. Using (...) Gärdenfors and Makinson's logic of belief revision based on epistemic entrenchment, we argue that Katz wrongly assumes that the constitutive principles are *statements* within a holistic empiricist's theory of the world. Instead, we show that constitutive principles are best seen as *properties* of a holistic empiricist's theory of scientific inquiry and we submit that, without Katz's mistaken assumption, the paradox cannot be formulated. We argue that our perspective on the status of constitutive principles is perfectly in line with Quinean orthodoxy. In conclusion, we compare our findings with van Fraassen's [2002] argument that we should think of empiricism as a stance, rather than as a doctrine. (shrink)

We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, whereas (...) Hilbert dismisses elucidation and consequently treats the primitives as schematic. (shrink)

‘Quantified pure existentials’ are sentences (e.g., ‘Some things do not exist’) which meet these conditions: (i) the verb EXIST is contained in, and is, apart from quantificational BE, the only full (as against auxiliary) verb in the sentence; (ii) no (other) logical predicate features in the sentence; (iii) no name or other sub-sentential referring expression features in the sentence; (iv) the sentence contains a quantifier that is not an occurrence of EXIST. Colin McGinn and Rod Girle have alleged that standard (...) first-order logic cannot adequately deal with some such existentials. The article defends the view that it can. (shrink)

The main idea or the concept of coherence can be expressed in the following way: The more the statements belonging to a given theory approximate a perfect supportive structure, the more coherent the theory. The degree of perfection of a supportive structure depends on the degree to which the following criteria of coherence are fulfilled: (1) the greatest possible number of supported statements belonging to the theory in question; (2) the greatest possible length of chains of reasons belonging to it; (...) (3) the greatest possible number of strongly supported statements belonging to the theory; (4) the greatest possible number of connections between various supportive chains belonging to the theory; (5) the greatest possible number of preference relations between various principles belonging to it; (6) the greatest possible number and complexity of reciprocal supportive relations between various statements belonging to the theory; (7) the greatest possible number of universal statements belonging to the theory; the greatest possible number of general concepts belonging to it; the highest possible degree of generality of concepts implemented within it; the greatest possible number of resemblances between concepts used within it; (8) the greatest possible number of conceptual cross‐connections between various theories; (9) the greatest possible number of cases covered by the theory; and (10) the greatest possible number of fields of life covered by the theory. (shrink)

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected]. (shrink)

In "Metaphysics" Gamma 3 Aristotle declares that the philosopher investigates things that are qua things that are and that he therefore should be able to state the firmest principles of everything. The firmest principle of all is identified as the principle of non-contradiction (PNC). The main focus of Gamma 3 is Aristotle's proof for this identification. This paper begins with remarks about Aristotle's notion of the firmness of a principle and then offers an analysis of the firmness proof for PNC. (...) It focuses on some key assumptions of the proof and on the range and force of the proof. Aristotle closes Gamma 3 with the claim that PNC is ultimate in the sense that all other principles somehow rest on it. This, rather controversial, claim is given a defensible reading and shown to be central to the chapter's effort to establish PNC as the firmest principle of all. As such it completes the firmness proof and is not simply an appended remark. (shrink)

The relation between religious and scientific explanations of events and states of affairs has been the subject of much debate. For example, are the statements ‘John's life was saved by surgery’ ‘John's life was saved in answer to prayer’ in competition with each other and, if so, in what way? They do not seem to be rival causal explanations, nor are they straightforwardly contradictory. Yet each seems to cast doubt on the other, or at least to make it to some (...) extent redundant. (shrink)

