It is argued that philosophers who adopt the perdurance theory of persistence and who subscribe to the principle of Unrestricted Mereological Composition (UMC) are in a position to regard “Phosphorus is Hesperus” as false.

The recent historiography of molecular biology features key technologies, instruments and materials, which offer a different view of the field and its turning points than preceding intellectual and institutional histories. Radioisotopes, in this vein, became essential tools in postwar life science research, including molecular biology, and are here analyzed through their use in experiments on bacteriophage. Isotopes were especially well suited for studying the dynamics of chemical transformation over time, through metabolic pathways or life cycles. Scientists labeled phage with (...) class='Hi'>phosphorus-32 in order to trace the transfer of genetic material between parent and progeny in virus reproduction. Initial studies of this type did not resolve the mechanism of generational transfer but unexpectedly gave rise to a new style of molecular radiobiology based on the inactivation of phage by the radioactive decay of incorporated phosphorus-32. These ‘suicide experiments’, a preoccupation of phage researchers in the mid-1950s, reveal how molecular biologists interacted with the traditions and practices of radiation geneticists as well as those of biochemists as they were seeking to demarcate a new field. The routine use of radiolabels to visualize nucleic acids emerged as an enduring feature of molecular biological experimentation. (shrink)

It was an empirical discovery that Phosphorus is Hesperus. According to Kripke, this was also the discovery of a necessary fact. Now, given Kripke’s theory of direct reference one could wonder what kind of discovery this is. For we already knew Phosphorus/Hesperus, and we also knew that any entity is, necessarily, identical to itself. So what is it that was discovered? I want to show that there is more to this widely known case than what usual readings, and (...) critics, reveal; and I want to show this under the Kripkean pattern that what was discovered is the plain fact of identity that Phosphorus is, and necessarily is, Hesperus. Moreover, I will show how both Kripkean theses, the necessity of identity and the direct theory of reference, should not be kept apart to understand the kind of discovery this is. In particular, understanding the kind of discovery we made will help us see how intuition is displayed in metaphysics, and how metaphysical impossibilities, and metaphysical modality in general, can be discerned by reason and separated from other modalities. The study of this discovery will help us see, in a line, how identity belongs to the inner and most profound structure of reality and to the most profound structure of cognition and language. (shrink)

Tobias Hansson Wahlberg argues in a recent article (2009) that the truth of “Hesperus is Phosphorus” depends on the assumption that the endurance theory of persistence is true. The statement is not true (or at least can reasonably be doubted), he argues, if one assumes (a) the theory of persistence according to which objects are four-dimensional entities, persisting through perdurance, i.e. by having temporal parts that are numerically distinct, and (b) the thesis of unrestricted mereological composition (UMC), that is, (...) that any two things, however scattered in space or time, compose a sum. (shrink)

In “On Sense and Reference,” surrounding his discussion of how we describe what people say and think, identity is Frege’s first stop and his last. We will follow Frege’s plan here, but we will stop also in the land of make-believe.

The objective of this study was to isolate endophytic bacteria from roots of Brachiaria humidicola cv. humidicola (Rendle) Schweick and to relate their presence to pH, organic matter and phosphorus contents of the soil of cattle farms located in the municipality of San Benito Abad. Soil sampling was carried out with roots of B. humicola for the isolation and counting of the population density of endophytic bacteria and soil samples were also collected for the determination of pH, organic matter (...) and phosphorus parameters. The results found indicate that there is an amount of endophytic bacteria in roots of B. humidicola when the soil contains optimum pH values of (6.1 ± 6.98); low to moderate phosphorus content (10.8 ± 16.28 mg/kg) and low to moderate organic matter content (1.7 ± 2.31%). The presence of endophytic bacteria was observed in a range of 3.0 ± 8.0 X 106 CFU/g of roots. There is a worldwide need to establish a relationship between endophytic bacteria and soil physical-chemical quality indicator parameters to predict a change in functional diversity under physical, chemical and biological conditions of the soil ecosystem. (shrink)

