Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic differences between (...) nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)

Aristotle classifies opposition (ἀντικεῖσθαι) into four groups: relatives (τὰ πρός τι), contraries (τὰ ἐναντία), privation and possession (στρέσις καὶ ἓξις) and affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) His example of relatives are the double and the half. Aristotle’s description of relatives as a kind of opposition is as such: ‘Things opposed as relatives are called just what they are, of their opposites (αὐτὰ ἃπερ ἐστι τῶν ἀντικειμένων λέγεται) or in some other way in relation to them. (...) For example, the double is called just what it is double of the other (οἷον τὸ διπλάσιον, αὐτὸ ὃπερ ἐστίν, ἑτέρου διπλάσιον λέγεται). Again, knowledge and the knowable are opposed as relatives, and knowledge is called just what it is, of the knowable, and the knowable too is called just what it is, in relation to its opposite, knowledge; for the knowable is called knowable by something-by knowledge.’ (Cat., 10, 11b24-30) 2) Senses of relatives In Met., Δ, 1020b26-32 Aristotle distinguishes three senses of relatives: i) That which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded. E.g. double to half ii) The active to the passive; e.g. that which can heat to that which can be heated iii) The measurable to the measure, e.g. the knowable to knowledge and the perceptible to perception. 3) Relatives and contraries Aristotle’s discussion of relatives is unbelievably ambiguous. While he enumerates relatives besides contraries, privation-possession and affirmation-negation as four types of opposition (Cat., 10, 11b15-23), not only does not he restrict relatives to oppositions but he also does not totally differentiate it from contraries. Aristotle distinguishes between two senses of relatives one of which is contraries: ‘We have distinguished elsewhere the two senses in which relatives are so called-some as contraries (ὡς ἐναντία), others as knowledge to things known, a term being called relative because what is said one to the other is said by the other to itself (τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό). (Met., I, 1056b34-1057a1) It seems that this differentiation is the same as, and maybe the one he himself refers to, the differentiation between the second and the third senses of relatives in Met., Δ, 1021a27-32: ‘Relative terms which imply number or capacity, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else is related to it (πρός τι πὰντα ἐστὶ πρός τι τῷ ὃπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὃ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεινο); but that which is measurable or knowable or thinkable is called relative because something else is related to it. For the thinkable implies that there is thought of it, but the thought is not relative to that of which it is the thought; for we should then have said the same thing twice.’ Although Aristotle confirms contrariety in relatives (e.g. virtue to vice and knowledge to ignorance), he denies that there is a contrary ‘to every relative’ as there can be no contrary to what is double or treble. (Cat., 7, 6b15-19) The fact that Aristotle dedicates one sense of relatives to contraries means that the fourfold division of oppositions is not such a strict division without any kind of community between them. In his example of the first sense, however, Aristotle says: ‘One and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed.’ (Met., I, 1057a4-6) Now, the question is: Is Aristotle’s first sense of relative a contrary or not? Aristotle tells us that the opposition in this sense of relatives is the opposition of measure and measurable. The second sense has two differences with the first one: i) it is not a contrary and ii) what is said by one of the relatives to the other is also said by the latter to the former. To differentiate it from the first sense, when the one is the measure of the other, the latter will be the measure of the former as well: ‘But though knowledge is similarly spoken of as related to the knowable, the relation does not work out similarly for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact is that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.’ (Met., I, 1057a7-12) Aristotle’s assertion at Met., I, 1057a36-37 that ‘of relative terms, those which are not contrary have no intermediate’ ensures us that we must take the first sense as contraries. Here he mentions a criterion of differentiation between two senses: while the first sense accepts intermediates (as, for example, great and small do), the second one does not. (Met., I, 1057a37-b1) It seems, however, that it is only the second sense that is the essential sense of relatives because the first sense, Aristotle says, is an accidental sense: ‘The one is opposed then to the many in numbers as measure to things measureable; and these are opposed as relatives which are not from their very nature relatives.’ (Met., I, 1056b32-34) 4) Definition of relative Aristotle’s first definition of the category of relative (πρός τι) is as such: ‘We call relative all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else (Πρός τι δὲ τὰ τοιαῦτα λέγεται, ὃσα αὐτὰ ἃπερ ἐστὶν ἓτερων εἶναι λέγεται, ἢ ὁπωσοῦν ἄλλως πρὸς ἓτερον). (Cat., 7, 6a36-37; repeated almost without any change in: Cat., 7, 6b6-8) Aristotle’s examples are larger (because it is what it is than something else (τοῦθ᾿ ὃπερ ἐστὶν ἑτέρου λέγεται) that means it is called larger than something) and double. (Cat., 7, 6a37-b1) Aristotle’s aporia regarding relative is about their relation with substances: whether no substance is spoken of as a relative, or whether this is possible with regard to some secondary substances. (Cat., 7, 8a13-15) In the case of primary substances, it seems that he is confident, at least at first, that neither themselves nor their parts are spoken of in relation to anything: neither an individual man is called someone’s individual man nor an individual hand is called someone’s individual hand (but someone’s hand). (Cat., 7, 8a15-21) Although it is obvious that most of secondary substances are not spoken of as relatives (a man is not called someone’s man) (Cat., 7, 8a21-25), there are some with them there is room for dispute: a head is someone’s head and a hand is called someone’s hand, which seem to be relatives. (Cat., 7, 8a25-28) Aristotle thinks this must be due to the previous definition’s being problematic: with that definition ‘it is either exceedingly difficult or impossible to reach the solution that no substance is spoken of as a relative.’ (Cat., 7, 8a28-32) Thus, Aristotle changes his previous definition to a new one: ‘Those things are relatives for which being is the same as being somehow related to something’ (ἔστι τὰ πρός τι οἷς τὸ εἶναι ταὐτόν ἐστι τῷ πρός τί). (Cat., 7, 8a32-34) Although the first definition does indeed apply to all relations, its problem is that it does not take ‘their own being relative’ (τῷ πρός τι αὐτοῖς εἶναι) the same as ‘their being what they are of other things’ (ἃπερ ἐστὶν ἑτέρων λέγεσθαι). (Cat., 7, 8a34-37) Although this change of definition is to exclude all substances from being relative, what Aristotle says in Topics (To., Z, 8, 146a39- ), seems to ignore this: ‘For of everything relative the substance is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something.’ 5) Necessary knowledge of the related Knowledge of that in relation to which a relative is spoken of is necessary when one knows the relative: it is impossible to know a relative and at the same time not to know that in relation to which it is spoken of. (Cat., 7, 8a37-b3) To prove this, Aristotle adheres to the definition of relatives: ‘If someone knows of a certain ‘this’ that it is a relative, and being for relatives is the same as being somehow related to something, he knows that also to which this is somehow related.’ (Cat., 7, 8a37-b3; cf. 7, 8b3-15 for Aristotle’s examples) This necessary knowledge of the related, if we call it so, dedicates Aristotle an epistemological reason, besides the ontological one mentioned in his definition, for the exclusion of substances. As we noted in our discussion of Aristotle’s definition of relatives, he changed his first definition to exclude all substances from being relatives. Therefore, it is evident that for him relatives must not include substances, either primary or secondary. Aristotle does have no problem with primary substances simply because it is evident for him that they cannot be relatives. The same can be said about most of the secondary substances as well. The problem for which he changed the definition of substances was about some secondary substances like ‘head’ or ‘hand’: the fact that it is possible to know a hand or head without necessarily knowing definitely that in relation to which it is spoken of proves that they are not relatives. (Cat., 7, 8b15-21) 6) Reciprocation Aristotle regards reciprocation (ἀντιστρέφειν) necessary in all relations: ‘All relatives are spoken of in relation to correlatives that reciprocate.’ (Cat., 7, 6b28-29; cf. Cat., 10, 12b21-24) The sense of reciprocation is clear by his own examples: ‘The slave is called slave of a master and the master is called master of a slave; the double double of a half, and the half half of a double.’ (Cat., 7, 6b29-31) Reciprocation of relatives is so necessary that if there seems that we do not have reciprocation, it must necessarily be due to a mistake and that in relation to which something is spoken of must have not been given properly. (Cat., 7, 6b36-7a1) Aristotle’s example is this: If a wing is given as of a bird, ‘bird of a wing’ does not reciprocate because it has not been given properly: a wing is of a winged and not of a bird; a wing is wing of a winged and a winged is winged with a wing. (Cat., 7, 7a1-5) Even if we do not have a proper name to have a proper reciprocation, Aristotle points, we must invent names. (Cat., 7, 7a5-15 and 7b10-14) Thus, having proper names is the condition of necessary reciprocation: ‘All relatives are spoken of in relation to correlatives that reciprocate, provided they are properly given.’ (Cat., 7, 7a22-23) This condition is also said in another way: there is no reciprocation if a relation is given as related to some chance thing or to something that is accidentally the related thing like when, for example, a slave is given as of a man or a biped instead of being given as of a master. (Cat., 7, 7a25-31) 7) Simultaneity of relatives Aristotle believes that in most cases relatives are simultaneous: double and half or master and slave must exist at the same time: when there is a half, there is a double and when there is a slave, there is a master. (Cat., 7, 7b10-14) However, this receives some exceptions like knowable, which is prior and can, thus, exist before and without knowledge. (Cat., 7, 7b22-27) What approves this non-simultaneousness for Aristotle is that the destruction of knowledge does not carry the knowable to destruction. (Cat., 7, 7b27-31) The same is said about perception and perceptible. (Cat., 7, 7b35-8a9) Aristotle attaches simultaneity to reciprocation. This reciprocation, however, is not a simple reciprocation but ‘reciprocation as to implication of existence’ (ἀντιστρέφει μὲν κατὰ τὴν τοῦ εἶναι) with the condition that neither be in any way the cause of the other’s existence. (Cat., 13, 14b27-29; the same is said also at: Cat., 13, 15a4-11) Aristotle’s examples are the double and the half because when there is a double there is a half and when there is a half there is a double but neither is the cause of the other’s existence. (Cat., 13, 14b29-32) (We have ‘reciprocation as to implication of existence’ also in relation between genus and species but it seems that this has a totally different sense there. 8) Having no independent reality That a relative cannot be a substance, either a primary or a secondary substance, is discussed in our review of both the definition of relatives and their reciprocation. The differentiation of relatives and substances are so deep for Aristotle that after questioning the possibility of any common element or principle for substances and relatives (Met., Λ, 1070a33-36), he asserts that no substance, on the one hand, is the element of relatives and none of the relatives, on the other hand, is the element of substances. (Met., Λ, 1070b3-4) Aristotle does not, however, suffice to this. For him, relatives have the least substantiality, which is, for him, almost the same as reality: ‘The relative is least of all categories a real thing (φύσις τις) or substance, and less than quality and quantity; and the relative is an affection of quantity.’ (Met., M, 1088a22-25) Aristotle believes that an evidence of this least reality (ὄν) and substantiality is that relatives have no proper generation, destruction or movement while each of substance, quality and quantity have them. (Met., M, 1088a29-35) Moreover, neither motion (Phy., E, 1) nor any kind of change is applicable to relatives so that relatives are neither themselves alterations nor the subject of alterations (Phy., Z, 3) and the process of losing and acquiring states cannot be considered as alterations because these are the result of the alterations of non-relative things of which they are states. (Phy., Z, 3) Relative is not even matter but is something different. (Met., M, 1088a24-25) The reason is that the matter is potentially of a nature but relative is neither potentially nor actually of a nature. (Met., M, 1088b1-2) To understand the status of relatives in Aristotle’s world, we have to make a tripartite classification; a classification that though Aristotle himself did not make, his assertions approve it. Based on this division, there are three kinds of being in the world: i) Independent beings: This class includes only substances. ii) Dependent beings: This class includes qualities and quantities. Although they are real, they are ‘in’ substances and cannot exist without them. iii) Super dependent beings: This class includes at least relatives. The fact that relatives must be considered in a third class different from substances, on the one hand, and qualities and quantities, on the other hand, is obvious not only from the previously mentioned texts (Met., M, 1088a22-25, 29-35 and b1-2) in which relatives’ reality is considered less than all substances, qualities and quantities and different from matters but from this text: ‘For there is nothing either great or small, many or few, or, in general, relative which is not something (τι ὄν) different (ἓτερον) [that is also] many or few or great or small’. (Met, N, 1088a27-30) Therefore, super dependent beings are those beings that must necessarily be also something else, i.e. an independent or dependent being. Ackrill (1963, 99) points that some of the words used by Aristotle to exemplify relational entities, e.g. slave, are endowed with a complete sense and do not need to be supplemented by a correlate. (Thus, the linguist criterion of incompleteness would be deficient. Some other instances of relative entities like ‘state,’ ‘knowledge’ and perception are not necessarily followed by the genitive case. 9) Extent of relatives What is the extent of relatives? What are or are not included in relatives either among categories or among other concepts? Which concepts or things Aristotle regard as relative? i) Aristotle includes state (ἓξις) and position (θέσις) among relatives. (Cat., 7, 6b2-6; Cat., 7, 6b11-14; Cat., 8, 11a20-24) ii) Although relative is not matter but is something different (Met., M, 1088a24-25), matter is ‘non-being’ only in virtue of an attribute (Phy., A, 9) and is, thus, a relative term. (Phy., B, 2, 194b9) 10) Property and relativity Aristotle draws a contrast between two types of giving a property, absolute and relative: ‘A property is given either in its own right and for always or relative to something else and for a time.’ (To., E, 1, ^128b15-18) Being a civilized man, for example, is an absolute property for man while to command is a relative property for the soul. The absolute property, however, is considered not only potential to be discussed or observed in relation to many things or periods of time, it in fact ‘belongs to its subject relatively to every single thing that there is, so that if the subject is not distinguished relatively to everything else, the property will not have been given correctly.’ (To., E, 1, 129a18-20) Therefore, an absolute property is a property that ‘is ascribed to a thing in comparison with everything else and distinguishes it from everything else.’ (To., E, 1, 128b33- ) An absolute property is, then, absolutely relative and not conditionally relative, i.e. relative to a specific thing. This is what differentiates it from a relative property, which is relative to a certain thing: ‘A property relative to something else is one which separates its subject off not from everything else but from a particular definite thing.’ (To., E, 1, 128b33- ) One important difference between absolute and relative properties is that while an accident can be a relative property, it can never be an absolute property. (To., I, 5, ^102b20-36) For example, sitting, which is an accident, is also a property relatively to those who are not sitting. (To., I, 5, ^102b20-36) 11) Platonic theories as relatives At least three of Platonic theories Aristotle attaches to relatives: i) Forms ‘It seems that a Form is always spoken of in relation to a Form-this desire itself is for the pleasure itself, and wishing itself is for the good itself.’ (To., Z, 8, 147a^10) Moreover, the theory of Forms takes the relative prior to the absolute as, for example, it takes not the dyad but the number as first. (Met., A, 990b15-17) Aristotle believes that this is against not only the necessities of the case but only the Platonists’ opinion because Forms must be substances only, if they can be shared. (Met., A, 990b27-29) There are, however, things like ‘equal’ which are only relative: they are only in relation to something else. Now the theory that ideas are supposed to be substances only should entail the substantiality of merely relatives. The reason being that Forms are not shared incidentally but each thing shares in that which is not predicated of a subject. (Met., A, 990b29-31) ii) Unequal The Platonic theory of great and small or unequal, which we know more from Aristotle and has, in Platonic philosophy, a role like that of matter in Aristotelian philosophy, is also called relative by Aristole. (Met., M, 1089b4-15) iii) Potentiality Aristotle says that Platonists take what potentially is a ‘this’ and a substance but not actually so a relative because it is ‘neither potentially the one or being, nor the contradictory of the one nor of being, but one among beings.’ (Met., N, 1089b15-20) 12) All things as relative Aristotle attaches the theory that ‘everything is true’ to relativity and thinks the consequence of believing in this theory is that everything is true: ‘He who says all things that appear are true, makes all things relative.’ (Met., Γ, 1011a17-20) 13) Genera and species of relatives There are some genera, Aristotle hints, that are relative but their species are not relative. In such cases, the genera are spoken of in relation to something, but none of the particular cases are so spoken. (Cat., 8, 11a20-36) Aristole’s examples are knowledge and grammar of which the former is a relative but the latter is a quality. The consequence of this is that there is nothing absurd for a thing to be in both genera of relative and quality. (Cat., 8, 11a37- ) However, when the species is a relative, the genera will be a relative too. (To., Δ, 4, 124b15- ) Moreover, Aristotle asserts that ‘the differentiae of relative terms are themselves relative.’ (To., Z, 6, 145a14-16) Things that are called relative are called so, Aristotle says, ‘because the classes that include them are of this sort, e.g. medicine is thought to be relative bcs its genus, knowledge, is thought to be relative,’ (Met., Δ, 1021b4-6) 14) Relatives as indefinite? Fabio Morales takes 1088a29-b1 as a textual evidence supporting the assumption that Aristotle regarded relational terms as indefinite. (shrink)