§13 of Principia Ethica contains G. E. Moore’s most famous open question arguments. Several of Moore’s contemporaries defended various forms of metaethical nonnaturalism—a doctrine Moore himself endorsed—by appeal to OQAs. Some contemporary cognitivists embrace the force of Moore’s OQAs against metaethical naturalism. And those who posit noncognitivist meaning components of ethical terms have traditionally used OQAs to fuel their own emotivist, prescriptivist, and expressivist metaethical programs. Despite this influence, Moore’s OQAs have been ridiculed in recent decades. Their deployment has been (...) labeled “accident prone,” “simple to dismiss,” and just plain invalid. Critics accuse Moore of begging the question. Others argue that his OQAs founder upon the paradox of analysis. And still others argue that Moore’s open question argumentation is incompatible with the Kripke–Putnam causal theory of reference and thus it “simply fails; it is bankrupt”. I aim to show that there is something of continuing value in Moore’s open question efforts. I present and criticize Nicholas Sturgeon’s influential interpretation of Moore’s OQAs as a means to motivate and explicate my own interpretation of Moore’s thoughts in §13 of Principia Ethica. I then articulate the role that OQAs are intended to play in Moore’s overall argumentative strategies to undermine metaethical naturalism and thereby provide some theoretical support for metaethical nonnaturalism. Finally, I attend to the most prominent objections to Moore’s theorizing and attempt to evaluate the extent to which Moore’s efforts are successful. My hope is to display both the promising portions of Moore’s metaethical argumentation in Principia Ethica as well as its limitations. (shrink)

We use quotation marks when we wish to refer to an expression. We can and do so refer even when this expression is composed of characters that do not occur in our alphabet. That's why Tarski, Quine, and Geach's theories of quotation don't work. The proposals of Davidson, Frege, and C. Washington, however, do not provide a plausible account of quotation either. (Section I). The problem is to construct a Tarskian theory of truth for an object language that contains quotation (...) marks, without appealing to quotation marks in the metalanguage. I propose to supply Tarski's truth definition with one axiom that determines the denotation of all expressions containing quotation marks. According to this axiom, quotation marks create a non-extensional context. Since admitting such contexts does not lead to any difficulties in the recursive truth characterization, we may indeed dispense with extensionalism. (Section II). Finally, I argue that we classify and denote expressions in the very same way that we classify and denote extralinguistic entities. Both tokens and types of written signs can be easily incorporated into the naturalist's worldview. (Section III). (shrink)

Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...) instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory. (shrink)

Saul Kripke's thesis that ordinary proper names are rigid designators is supported by widely shared intuitions about the occurrence of names in ordinary modal contexts. By those intuitions names are scopeless with respect to the modal expressions. That is, sentences in a pair like (a) Aristotle might have been fond of dogs, (b) Concerning Aristotle, it is true that he might have been fond of dogs will have the same truth value. The same does not in general hold for definite (...) descriptions. If one, like Kripke, accounts for this difference by means of the intensions of the names and the descriptions, the conclusion is that names do not in general have the same intension as any normal, identifying description. However, this difference can be accounted for alternatively by appeal to the semantics of the modal expressions. On the account we suggest, dubbed 'relational modality', simple singular terms, like proper names, contribute to modal contexts simply by their actual world reference, not by their descriptive content. That account turns out to be fully equivalent with the rigidity account when it comes to truth of modal and non-modal sentence (with respect to the actual world), and hence supports the same basic intuitions. Here we present the relational modality account and compare it with others, in particular Kripke's own. (shrink)

Reanimated for the contemporary literature in the writings of Quine, [16]) and Kuhn [7], the conventionalism of Duhem [2] and Poincaré [12] has emerged in the last few years as one of the genuinely interesting topics in the philosophy of science. The theory in question—let us follow Grünbaum [3] in calling it the D-thesis, after its founder, Pierre Duhem—claims three things: a single scientific hypothesis H is never disconfirmable in isolation from its fellow; every single hypothesis H of science presupposes, (...) explicitly or implicitly, the support of a conjunction A = A, • A2 • … • Am of auxiliary assumptions or hypotheses; the failure of an observational consequence of H in face of contradictory evidence disconfirms only the conjunction of H and A, not H alone—i.e. establishes only ∼. The logical picture is as follows. (shrink)