Many solar systems in the universe may be expected to contain rocky planets that have accreted organic compounds. These compounds are likely to be universally found. In addition, the chemistry of sulfur, phosphorus, and iron is likely to dominate energy transductions and monomer activation, leading to the eventual emergence of polymers. Proteins and polynucleotides provide living matter with function, structure, and information. The conceptual puzzle regarding their emergence is discussed. The fitness of various elements to serve various roles is (...) analyzed from the viewpoint of electron orbitals. Elements with d orbitals are of central importance. (shrink)

Bacteria have evolved advanced strategies for surviving during nutritional stress, including expression of specialized enzyme systems that allow them to grow on unusual nutrient sources. Inorganic phosphate (Pi) is limiting in most ecosystems, hence organisms have developed a sophisticated, enzymatic machinery known as carbon‐phosphorus (C‐P) lyase, allowing them to extract phosphate from a wide range of phosphonate compounds. These are characterized by a stable covalent bond between carbon and phosphorus making them very hard to break down. Despite the (...) challenges involved in both synthesizing and catabolizing phosphonates, they are widespread in nature. The enzymes required for the bacterial C‐P lyase pathway have been identified and for the most part structurally characterized. Nevertheless, the mechanistic principles governing breakdown of phosphonate compounds remain enigmatic. In this review, an overview of the C‐P lyase pathway is provided and structural aspects of the involved enzyme complexes are discussed with a special emphasis on the role of ATP‐binding cassette (ABC) proteins. (shrink)

In this paper I answer Aranyosi’s (Axiomathes 19(2):223–224, 2009) criticism of my “Is Phosphorus Hesperus?” (Axiomathes 19(1):101–102, 2009).

Phytase is an enzyme that frees the phosphorus bound in feed grains and thus reduces the amount of dicalcium phosphate supplementation required for non-ruminants, reducing phosphorous excretion and thus reducing water pollution. This innovation has been widely adopted by feed companies in the US due to decreased phytase production costs and increased dicalcium phosphate costs. The roles played by phytase characteristics and choice architecture in the widespread use of this win–win technology are examined. A recent survey has also revealed (...) that Midwestern farmers are largely unaware of this technology even though they are using it. One implication is that further research on win–win technologies that will be adopted by industries, rather than being dependent on adoption by individuals, may be beneficial. (shrink)

Arsenic and phosphorus are group 15 elements with similar chemical properties. Is it possible that arsenate could replace phosphate in some of the chemicals that are required for life? Phosphate esters are ubiquitous in biomolecules and are essential for life, from the sugar phosphates of intermediary metabolism to ATP to phospholipids to the phosphate backbone of DNA and RNA. Some enzymes that form phosphate esters catalyze the formation of arsenate esters. Arsenate esters hydrolyze very rapidly in aqueous solution, which (...) makes it improbable that phosphorous could be completely replaced with arsenic to support life. Studies of bacterial growth at high arsenic:phosphorus ratios demonstrate that relatively high arsenic concentrations can be tolerated, and that arsenic can become involved in vital functions in the cell, though likely much less efficiently than phosphorus. Recently Wolfe‐Simon et al. 1 reported the isolation of a microorganism that they maintain uses arsenic in place of phosphorus for growth. Here, we examine and evaluate their data and conclusions. (shrink)

: All known life requires phosphorus (P) in the form of inorganic phosphate (PO43x or Pi) and phosphate-containing organic molecules. Pi serves as the backbone of the nucleic acids that constitute genetic material and as the major repository of chemical energy for metabolism in polyphosphate bonds. Arsenic (As) lies directly below P on the periodic table and so the two elements share many chemical properties, although their chemistries are sufficiently dissimilar that As cannot directly replace P in modern biochemistry. (...) Arsenic is toxic because As and P are similar enough that organisms attempt this substitution. We hypothesize that ancient biochemical systems, analogous to but distinct from those known today, could have utilized arsenate in the equivalent biological role as phosphate. Organisms utilizing such ‘ weird life ’ biochemical pathways may have supported a ‘ shadow biosphere ’ at the time of the origin and early evolution of life on Earth or on other planets. Such organisms may even persist on Earth today, undetected, in unusual niches. (shrink)