Standard responses to the question of the nature of logic can be broadly classified into two, namely: logical monists that privilege traditional logic above non-traditional logic and logical pluralists who recognize the legitimacy of many-valued logic and use same to argue for some form of logical relativity. The line of distinction appears to be fairly clear as traditional, Aristotelian, two-valued and standard logic maintains fidelity with the principle of bivalence and the traditional laws of thought while non-traditional, non-Aristotelian, many-valued, non-standard (...) or alternative logics somehow break their fidelity to the principle of bivalence and the traditional laws of thought. It appears to be settled that relativity typically belongs only to non-traditional logics. Contrary to this understanding, this paper argued that some level of relativity Is presupposed in traditional logic by the legitimacy enjoyed by syllogistic, propositional and predicate logics as a body of systems that make up traditional logic. This paper called for the revision of monistic approaches to traditional logic. Since there is some measure of relativity among traditional systems of logic, de-emphasizing the differences among syllogistic, propositional and predicate logics while stressing their unity as 'traditional logic' leads to the fallacy of accent. This fallacy occurs when theorists place vocal emphasis on the unity among traditional logical systems while ignoring their differences. (shrink)

The theorizing about the doctrine of the Trinity by contemporary analytic philosophers of religion has recently been imbued with an air of enthusiastic excitement and self-confidence. My intuition is that there’s room for saying something more in support to the embarrassment and puzzlement traditionally related to the predication of God’s onefoldness and threefoldness. My purpose is to deliver a general argument for (weak) trinitarian skepticism. My view is that the argument provides substantive reasons in support to the common sense (...) intuition that either God’s onefoldness and threefoldness aren’t actually compatible or God’s onefoldness and threefoldness aren’t robustly construed. (shrink)

In assessing the veridicality of utterances, we normally seem to assess the satisfaction of conditions that the speaker had been concerned to get right in making the utterance. However, the debate about assessor-relativism about epistemic modals, predicates of taste, gradable adjectives and conditionals has been largely driven by cases in which seemingly felicitous assessments of utterances are insensitive to aspects of the context of utterance that were highly relevant to the speaker’s choice of words. In this paper, we offer an (...) explanation of why certain locutions invite insensitive assessments, focusing primarily on ’tasty’ and ’might’. We spell out some reasons why felicitous insensitive assessments are puzzling and argue briefly that recent attempts to accommodate such assessments (including attempts by John MacFarlane, Kai von Fintel and Anthony Gillies) all fail to provide more than hints at a solution to the puzzle. In the main part of the paper, we develop an account of felicitous insensitive assessments by identifying a number of pragmatic factors that influence the felicity of assessments. Before closing, we argue that the role of these factors extend beyond cases considered in the debate about assessor-relativism and fit comfortably with standard contextualist analyses of the relevant locutions. (shrink)

The relative merits of standard mereology have received quite a bit of attention in recent years from metaphysicians concerned with the part/whole properties of material objects. A question that has not been pursued to the same degree, however, is what sort of semantic repercussions a commitment to mereological sums in the standard sense might have in particular on the predicted behavior of singular terms and our practices of using such terms to refer to objects. The apparent mismatch between our (...) actual referential practices and the persistence conditions attributed to material objects by the supporters of standard mereology puts these philosophers, other things being equal, at a disadvantage compared to those whose ontology matches more closely the observed behavior of singular terms, as they are commonly used in ordinary discourse. To alleviate this problem, David Lewis leans heavily on his distinction between natural and non-natural properties. I argue in this paper that Lewis’ already heavily burdened natural/non-natural distinction among properties is not enough to avoid Quinean indeterminacy for singular terms. Those who are in the business of giving an analysis of constructions involving full-fledged predication, as opposed to the mere spatial overlap of denotations, will thus want to go in for an ontology that places more stringent structural constraints on the referents of singular terms than would be supplied by standard mereology. (shrink)

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are elaborated, (...) and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic (...) of relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

In this short piece I provide an interpretation of David Lewis' thesis of Composition as Identity.

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic (...) predicates. (shrink)

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying principles (...) through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation. (shrink)

The identity "relation" is misconceived since the syntax of "=" is misconceived as a relative term. Actually, "=" is syncategorematic; it forms (true) sentences with a nonpredicative syntax from pairs of (coreferring) flanking names, much as "&" forms (true) conjunctive sentences from pairs of (true) flanking sentences. In the conaming structure, nothing is predicated of the subject, other than, implicitly, its being so conamed. An identity sentence has both an objectual reading as a necessity about what is named, and (...) also a metalinguistic reading as a contingency about the names. Either way the claim about the subject referent has no extralinguistic content. The necessity of alteridentity (non-self-identity) statements is "lexical", due to contingencies of the names' reference, much like the necessity of analytic statements, due to contingencies of the predicates' sense, and unlike the necessity of logical truths (e.g., self-identities) whose truth is secured by syntax alone. Both alter-identity and analytic sentences are readable as objectual necessities and metalinguistic contingencies. Epistemically, alter-identity statements are not essentially unlike analyticities. "Greece is Hellas"/"g=h" and "Greeks are Hellenes"/"(x)(Gx<=>Hx)" are equally (un)informative; so too for "Azure is cobalt"/"a=c" and "Everything azure is cobalt"/"(x)(Ax<=>Cx)". The real epistemic contrast is between proper names (terms without predicative sense) and terms with a predicative sense (names and predicates of properties). Proper names refer to concrete objects, property names refer to abstract objects. That contrast is metaphysical and thus epistemic. (shrink)

Contemporary accounts of the Trinity and Incarnation sometimes employ aspects of Peter Geach's theory of relative identity. Geach's theory provides an account not merely of identity predicates, but also proper names and restricted quantification. In a previous work I developed an account of the doctrines of the Trinity and Incarnation incorporating these three aspects of Geach's theory and tried to show how each might contribute to our understanding of the doctrines. Joseph Jedwab has recently argued that my account—or any (...) that employs Geach's treatment of restricted quantifiers—leads to serious doctrinal errors. I reply to his criticisms. (shrink)

Āptamīmāṃsā – Deep Reflection On The Omniscient Lord – known also as Devāgama or Devāgamastotra, by Ācārya Samantabhadra (2nd century CE) is the cornerstone of Philosophy and Nyāya. It starts with a discussion, in a philosophical-cum-logical manner, on the concept of omniscience and the attributes of the Omniscient. Ācārya Samantabhadra questions the validity of the attributes that are traditionally associated with a praiseworthy deity and goes on to establish the logic of accepting the Omniscient as the most trustworthy and praiseworthy (...) Supreme Being. Employing the doctrine of conditional predication (syādvāda) – the logical expression of reality in light of the foundational principle of non-absolutism (anekāntavāda) – he faults certain conceptions based on absolutism: existence (bhāvaikānta) and non-existence (abhāvaikānta), non-dualism (advaita-ekānta) and separateness (pŗthaktva-ekānta), and permanence (nityatva-ekānta) and momentariness (kṣaṇika-ekānta). He elucidates the important concept of the ‘seven-nuance system’ (saptabhaṅgī). It embraces the seven limbs (saptabhaṅga) of assertion, the one-sided but relative method of comprehension called the standpoint (naya), and also the acceptance and rejection of the assertion. Ācārya Samantabhadra finally elucidates correct perspective on issues including fate (daiva) and human-deed (pauruṣa), and the bases of merit (puṇya) and demerit (pāpa). The book includes a comprehensive Index of Sanskrit terms. (shrink)

Our topic is the theory of topics. My goal is to clarify and evaluate three competing traditions: what I call the way-based approach, the atom-based approach, and the subject-predicate approach. I develop criteria for adequacy using robust linguistic intuitions that feature prominently in the literature. Then I evaluate the extent to which various existing theories satisfy these constraints. I conclude that recent theories due to Parry, Perry, Lewis, and Yablo do not meet the constraints in total. I then introduce the (...) issue-based theory—a novel and natural entry in the atom-based tradition that meets our constraints. In a coda, I categorize a recent theory from Fine as atom-based, and contrast it to the issue-based theory, concluding that they are evenly matched, relative to our main criteria of adequacy. I offer tentative reasons to nevertheless favour the issue-based theory. (shrink)