By a logical theory I mean a formal system together with its semantics, meta-theory, and rules for translating ordinary language into its notation. Logical theories can be used descriptively (for example, to represent particular arguments or to depict the logical form of certain sentences). Here the logician uses the usual methods of empirical science to assess the correctness of his descriptions. However, the most important applications of logical theories are normative, and here, I argue, the epistemology is that of wide (...) reflective equilibrium. The result is that logic not only assesses our inferential practice but also changes it. I tie my discussion to Thagard's views concerning the relationship between psychology and logic, arguing against him that psychology has and should have only a peripheral role in normative (and most descriptive) applications of logic. (shrink)

In the predicate calculus, variables provide a flexible indexing service which selects the actual arguments to a predicate letter from among possible arguments that precede the predicate letter (in the parse of the formula). In the process of selection, the possible arguments can be permuted, repeated (used more than once), and skipped. If this service is withheld, so that arguments must be the immediately preceding ones, taken in the order in which they occur, the formula is said to be fluted. (...) Quine showed that if a fluted formula contains only homogeneous conjunction (conjoins only subformulas of equal arity), then the satisfiability of the formula is decidable. It remained an open question whether the satisfiability of a fluted formula without this restriction is decidable. This paper answers that question. (shrink)

The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.

I invoke the conceptual machinery of contemporary possible-world semantics to provide an account of the metaphysical status of "bridge laws" in intertheoretic reductions. I argue that although bridge laws are not definitions, and although they do not necessarily reflect attribute-identities, they are supervenient. I.e., they are true in all possible worlds in which the reducing theory is true.

The ontological question of what there is, from the perspective of common sense, is intricately bound to what can be perceived. The above observation, when combined with the fact that nouns within language can be divided between nouns that admit counting, such as ‘pen’ or ‘human’, and those that do not, such as ‘water’ or ‘gold’, provides the starting point for the following investigation into the foundations of our linguistic and conceptual phenomena. The purpose of this paper is to claim (...) that such phenomena are facilitated by, on the one hand, an intricate cognitive capacity, and on the other by the complex environment within which we live. We are, in a sense, cognitively equipped to perceive discrete instances of matter such as bodies of water. This equipment is related to, but also differs from, that devoted to the perception of objects such as this computer. Behind this difference in cognitive equipment underlies a rich ontology, the beginnings of which lies in the distinction between matter and objects. The following paper is an attempt to make explicit the relationship between matter and objects and also provide a window to our cognition of such entities. (shrink)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

The notion of similarity plays a central role in Quine's theory of Universals and it is with the help of this notion that Quine intends to define the concept of kind which also plays a central role in the theory. But as Quine has admitted, his attempts to define kinds in terms of similarities were unsuccessful and it is mainly because of this shortcoming that Quine's theory has been ignored by several philosophers. Nominalism and realism: Universals and Scientific realism. Cambridge: (...) Cambridge University Press). In the present paper, I propose an alternative framework that accounts for the phenomena that Quine intends to explain with his resemblance theory. The framework agrees with Quine's austere ontology; in particular, it does not assume the existence of properties and of possible worlds.. Resemblance nominalism: A solution to the problem of Universals. Oxford: Clarendon Press.) Moreover, the framework is extensionalist since the abstract entities it assumes are classes and these can be individuated extensionally, for classes are identical if their members are identical. Finally, I will refute some of the objections to Quine's approach that have been raised by Armstrong and Oliver [. The metaphysics of properties. Mind, 105, 1-80.] and I will argue that, contrary to what has been claimed by Oliver in a comment on Lewis [. On the plurality of worlds. Oxford: Blackwell.], Quine is able to specify an important set of sparse properties. (shrink)

This article examines the traditional and modern doctrines of categorical propositions and argues that both doctrines have serious problems. While the doctrines disagree about existential imports...

The Löwenheim-Hilbert-Bernays theorem states that, for an arithmetical first-order language L, if S is a satisfiable schema, then substitution of open sentences of L for the predicate letters of S...

McCall (1984) offered a semantics of counterfactual conditionals based on “real possible worlds” that avoids using the vague notion of similarity between possible worlds. I will propose an interpretation of McCall’s counterfactuals in a formal framework based on Baltag-Moss-Solecki events and protocols. Moreover, I will argue that using this interpretation one can avoid an objection raised by Otte (1987).