We examine the framing mechanisms used to maintain a cross-sector partnership that was created to address a complex long-term social issue. We study the first 8 years of existence of an XSP that aims to create a market for recycled phosphorus, a nutrient that is critical to crop growth but whose natural reserves have dwindled significantly. Drawing on 27 interviews and over 3000 internal documents, we study the evolution of different frames used by diverse actors in an XSP. We (...) demonstrate the role of framing in helping actors to avoid some of the common pitfalls for an XSP, such as debilitating conflict, and in creating sufficient common ground to sustain collaboration. As opposed to a commonly held assumption in the XSP literature, we find that collaboration in a partnership does not have to result in a unanimous agreement around a single or convergent frame regarding a contentious issue. Rather, successful collaboration between diverse partners can also be achieved by maintaining a productive tension between different frames through “optimal” frame plurality—not excessive frame variety that may prevent agreements from emerging, but the retention of a select few frames and the deletion of others toward achieving a narrowing frame bandwidth. One managerial implication is that resources need not be focussed on reaching a unanimous agreement among all partners on a single mega-frame vis-à-vis a contentious issue, but can instead be used to kindle a sense of unity in diversity that allows sufficient common ground to emerge, despite the variety of actors and their positions. (shrink)

Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic : Frege’s “Hesperus-Phosphorus” problem—how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as Quine’s “Double Vision” problem and problems of self-knowledge. In this paper, we lay out a philosophical approach to epistemic predicate logic, implemented formally in (...) Melvin Fitting’s First-Order Intensional Logic, that we argue solves these and other conceptual problems. Topics covered include: Quine on the “collapse” of modal distinctions; the rigidity of names; belief reports and unarticulated constituents; epistemic roles; counterfactual attitudes; representational vs. interpretational semantics; ignorance of co-reference vs. ignorance of identity; two-dimensional epistemic models; quantification into epistemic contexts; and an approach to multi-agent epistemic logic based on centered worlds and hybrid logic. (shrink)

When I say ‘Hesperus is Phosphorus’, I seem to express a proposition. And when I say ‘Joan believes that Hesperus is Phosphorus’, I seem to ascribe to Joan an attitude to the same proposition. But what are propositions? And what is involved in ascribing propositional attitudes?

In this paper, I defend a well-known theory of belief reports from an important objection. The theory is Russellianism, sometimes also called `neo-Russellianism', `Millianism', `the direct reference theory', `the "Fido"-Fido theory', or `the naive theory'. The objection concernssubstitution of co-referring names in belief sentences. Russellianism implies that any two belief sentences, that differ only in containing distinct co-referring names, express the same proposition (in any given context). Since `Hesperus' and `Phosphorus' both refer to the planet Venus, this view implies (...) that all utterances of (1) and.. (shrink)

An influential tradition holds that thoughts are public: different thinkers share many of their thoughts, and the same applies to a single subject at different times. This ‘publicity principle’ has recently come under attack. Arguments by Mark Crimmins, Richard Heck and Brian Loar seem to show that publicity is inconsistent with the widely accepted principle that someone who is ignorant or mistaken about certain identity facts will have distinct thoughts about the relevant object—for instance, the astronomer who does not know (...) that Hesperus is Phosphorus will have two distinct thoughts Hesperus is bright and Phosphorus is bright. In this paper, I argue that publicity can be defended if we adopt a relational account on which thoughts are individuated by their mutual relations. I then go on to develop a specific relational theory—the ‘linking account’—and contrast it with other relational views. (shrink)

I argue that the key motivation for the essentialist is that modal intuitions, such as "Humphrey might have won", are not to be explicated in terms of persons in other possible situations who are similar to the actual Humphrey. However, because of a need to preserve the necessity of identity, the essentialist must claim that certain other intuitions (such as "Hesperus might not have been Phosphorus") have to be understood in terms of similarity (as in Kripke) or have to (...) be rejected (as in Yablo). This move leads to ineliminable doubts about the essentialist's rejection of similarity, and so it leads to an undermining of the motivation for essentialism itself. (shrink)