Some contextually sensitive expressions are such that their context independent conventional meanings need to be in some way supplemented in context for the expressions to secure semantic values in those contexts. As we’ll see, it is not clear that there is a paradigm here, but ‘he’ used demonstratively is a clear example of such an expression. Call expressions of this sort supplementives in order to highlight the fact that their context independent meanings need to be supplemented in context for them (...) to have semantic values relative to the context. Many philosophers and linguists think that there is a lot of contextual sensitivity in natural language that goes well beyond the pure indexicals and supplementives like ‘he’. Constructions/expressions that are good candidates for being contextually sensitive include: quantifiers, gradable adjectives including “predicates of personal taste”, modals, conditionals, possessives and relational expressions taking implicit arguments. It would appear that in none of these cases does the expression/construction in question have a context independent meaning that when placed in context suffices to secure a semantic value for the expression/construction in the context. In each case, some sort of supplementation is required to do this. Hence, all these expressions are supplementives in my sense. For a given supplementive, the question arises as to what the mechanism is for supplementing its conventional meanings in context so as to secure a semantic value for it in context. That is, what form does the supplementation take? The question also arises as to whether different supplementives require different kinds of supplementation. Let us call an account of what, in addition to its conventional meaning, secures a semantic value for a supplementive in context a metasemantics for that supplementive. So we can put our two questions thus: what is the proper metasemantics for a given supplementive; and do all supplementives have the same metasemantics? In the present work, I sketch the metasemantics I formulated for demonstratives in earlier work. Next, I briefly consider a number of other supplementives that I think the metasemantics I propose plausibly applies to and explain why I think that. Finally, I consider the prospects for extending the account to all supplementives. In so doing, I take up arguments due to Michael Glanzberg to the effect that supplementives are governed by two different metasemantics and attempt to respond to them. (shrink)

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. Instead, I argue (...) that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)

Almost entirely ignored in the linguistic theorising on names and descriptions is a hybrid form of expression which, like definite descriptions, begin with 'the' but which, like proper names, are capitalised and seem to lack descriptive content. These are expressions such as the following, 'the Holy Roman Empire', 'the Mississippi River', or 'the Space Needle'. Such capitalised descriptions are ubiquitous in natural language, but to which linguistic categories do they belong? Are they simply proper names? Or are they definite descriptions (...) with unique orthography? Or are they something else entirely? This paper assesses two obvious assimilation strategies: (i) assimilation to proper names and (ii) assimilation to definite descriptions. It is argued that both of these strategies face major difficulties. The primary goal is to lay the groundwork for a linguistic analysis of capitalised descriptions. Yet, the hope is that clearing the ground on capitalised descriptions may reveal useful insights for the on-going research into the semantics and syntax of their lower-case or 'the'-less relatives. (shrink)

The concept of “life” certainly is of some use to distinguish birds and beavers from water and stones. This pragmatic usefulness has led to its construal as a categorical predicate that can sift out living entities from non-living ones depending on their possessing specific properties—reproduction, metabolism, evolvability etc. In this paper, we argue against this binary construal of life. Using text-mining methods across over 30,000 scientific articles, we defend instead a degrees-of-life view and show how these methods can contribute to (...) experimental philosophy of science and concept explication. We apply topic-modeling algorithms to identify which specific properties are attributed to a target set of entities (bacteria, archaea, viruses, prions, plasmids, phages and the molecule of adenine). Eight major clusters of properties were identified together with their relative relevance for each target entity (two that relate to metabolism and catalysis, one to genetics, one to evolvability, one to structure, and—rather unexpectedly—three that concern interactions with the environment broadly construed). While aligning with intuitions—for instance about viruses being less alive than bacteria—these quantitative results also reveal differential degrees of performance that have so far remained elusive or overlooked. Taken together, these analyses provide a conceptual “lifeness space” that makes it possible to move away from a categorical construal of life by empirically assessing the relative lifeness of more-or-less alive entities. (shrink)

My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...) of sui generis non-natural PROPERTIES. Semantic autonomy insists on a realm of sui generis non-natural PREDICATES which do not mean the same as any natural counterparts. Logical Autonomy maintains that moral conclusions cannot be derived from non-moral premises.-moral premises with the aid of logic alone. Logical Autonomy does not entail Semantic Autonomy and Semantic Autonomy does not entail Ontological Autonomy. But, given some plausible assumptions Ontological Autonomy entails Semantic Autonomy and given the conservativeness of logic – the idea that in a valid argument you don’t get out what you haven’t put in – Semantic Autonomy entails Logical Autonomy. So if Logical Autonomy is false – as Prior appears to prove – then Semantic and Ontological Autonomy would appear to be false too! I develop a version of Logical Autonomy (or NOFI) and vindicate it against Prior’s counterexamples, which are also counterexamples to the conservativeness of logic as traditionally conceived. The key concept here is an idea derived in part from Quine - that of INFERENCE-RELATIVE VACUITY. I prove that you cannot derive conclusions in which the moral terms appear non-vacuously from premises from which they are absent. But this is because you cannot derive conclusions in which ANY (non-logical) terms appear non-vacuously from premises from which they are absent Thus NOFI or Logical Autonomy comes out as an instance of the conservativeness of logic. This means that the reverse entailment that I have suggested turns out to be a mistake. The falsehood of Logical Autonomy would not entail either the falsehood Semantic Autonomy or the falsehood of Ontological Autonomy, since Semantic Autonomy only entails Logical Autonomy with the aid of the conservativeness of logic of which Logical Autonomy is simply an instance. Thus NOFI or Logical Autonomy is vindicated, but it turns out to be a less world-shattering thesis than some have supposed. It provides no support for either non-cognitivism or non-naturalism. (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)

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...) describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negation. (shrink)

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David Bostock (...) and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation. (shrink)

Slurs are incendiary terms so much that many ordinary speakers and theorists deny that sentences containing them can ever be true, and utterances where they occur embedded within normally "quarantining" contexts, like conditionals and indirect reports, are still typically offensive. At the same time, however, many speakers and theorists also find it obvious that sentences containing slurs can be true; and there are clear cases where embedding does inoculate a speaker from the slur's offensiveness. I argue that four standard accounts (...) of the "other" element that differentiates slurs from their more neutral counterparts semantic content, perlocutionary effect, presupposition, and conventional implicature all fail to account for this puzzling mixture of intuitions about truth, and for this mixture of projection and quarantining. Instead, I propose that slurs make two distinct, coordinated contributions to a sentence's conventional communicative role: predication of group membership and endorsement of a derogating perspective on the group. Predication of group membership is "at issue" by default, but different semantic and conversational contexts can alter the relative prominence and scope of the two contributions. (shrink)

Is a bank note identical with the piece of paper of which it consists? On the one hand, John Searle, in his reply to Barry Smith, suggests that they are “one and the same object” that is a social or non-social object only under certain descriptions. On the other hand, Lynne Rudder Baker puts forward the claim that bank note and paper are distinct entities that are bound together by the relation of material constitution. I suggest two possible analyses for (...) Searle’s description relativity claim, the Alternative Subject Analysis and the Predicate Modification Analysis. On both accounts his identity claim gets into serious trouble. While Baker’s definition of material constitution deals well with the bank note example, it fails to account for the constitution of bearerless social entities and groups. I point out five respects in which social constitution can differ from Baker’s account of material constitution and discuss compositional, institutional and interactional constitution as additional varieties of social constitution. (shrink)

My aim is to defend a peculiar epistemic version of the particularity thesis, which results from a sui generis combination of what I call the ‘singular relational view’ and what I call the ‘relativistic content view.’ Particulars are not represented as part of putative singular content. Instead, we are perceptually acquainted with them in the relevant sense that experience puts us in direct perceptual contact with them. And the content of experience is best modeled as a propositional function, that is, (...) the content of a complex predicate that is true or false only relative to some circumstances of evaluation. (shrink)

Many believe that, if true, reason-statements of the form ‘that X is F is a reason to φ’ describe a ‘favouring-relation’ between the fact that X is F and the act of φing. This favouring-relation has been assumed to share many features of other, more concrete relations. This combination of views leads to immediate problems. Firstly, unlike statements about many other relations, reason-statements can be true even when the relata do not exist, i.e., when the relevant facts do not obtain (...) and the relevant acts are not done. Secondly, the previous combination of views also makes it very difficult to draw the distinction between agent-relative and agent-neutral reasons. I argue that we should think that the predicate ‘is a reason to’ creates non-extensional contexts in the statements in which it is used. This would both solve the previous problems and avoid the awkward consequences of the so-called slingshot argument. (shrink)

The paper discusses the Inconsistency Theory of Truth (IT), the view that “true” is inconsistent in the sense that its meaning-constitutive principles include all instances of the truth-schema (T). It argues that (IT) entails that anyone using “true” in its ordinary sense is committed to all the (T)-instances and that any theory in which “true” is used in that sense entails the (T)-instances (which, given classical logic, entail contradictions). More specifically, I argue that theorists are committed to the meaning-constitutive principles (...) of logical constants, relative to the interpretation they intend thereof (e.g., classical), and that theories containing logical constants entail those principles. Further, I argue, since there is no relevant difference from the case of “true”, inconsistency theorists’ uses of “true” commit them to the (T)-instances. Adherents of (IT) are recommended, as a consequence, to eschew the truth-predicate. I also criticise Matti Eklund’s account of how the semantic value of “true” is determined, which can be taken as an attempt to show how “true” can be consistently used, despite being inconsistent. (shrink)