Quine’s argument for a naturalized epistemology is routinely perceived as an argument from despair: traditional epistemology must be abandoned because all attempts to deduce our scientific theories from sense experience have failed. In this paper, I will show that this picture is historically inaccurate and that Quine’s argument against first philosophy is considerably stronger and subtler than the standard conception suggests. For Quine, the first philosopher’s quest for foundations is inherently incoherent; the very idea of a self-sufficient sense datum language (...) is a mistake as there is no science-independent perspective from which to validate science. I will argue that a great deal of the confusion surrounding Quine’s argument is prompted by certain phrases in his seminal ‘Epistemology Naturalized’. Scrutinizing Quine’s work both before and after the latter paper provides a better key to understanding his remarkable views about the epistemological relation between theory and evidence. -/- . (shrink)

Compared to the extensive amount of literature on various themes of W.V.O. Quine’s philosophy, his immanent concept of truth remains a relatively unexplored topic. This relative lack of research contributes to a persistent confusion on the deflationary and inflationary details of Quine’s truth. According to a popular reading, Quine’s disquotational definition of the truth predicate exhausts the content of truth, thus amounting to a deflationary view. Others promote opposing interpretations. I argue that by relying on Tarski’s semantic conception of truth, (...) Quine’s disquotational account inherits a commitment to classical correspondence intuitions. Based on this, Quine posits a firm constitution for truth as an intermediary between language and the world. From this constitution claim follows that the disquotational account proves incompatible with both the general deflationary thesis and, more specifically, the minimalist account, which deny any constitution for truth past what is given by the preferred deflationary schema. This reading is significant for refuting the widespread misrepresentations of Quine as a prominent deflationist. (shrink)

An analogy is made between two rather different domains, namely: logic, and football. Starting from a comparative table between the two activities, an alternative explanation of logic is given in terms of players, ball, goal, and the like. Our main thesis is that, just as the task of logic is preserving truth from premises to the conclusion, footballers strive to keep the ball as far as possible until the opposite goal. Assuming this analogy may help think about logic in the (...) same way as in dialogical logic, but it should also present truth-values in an alternative sense of speech-acts occurring in a dialogue. The relativity of truth-values is focused by this way, thereby leading to an additional way of logical pluralism. (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us to (...) rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

Epistemic rationality seems to permit a more steadfast response to disagreements over our fundamental convictions than it does for our ordinary beliefs. Why is this? This essay explores three answers to this question: web-of-belief conservatism, moral encroachment, and hinge theories, and argues that hinge theories do a better job than the alternatives at vindicating the intuition that there is a rationally permissible asymmetry in our responses to disagreements over ordinary beliefs and fundamental convictions. The essay also shows how hinge theorists (...) can explain the existence of moral hinge propositions, which enables them to account for the rational permissibility of being steadfast in response to disagreements over fundamental moral convictions. (shrink)

First-order formalisations are often preferred to propositional ones because they are thought to underwrite the validity of more arguments. We compare and contrast the ability of some well-known logics—these two in particular—to formally capture valid and invalid arguments. We show that there is a precise and important sense in which first-order logic does not improve on propositional logic in this respect. We also prove some generalisations and related results of philosophical interest. The rest of the article investigates the results’ philosophical (...) significance. A first moral is that the correct way to state the oft-cited superiority of first-order logic vis-`a-vis propositional logic is more nuanced than often thought. The second moral concerns semantic theory; the third logic’s use as a tool for discovery. A fourth and final moral is that second-order logic’s transcendence of first-order logic is greater than first-order logic’s transcendence of propositional logic. (shrink)

Geach's account of the Aristotelian logic of categorical sentences supplemented the views shared by Frege, Russell, Quine and others. I argue that this particular predicate logic approach and Geach's points apply to only one variety of natural language categorical sentences. For example, it takes the universal categorical as a universal conditional “If anything is a man, then it is mortal”. A different natural language form can and should be invoked: “Every man is a mortal.” Employing special restricted quantifiers in a (...) version of predicate logic, we justify a full square of opposition and the rules of quality and quantity that Geach rejected. (shrink)