The book is devoted to the contemporary stage of quantum mechanics – quantum information, and especially to its philosophical interpretation and comprehension: the first one of a series monographs about the philosophy of quantum information. The second will consider Be l l ’ s inequalities, their modified variants and similar to them relations. The beginning of quantum information was in the thirties of the last century. Its speed development has started over the last two decades. The main phenomenon is entanglement. (...) The subareas are quantum computer, quantum communication (and teleportation), and quantum cryptography. The book offers the following main conceptions, theses and hypotheses: – dualistic Phythagoreanism as a new kind among the interpretations of quantum mechanics and information: arithmetical, logical, and metamathematical one; – Gödel ’ s first incompleteness theorem is an undecidable proposition, and consequently the second one,too. – a partial rehabilitation of Hilbert ’ s program for the self-foundation of mathematics; – the dual-foundation of mathematics; – Skolemian relativity between: Cantor ’s kinds of infinity, finiteness and infinity, discreteness and continuity, completeness and incompleteness, etc.; – information is a physical quantity representing the non-reducibility of a system to its parts, particularly nonaddtivity; – there exist pure relations «by itself», which cannot be reduced to predications; – energy conservation can and should be generalized; – Einstein’ s «general covariance» or «principle of relativity» can and should be generalized to cover discrete morphisms where the notion of velocity does not make sense. (shrink)

Hobbs (2010) introduced ‘clause-internal coherence’ (CIC) to describe inferences in, e.g., ‘A jogger was hit by a car,’ where the jogging is understood to have led to the car-hitting. Cohen & Kehler (2021) argue that well-known pragmatic tools cannot account for CIC, motivating an enrichment account familiar from discourse coherence research. An outstanding question is how to compositionally derive CIC from coherence relations. This paper takes strides in answering this question. It first provides experimental support for the existence of CIC (...) via offline evidence that attributive (non-)deverbal adjectives can trigger the same causal inferences within clauses that their predicative counterparts can trigger across clauses, albeit more weakly. To explain the experimental results, we use tools in Segmented Discourse Representation Theory (SDRT), which allows us to show that causal inferences can be derived in various ways, depending on whether deverbal adjectives are used attributively or predicatively. If the former, they are presupposition triggers and the coherence relations Elaboration/Continuation compete with Background; if the latter, Explanation/Result compete with Background. These different competitions -- cashed out in terms of interaction between default axioms -- correlate with the difference in the relative salience of the causal inferences. (shrink)

The central topic of this inquiry is a cross-linguistic contrast in the interaction of conjunction and negation. In Hungarian (Russian, Serbian, Italian, Japanese), in contrast to English (German), negated definite conjunctions are naturally and exclusively interpreted as `neither’. It is proposed that Hungarian-type languages conjunctions simply replicate the behavior of plurals, their closest semantic relatives. More puzzling is why English-type languages present a different range of interpretations. By teasing out finer distinctions in focus on connectives, syntactic structure, and context, the (...) paper tracks down missing readings and argues that it is eventually not necessary to postulate a radical cross-linguistic semantic difference. In the course of making that argument it is observed that negated conjunctions on the `neither’ reading carry the expectation that the predicate hold of both conjuncts. The paper investigates several hypotheses concerning the source of this expectation. (shrink)

In this article I argue for an empiricist view on laws. Some laws are fundamental in the sense that they are the result of inductive generalisations of observed regularities and at the same time in their formulation contain a new theoretical predicate. The inductive generalisations simul- taneously function as implicit definitions of these new predicates. Other laws are either explicit definitions or consequences of other previously established laws. I discuss the laws of classical mechanics, relativity theory and electromagnetism in detail. (...) Laws are necessary, whereas acciden- tal generalisations are not. But necessity here is not a modal concept, but rather interpreted as short for the semantic predicate “... is necessarily true”. Thus no modal logic is needed. The neces- sity attributed to law sentences is in turn interpreted as “necessary condition for the rest of the the- ory”, which is true since fundamental laws are implicit definitions of theoretical predicates use in the theory. (shrink)

This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. -/- In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical (...) realism. In Chapter I, I present an argument of his to the effect that logico-metaphysical structure provides the only good explanation of the semantic determinacy of the logical constants. I argue that other explanations are possible. In Chapter II, I present another argument of his to the effect that logico-metaphysical structure is something that comes along with ontological realism: the view that there is a non-language-relative fact of the matter about what exists. I argue that the connection between logical and ontological realism is not as close as Sider makes it out to be. -/- In the second part of this thesis (Chapters III – V) I set out a positive view of the logical constants that can explain both why their meanings are semantically determinate, and why they form part of our vocabulary. On that view, the primary bearers of logical structure are propositional attitudes, and the logical constants are in our language as vehicles for the expression of logically complex propositional attitudes. In Chapter III, I set out an expressivist theory of propositional logic. In Chapter IV, I use this theory to explain how the logical connectives end up having determinate meanings. In Chapter V, I extend the expressivist theory to predicate logic. (shrink)

One aim of this essay is to contribute to understanding aesthetic communication—the process by which agents aim to convey thoughts and transmit knowledge about aesthetic matters to others. Our focus will be on the use of aesthetic adjectives in aesthetic communication. Although theorists working on the semantics of adjectives have developed sophisticated theories about gradable adjectives, they have tended to avoid studying aesthetic adjectives—the class of adjectives that play a central role in expressing aesthetic evaluations. And despite the wealth of (...) attention paid to aesthetic adjectives by philosophical aestheticians, they have paid little attention to contemporary linguistic theories of adjectives. We take our work to be a first step in remedying these lacunae. In this paper, we present four experiments that examine one aspect of how aesthetic adjectives ordinarily function: the context-sensitivity of their application standards. Our results present a prima facie empirical challenge to a common distinction between relative and absolute gradable adjectives because aesthetic adjectives are found to behave differently from both. Our results thus also constitute a prima facie vindication of some philosophical aestheticians’ contention that aesthetic adjectives constitute a particularly interesting segment of natural language, even if the boundaries of this segment might turn out to be different from what they had in mind. (shrink)

Meontology of Gorgias vs. Nihilism. The purpose of this paper is to challenge Gorgias’ image of a “nihilist existentialist”. The original thesis ouden estin, too frequently rendered as „nothing exists”, thus reducing the verb “to be” to denote “bare” existence, and ouden to denote “nothingness”. On close inspection, it turns out that, in Gorgias, neither do we have a negation of reality nor an affirmative treatment of the word “nothingness”.Therefore, ouden” should not be understood as a negation of all reality (...) or a kind of affirmative “nothingness”, whereas “estin” should not be reduced to “bare” existence. (When existence is negated what we obtain is annihilation). Such practices still affect the various translations of Gorgias’ treaty On the non-being or on Nature. Gorgias’ “sophist” thought is typically interpreted as a joke or a parody of dialectical thinking of the Eleatics. In fact, as it turns out, he made no parody of dialectic but applied the elenctic, apagogic method in Zeno’s masterly manner. He did so not for an artificial purpose but to prove the absurdity of the hypothesis of absolute, transcendent (hence incognizable) one Truth-Being, which eliminates the non-being of becoming as absolute non-being. Gorgias argued in earnest in favour of relative being as such, Becoming as the only reality, which from the point of view of absolute being is after all non-being, but not-this-being, or relative non-being but not non-relative non-being, as the Eleatics had claimed. Gorgias’ positions appears to be an apologia of non-being which is, that is of Becoming. We do not transform the “nothing” into a “no thing”. The main question of the treaty is: what is predicated by the word “nothing”? Gorgias’ position can be recapitulated as “nothing is sc. true, there is no criterion because, after all, everything is opinion. It is reinforced further by meontological, i.e. anti-eleatic Gorgias’ emphasis: “No thing is Being (substance)”, because everything is Becoming. Thus the title if Gorgias’ treaty can thus be treated as as an antithesis to that of Melissos’, which – in our opinion – is to emphasize the “non-beingness” of nature, the non-substantiality of things. Therefore, if Gorgias’ text was polemical, and it questioned (while at the same time maintaining the positivity of Becoming as non-being) only the immutability of things, and thus we cannot speak of the existence or the cognizability of natures or of essences of things. In sum, the reasoning of Zeno and Melissos was of a kind that is apt to cut both ways, and that is what Gorgias showed. The argument given as peculiar to himself was to this effect. “What is not” is not, so, it is just as much as “what is”. It is as if the onset of the issues that Plato will take up in The Sophist as the problem of non-being understood as difference. The axis of Gorgias’s anti-eleatic critique, in our view, is his polemic with Parmenides’ famous thesis B3 regarding the relationship of identity or equality between noein and einai. It is an additional and perhaps the most important point of his critique that aims at demonstrating that such relationship is impossible. In brief, things are not words just as thoughts are not words. (shrink)

The Role of Negation in the Description of the World According to Aristote’s Metaphysics. The notions of ‘being’ and ‘non-being’ have entered philosophical language, forming the basis of ontology and meontology, as the counterparts of the Greek expressions to on and to me on (nominalised forms, affirmative and negative, of the participle of the verb einai). Originally, however, these expressions did not have any objectifying meaning, but played the role of meta-language names, representing the copula einai in all its forms, (...) most generally in its affirmative and negative forms. The copula itself, which in later philosophy took on the existential meaning, had functioned only as a semantically empty connective of predicates. Over time the participle on has been used as a universal name of all predicates. The above-mentioned expressions became central in Greek philosophical terminology thanks to the debates, initiated by Parmenides, on the role of negation in the description of the world. Parmenides himself proposed a complete excision of negative sentences as describing by elimination, and created a positive-monistic system which abandoned multiplicity, divisibility, and variability. Later philosophers defended negation, fighting back against the paradoxes formulated by the Eleatics and later by the Sophists. Plato observed that without negation it is impossible to describe the multiplicity of things. He also distinguished a relative negation which does not eliminate anything but makes it possible to confront some things with others. According to the atomists, the divisibility of physical things forces us to accept that they consist of a positive element in the form of an impenetrable body, and of another element lacking any characteristics, i.e. the void. Finally, Aristotle, when analysing the process of change, justified the consistency of the statement that something comes out of “not being” and “being”, under the assumption that the former is understood as being actual, and the latter as being potential. In all these conceptions there is nothing non-existent, there are only proposals of how to identify the aspects of reality whose explanation justifies the use of negation. The affirmative and negative forms of the above expressions have also provoked reflection on the problem of truth and falsity. It has been observed that they are used in everyday language not only to state an agreement or disagreement with the actual facts of the matter, but also to affirm or deny something. (shrink)

The notion of rigidity looms large in philosophy of language, but is beset by difficulties. This paper proposes a simple theory of rigidity, according to which an expression has a world-relative semantic property rigidly when it has that property at, or with respect to, all worlds. Just as names, and certain descriptions like The square root of 4, rigidly designate their referents, so too are necessary truths rigidly true, and so too does cat rigidly have only animals in its (...) extension. After spelling out the theory, I argue that it enables us to avoid the headaches that attend the misbegotten desire to have a simple rigid/non-rigid distinction that applies to expressions, giving us a simple solution to the problem of generalizing the notion of rigidity beyond singular terms. (shrink)

Determiner phrases embedded under a propositional attitude verb have traditionally been taken to denote answers to implicit questions. For example, 'the capital of Vermont' as it occurs in 'John knows the capital of Vermont' has been thought to denote the proposition which answers the implicit question 'what is the capital of Vermont?' Thus, where 'know' is treated as a propositional attitude verb rather than an acquaintance verb, 'John knows the capital of Vermont' is true iff John knows that Montpelier is (...) the capital of Vermont. The traditional view lost its popularity long ago, because it was thought to rest on the controversial assumption that determiner phases embedded under a propositional attitude verb function semantically in the same way as the corresponding wh-clauses. Here we defend the traditional assumption against objections. We then argue that wh-clauses are not to be given a uniform treatment as indirect questions. When occurring under a propositional attitude verb, wh-clauses are better treated as having a predicate-type semantic value. We conclude by considering some possible objections to the predicate view. (shrink)

In this paper I provide some formal schemas for the analysis of vague predicates in terms of a set of semantic relations other than classical synonymy, including weak synonymy (as between "large" and "huge"), antonymy (as between "large" and "small"), relativity (as between "large" and "large for a dog"), and a kind of supervenience (as between "large" and "wide" or "long"). All of these relations are representable in the simple comparative logic CL, in accordance with the basic formula: the more (...) something is F, the more (or less) it is G. I use Carnapian meaning postulates to define these relations as constraints on interpretations of the formal language of CL. (shrink)

Contemporary discussions do not always clearly distinguish two different forms of vagueness. Sometimes focus is on the imprecision of predicates, and sometimes the indefiniteness of statements. The two are intimately related, of course. A predicate is imprecise if there are instances to which it neither definitely applies nor definitely does not apply, instances of which it is neither definitely true nor definitely false. However, indefinite statements will occur in everyday discourse only if speakers in fact apply imprecise predicates to such (...) indefinite instances. (What makes an instance indefinite is, it should be clear, predicate-relative.) The basic issue in the present inquiry is whether this indefiniteness ever really occurs; the basic question is, Why should it ever occur? (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and a four place (...) predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

A. Accident 1. We call an accident (συμβεβηκὸς) that which attaches to something and can be truly asserted, but neither of necessity nor usually.’ (Met. , Δ, 1025a14-16) 2. Whenever an accident attaches to a subject, it attaches to it not because it is that subject (μὴ διότι τοδὶ ἧν). (Met., Δ, 1025a21-24) 3. ‘There is no definite cause for an accident, but a chance cause, i.e. an indefinite one.’ (Met., Δ, 1025a24-25) 4. ‘The accident has happened or exists, -not (...) in virtue of itself, however, but of something else. (Met., Δ, 1025a28-29) 5. ‘What attaches to each thing in virtue of itself but is not in its substance is an accident.’ (Met., Δ, 1025a30-32) 6. ‘An accident is something which, though it is … neither a definition nor a property nor a genus, yet belongs to the thing.’ (To., I, 5, 102b4-) 7. An accident is ‘something which may either belong or not belong to any one and the self-same thing, as (e.g.) being seated may belong or not belong to some self-same thing.’ (To., I, 5, 102b4-) 8. ‘There is nothing to prevent an accident from becoming a temporary or relative property … [and] there is nothing to prevent an accident from becoming both a relative and a temporary property; but a property absolutely it will never be.’ Aristotle’s example is ‘being seated.’ That it is a temporary property is evident. It is also a relative property to those who are not seating when he is the only person sitting. Therefore, it is a temporary and also a relative property. 9. ‘In the case of accidents and in no other it is possible for something to be true in a certain respect and not universally’ and ‘there is nothing to prevent an attribute belonging in part’ so that it is open to dispute accidents e.g. being white or just about a man because he might be white or just in part only. Thus, ‘conversion is not a necessary process in the case of accidents.’ (To., B, 1, 109a9-) B. Essential versus accidental Aristotle distinguishes between two senses of being (τὸ ὄν): accidental sense (κατὰ συμβεβηκός) and essential sense (καθ᾿ αὑτό). The accidental sense happens when something is said to be another thing while there is in fact a third thing which is both of them. Thus, being the first thing is not by itself the second thing. a) Aristotle speaks of three ways in which one thing is said in an accidental sense to be another. (Met., Δ, 1017a8-22) i) When both the subject and the predicate are accidents of a third thing and it is in fact the third thing which ‘is’ by its own. Thus, when it is said e.g. that ‘The just is musical’ it is said accidentally because it is in fact a third thing, Socrates for example, which is just and musical. (Met., Δ, 1017a13-19) ii) When that to which the attribute belongs is. The example of this must be ‘the man is musical’ because it is in fact the man which is. iii) When the subject which has as an attribute that of which it is itself predicated, itself is. The example of this must be Aristotle’s third example: ‘The musical is man.’ b) Aristotle rejects the essential sense to categories: ‘Those things are said in their own right to be that are indicated by the figures of predication; for the senses of ‘being’ are just as many as these figures.’ (Met., Δ, 1017a22-24) Aristotle does not give us any example of the essential sense. Daniel W. Graham suggests that while essential predication is of the logical form of ‘S is P,’ the logical form of the accidental predication is ‘S has P.’ Although he concedes that the is/has contrast is not Aristotle’s, for which he thinks Aristotle prefers ‘said of’/’in’ terminology, he points to the discussion of ‘have’ in Cat. 15 as an evidence of its potential value for an analysis of predication. Kirwan analyses the distinction of essential and accidental predicate as such: while essential predicates ‘are identical with the subjects of which they are predicated; other predications are true in virtue of the fact that two distinct items, e.g. a substance and a quality, ‘coincide.’ Herman Weidemann believes ‘what divides a predicative statement which predicates essentially from a predicative statement which predicates accidentally is the fact that the former does- whereas the latter does not- answer the question what its subject cannot fail to be without ceasing to exist, as the somewhat its subject goes on existing, no matter what happens to be true of it during its existence, or, what kind of things its subject must be in order to be identifiable as one and the same object as long as it exists.’ C. Essential 1. Either the formula or the name of the subject of an essential attribute is involved in it. For example, animal is involved in female but not in white. (Met., Z, 1030b23-26) 2. Essential attributes, combined together, form a unity. Thus, e.g. animal and biped form a unity because they are both essential of man. (OI., II, 11, 21a14-16) 3. Aristotle distinguishes between two kinds of essential attributes (PsA., A, 4, 73a34-b3; 22, 84a12-17): a) Those attributes that belong to their subject as elements in its essential nature as e.g. line belongs to triangle or point to line. Here the very being of triangle is composed of line or that of line is composed of points: line is contained in the formula of triangle and point in that of line. b) Those attributes whose subjects are contained in their own defining formula as e.g. straight is an essential attribute of line because line is part of the defining formula of straight or odd belongs to number because number is part of the defining formula of odd. Every attribute that is related in neither of these two ways to its subject, it is not an essential but an accidental attribute. (PsA., A, 4, 73b3-5) 4. That attribute which is not predicated of a subject other than itself is an essential attribute. A substance cannot be predicated of anything but itself and is, thus, essential. (PsA., A, 4, 73b5-10) 5. A thing consequently co-stated with anything is essential. For example, if a beast dies when its throat is being cut, its death is also essentially connected with the cutting because the cutting was the cause of death, not death a coincidence of cutting. (PsA., A, 4, 73b10-15) 6. Essential attributes in both of this sense, either in the sense that their subjects are contained in them or in the sense that they are contained in their subjects, are necessary as well as consequently co-stated with their subjects. The reason is that it is impossible for them to inhere in their subjects either simply or in the qualified sense (that one or other of a pair of opposites must inhere in the subject as e.g. one of straight or curve must be necessarily predicable of a line or one of odd or even of number). (PsA., A, 4, 73b16-21; 6, 74b5-12; B, 96b1-5) 7. Only those attributes that are within a genus are essential and possessed by their respective subjects as such and, thus, are necessary. Thereupon, both the conclusion and the premises of demonstrations which produce scientific knowledge are essential. (PsA., A, 6, 75a28-31) Therefore, ‘the extreme and the middle terms must be drawn from the same genus; otherwise, as predicated, they will not be essential and will thus be accidents.’ (PsA., A, 6, 75b10-12) Also, the theorems of a science can be demonstrated by means of another science only when they are related as subordinate to superior. (PsA., A, 6, 75b13-) 8. Our knowledge of the connexion of an attribute with a subject is essential only when ‘we know that connexion through the middle term in virtue of which it inheres (καθ᾿ὃ ὑπἀρχει), and as an inference from basic premises essential and ‘appropriate’ to the subject.’ The essential belonging of the middle to the minor has a necessary connexion with its belonging to the same genus of the major and minor: ‘If that middle term also belongs essentially to the minor, the middle must belong to the same genus as the major and minor terms (ἀνάγκη τὸ μέσον ἐν τῇ αὐτῇ συγγενείᾳ εἶναι). (PsA., A, 9, 76a4-9) 9. In an essential predication, the predicate is signified of a subject identical with itself or with a species of itself. Since only predicates which signify substance signify that the subject is identical with the predicate or with a species of the predicate, predicates signifying substance are essentially predicated and any other predicate is accidental or coincidental. Thus, while animal is essentially predicated of man because man is identical with a species of animal, white is accidentally predicated of man because man is neither identical with white nor a species of it. (PsA., A, 22, 83a24-32) Weidemann discusses the confusion between essential predications and statements of identity. He warns that the expression ‘(to be) just what a man is’ (analogous to the Greek phrase ‘(εἶναι) ὃπερ ἀνθρώπον) ought not to be confused with the expression ‘just what it is for a man to be,’ which renders the phrase τὸ ὃπερ ἀνθρώπῳ εἶναι’ (1007a22, 23, 27-28); a confusion Kirwan discusses. 10. ‘Demonstration proves the inherence of essential attributes in things.’ (PsA., A, 22, 84a11-12) 11. ‘Nothing which does not happen to belong to the genus is essentially the genus; e.g. a white man is not essentially a color.’ Thus, while justice falls within the genus, a just man does not. (To., Γ, 1, ^116a24-) 12. There is no syllogism of essence (ti esti). Nevertheless, we come to know ti esti through a demonstration. (93b15-20; cf. 93b25-28) D. Accidental 1. An accidental attribute cannot be predicated of a subject universally. Thus, we cannot say ‘Every man is musical.’ The reason is that ‘universal attributes belong to things in virtue of their nature.’ Therefore, accidental predicates are predicated only of the individuals. (Met., Δ, 1017b33-1018a2) 2. An accidental is a mere name. (Met., E, 1026b13-) 3. An accidental is obviously akin to non-being. (Met., E, 1026b21) 4. ‘That which is neither always nor for the most part we call accidental.’ (Met., E, 1026b27-33) 5. The matter (ὕλη) is the cause of the accidental because it is matter which is capable of being otherwise than as it for the most part is. (Met., E, 1027a13-16) In fact, there is cause or principle of the incidental of the same kind as there are of the essential because if there were, everything would be of necessity. (Met., K, 1065a6-8) The causes of accidental are unordered and indefinite. (Met., K, 1065a25-26) 6. Since all science is either of that which is always or of that which is for the most part, there is no science of the accidental. (Met., E, 1027a19-24; K, 1064b30-1065a6) Therefore, since an accident may also not inhere and, thus, it is impossible to prove its inherence as a necessary conclusion, there is no demonstrative knowledge of accidents. (PsA., A, 6, 75a18-23) 7. The accidental is not necessary but indeterminate. (Met., K, 1065a24-26) 8. The co-positing of a subject and a predicate which are accidental either to the same subject or to one another, whiteness and being musical for instance, does not form a unity. (OI, II, 11, 21a7-14) 9. Negative predicates, i.e. predicates including a ‘not,’ are accidental predicates. Thus, if good be an essential predicate of a subject, ‘not bad’ cannot be essential but is accidental. (OI., II, 14, 23b15-20) 10. Every attribute which does not belong to its subject in either of two senses of essential attribute (cf. PsA., A, 4, 73a34-b3), namely, belonging to their subjects as an element of its formula or their subjects belonging to them as an element of them, is an accidental attribute. (PsA., A, 4, 73b3-5) 11. Those attributes that are predicated of a subject other than themselves are accidental attributes. Thus, everything except substance is an accidental in this sense. (PsA., A, 4, 73b5-10) 12. A thing not consequentially connected with anything is accidental. For example, in ‘while he was walking it lightened,’ the lightening was not due to his walking but was a coincidence. (PsA., A, 4, 73b10-15) 13. Those attributes that are not within a genus are accidental attributes. (PsA., A, 6, 75a28-31) Therefore, the extreme and middle terms that are not drawn from the same genus are accidents. (PsA., A, 6, 75b10-12) Moreover, to apply an attribute to subjects in different genera afford knowledge of the attribute, only as inhering accidentally, not as belonging to its subject as such.’ (PsA., A, 9, 75b38-76a3) . (shrink)

There are four ways in which things are said to oppose (ἀντικεῖσθαι) each other: as relatives (τὰ πρός τι), as contraries (τὰ ἐναντία), as privation and possession (στρέσις καὶ ἓξις) and as affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) Aristotle’s examples are: double and half for relatives, good and bad for contraries, blindness and sight for privation and possession and ‘He is sitting’ and ‘he is not sitting’ for affirmation and negation. We discussed relatives separately thus we (...) ignore it here. A. Contraries Contraries (ἐναντία) have the following features: 1) They are not said of each other (οὐδαμῶς πρὸς ἄλληλα λέγεται) as relatives are said of each other. (Cat., 10, 11b15-23) 2) Contraries are of two kinds: a) Non-intermediables: Those that it is necessary for one or the other of them to belong to the things they naturally occur in or predicated of and accept no intermediate between themselves. Since it is necessary for one of e.g. health and sickness to occur in an animal’s body or odd and even to belong to a number, there is no intermediate between health and sickness or odd and even. (Cat., 10, 11b38-12a9; 12b28-34) b) Intermediables: Those that it is not necessary for one of them to belong to the things they naturally occur in or predicated of and accept intermediates between themselves. It is not necessary for one of e.g. black and white to belong to a body and there may be some intermediates between them. (Cat., 10, 12a9-25; 12b34-40) 3) Contraries can change to one another when the thing capable of receiving them is there. (Cat., 13a18-21) The only exception is when one of the contraries belongs to something by nature. In such cases, change is not possible as the hotness of fire cannot change to coldness while fire is still there. 4) Contraries belong to the same thing, either the same in species or in genus as e.g. sickness and health in an animal’s body or whiteness and blackness in body simply. (Cat., 10, 14a15- ) In Metaphysics (I, 1058a8-10) Aristotle asserts that contraries are in the same genus. 5) There are three possibilities about the genera of contraries: they either are in the same genus, e.g. black and white, or in the contrary genera, e.g. justice and injustice, or are themselves genera, e.g. good and bad. (Cat., 11, 14a19-25) 6) Doing and being affected admit of contrariety, e.g. heating is contrary to cooling. (Cat., 9, 11b1-4) 7) Substances only are able to receive contraries. (Cat., 5, 4a10-17) 8) There is nothing contrary to a substance, whether primary or secondary. (Cat., 5, 3b24-27) Thus, neither man nor an individual man has a contrary. 9) There is no contrary to a quantity: e.g. four-foot ot ten has no contrary. (Cat., 5, 3b27-32) 10) Otherness in species means to be contraries. (Met., I, 1058a17-20) 11) Contrariety is complete difference. Two things that have the same genus but are different in species are other than one another in the highest degree and their difference is complete, i.e. they cannot be present along with one another. (Met., I, 1058a10-16) 12) One of the contraries is a privation, which is a denial of a predicate to a determinate genus. (Met., Γ, 1011b18-20) 13) ‘Neither true judgments nor true propositions can be contrary the one to the other.’ (OI., II, 14, 24b6-7) B. Privation and possession Privation and possession are said in connection with the same thing in which the possession naturally occurs. Only that thing which is capable of receiving a possession and only when it is entirely absent from that which naturally has it and only at the time when it is natural for it to have it, is called to be deprived of it. (Cat., 10, 12a26-30) A thing is not called e.g. blind if it has never had or was not supposed to have sight. That privation and possession are not relatives is obvious from the fact that none is called just what it is, of its opposite. (Cat., 10, 12b16-21) Moreover, while relatives reciprocate, they do not. (Cat., 10, 12b21-25) That they are not contraries is explained by the classification of contraries to intermediable and non-intermediable contraries. The latter are different from privation and possession because it is necessary for one of such contraries to be predicated of absolutely everything while it is not the case about privation and possession because they are necessary only in things naturally capable of their predication. Intermediable contraries are different from privation and possession because while the former are not necessary the latter are necessary in their subject matters. (Cat., 13a3-17) Unlike contraries for each of which it is possible to change to the other, change in privation and possession is allowed only from possession to privation and not vice versa: neither a blind man gets sight nor a bald man regain his hair. (Cat., 13a18-36) C. Affirmation and negation Aristotle regards the reception of truth and falsity as the main difference affirmation and negation opposition has in respect of other three kinds of opposition: it is only affirmation and negation that it is always necessary for one of them to be true and the other to be false (Cat., 13a37-b26), no matter the subject of affirmation or negation exists or not. (Cat., 10, 13b27-35) ‘It is impossible that contradictory propositions should both be true of the same subject.’ (OI., II, 12, 21b17-18) It is evident both about relatives and those contraries that include no co-positing, e.g. health and sickness. The only cases that resemble affirmation and negation are those contraries that are said with co-positing, e.g. ‘Socrates is well’ and ‘Socrates is sick.’ Yet, Aristotle points, not even with these is it necessary always for one to be true and the other false because if Socrates does not exist, neither will be true. (Cat., 10, 13b12-19) This is true also about privation and possession: neither ‘Socrates has sight’ nor ‘Socrates is blind’ are true if he does not exist. Moreover, it is not necessary for one or the other of them to be true or false even if he exists because until the time when it is natural for Socrates to have sight, both are false. (Cat., 10, 13b20-26) . (shrink)

Can fictional narration yield knowledge in a way that depends crucially on its being fictional? This is the hard question of literary cognitivism. It is unexceptional that knowledge can be gained from fictional literature in ways that are not dependent on its fictionality (e.g., the science in science fiction). Sometimes fictional narratives are taken to exhibit the structure of suppositional argument, sometimes analogical argument. Of course, neither structure is unique to narratives. The thesis of literary cognitivism would be supported if (...) some novels exhibit a cogent and special argument structure restricted to fictional narratives. I contend that this is the case for a kind of transcendental argument. The reason is the inclusion and pattern of occurrence of the predicate ‘believable’ in the schema. Believability with respect to fictional stories is quite a different thing than it is with respect to nonfictional stories or anything else. (shrink)

In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in (...) terms of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way that things actually are, there is a unique actual space which represents the way that first-order modality actually is. -/- One might wonder what the accessibility relation itself is like. Presumably, if it is logical or metaphysical modality that is being dealt with, it is reflexive; but is it also symmetric, or transitive? Especially in the case of metaphysical modality, the answer is not clear. And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent different ways that first-order modality could have been? -/- To be clear, the idea behind my proposal is not just that some things which are possible or necessary might not have been so at the first order, as determined by the actual accessibility relation, but also that the actual accessibility relation, and hence the nature or structure of actual modality, could have been different at some higher order of modality. Even if the accessibility relation is actually both symmetric and transitive, perhaps it could (second-order) have been otherwise: There is a (second-order) possible space of worlds in which it is different, where it fails to be symmetric, or transitive. We must, therefore, introduce the notion of a higher-order accessibility relation, one that in this case relates spaces of first-order worlds. The question then arises as to whether that relation is symmetric, or transitive. We can then consider third-order modalities, spaces of spaces of spaces of possible worlds, where the second-order accessibility relation differs from how it actually is. I can see no reason why there should be a limit to this hierarchy of higher-order modalities, any more than I can see a reason why there should be a limit to the hierarchy of higher-order properties. There will thus be an infinity of orders, one for each positive integer, and each order will have an accessibility relation of its own. To keep things as clear as possible, a space of first-order points (i.e., of possible worlds) shall be called a galaxy, a space of second-order points, a universe, and a space of any higher order, a cosmos. However, to keep things as simple as possible, in what follows I will deal with but a single cosmos, and hence will not deal with modalities higher than the third order. -/- The accessibility relation is not the only thing that might be thought to vary between spaces of worlds: Perhaps the contents of the spaces can vary as well. While I presume that the contents of the worlds themselves remain constant—it makes doubtful sense to suppose that in one space some entity e exists in a world w and in another space e doesn’t exist in that same world w—we may suppose that different spaces differ as to which worlds they contain, just as different worlds may differ as to which objects they contain. Thus we might have a higher-order analogue of a variable-domain modal logic. There seem, then, to be three ways in which spaces can differ: First, as to the properties of the accessibility relation; second, as to which worlds the relation relates; and third, as to which worlds or spaces are parts of their domains. -/- The paper will be structured as follows. In Section 2 I provide some reasons why one might want to pursue this kind of project in the first place. In Section 3 I outline the syntax and semantics of my proposed logic. Section 4 covers semantic tableaux for this system; and after giving the rules for their construction, I construct a few of them myself to establish some logical consequences of the system and give the reader a feel for how it works. In Sections 5, 6 and 7 I explore some of its potential philosophical implications for areas besides logic, namely the philosophy of language; metaphysics, including the metaphysics of modality and the philosophy of time, and finally the philosophy of religion, before concluding the paper in Section 8. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their own, (...) but have also produced a deeper understanding of the notion of predicativity, therefore witnessing the " light logic throws on problems in the foundations of mathematics. " (Feferman 1998, p. vii) Predicativity has been at the center of a considerable part of Feferman's work: over the years he has explored alternative ways of explicating and analyzing this notion and has shown that predicative mathematics extends much further than expected within ordinary mathematics. The aim of this note is to outline the principal features of predicativity, from its original motivations at the start of the past century to its logical analysis in the 1950-60's. The hope is to convey why predicativity is a fascinating subject, which has attracted Feferman's attention over the years. (shrink)

According to indexical contextualism, the perspectival element of taste predicates and epistemic modals is part of the content expressed. According to nonindexicalism, the perspectival element must be conceived as a parameter in the circumstance of evaluation, which engenders “thin” or perspective-neutral semantic contents. Echoing Evans, thin contents have frequently been criticized. It is doubtful whether such coarse-grained quasi-propositions can do any meaningful work as objects of propositional attitudes. In this paper, I assess recent responses by Recanati, Kölbel, Lasersohn and MacFarlane (...) to the “incompleteness worry”. None of them manages to convince. Particular attention is devoted to an argument by John MacFarlane, which states that if perspectives must be part of the content, so must worlds, which would make intuitively contingent propositions necessary. I demonstrate that this attempt to defend thin content views such as nonindexical contextualism and relativism conflates two distinct notions of necessity, and that radical indexicalist accounts of semantics, such as Schaffer’s necessitarianism, are in fact quite plausible. (shrink)

The primary purpose of this note is to demonstrate that predicative Frege arithmetic naturally interprets certain weak but non-trivial arithmetical theories. It will take almost as long to explain what this means and why it matters as it will to prove the results.