I observe that the “concept-generator” theory of Percus and Sauerland (2003), Anand (2006), and Charlow and Sharvit (2014) does not predict an intuitive true interpretation of the sentence “Plato did not believe that Hesperus was Phosphorus”. In response, I present a simple theory of attitude reports which employs a fine-grained semantics for names, according to which names which intuitively name the same thing may have distinct compositional semantic values. This simple theory solves the problem with the concept-generator theory, but, (...) as I go on to show, it has problems of its own. I present three examples which the concept-generator theory can accommodate, but the simple fine-grained theory cannot. These examples motivate the full theory of the paper, which combines the basic ideas behind the concept-generator theory with a fine-grained semantics for names. The examples themselves are of interest independently of my theory: two of them constrain the original concept-generator theory more tightly than previously discussed examples had. (shrink)

How do we know what's (metaphysically) possible and impossible? Arguments from Kripke and Putnam suggest that possibility is not merely a matter of (coherent) conceivability/imaginability. For example, we can coherently imagine that Hesperus and Phosphorus are distinct objects even though they are not possibly distinct. Despite this apparent problem, we suggest, nevertheless, that imagination plays an important role in an adequate modal epistemology. When we discover what is possible or what is impossible, we generally exploit important connections between what (...) is possible and what we can coherently imagine. We can often come to knowledge of metaphysical modality a priori. (shrink)

De se thoughts have traditionally been seen to be exceptional in mandating a departure from orthodox theories of attitudes. Against this, skeptics about the de se have argued that the de se phenomena demand no more of our theories of attitudes than traditional Frege cases. In this camp one view is that the de se can be accounted for by MOPs in the same way that MOPs can account for how it can be rational to believe, for instance, ”Hesperus is (...) shining” while also believing ”Phosphorus is shining.” This paper formulates some minimal conditions that de se MOPs must have in order to explain the relevant de se phenomena. Some potential replies are answered. I conclude that de se MOPs are not exceptional. (shrink)

The known facts of quantum physics and biology strongly suggest the following hypotheses: atoms and the fundamental particles have a rudimentary degree of consciousness, volition, or self-activity; the basic features of quantum mechanics are a result of this fact; the quantum mechanical wave properties of matter are actually the conscious properties of matter; and living organisms are a direct result of these properties of matter. These hypotheses are tested by using them to make detailed predictions of new facts, and then (...) by showing that the predictions can be verified. The hypotheses are used to predict successfully that the quantum wave properties of matter are strongly predominant in proteins, to explain the presence and relative abundance of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur in proteins, and to explain diffraction phenomena, the behavior of helium II, the exclusion principle, and causality and determinism in modern science, thus closely relating physics and biology. (shrink)

The specific objectives of the study were 1) To create a “ke-kame-tu” formula (15-60-25), 2) To create nuggets as a PMT product based on the ke-kame-tu formula, 3) To analyze the proximate content, amino acids, zinc, calcium, phosphorus and magnesium of PMT products, 4) To determine the preferred PMT product based on the acceptance test by toddlers. The making of the “ke-kame-tu” formula (15-60-25) used a randomized block design (RAK) with one treatment and three replications. The PMT product was (...) made using the ke-kame-tu formula (15-60-25) and the acceptability test used 30 toddler panelists. Analysis of protein, calcium, phosphorus and magnesium (HPLC/AAS and spectrophotometry). To determine the acceptability of the PMT product, a limit of ≥50% of toddlers stated that they liked it was used. Nuggets made using a modified recipe with the addition of 100 grams of ke-kame-tu formula. The results of the protein analysis were 16.60%, calcium 0.07 mg%, phosphorus 0.15 mg%, magnesium 0.02 mg%, zinc 1.95 mg%. If toddlers consume 100 grams of this nugget, it will be able to meet the nutritional needs, especially protein for toddlers aged 6-11 months by 110.6%, 1-3 years by 83% and 4-6 years by 66.4%. The results of the trial on toddler panelists showed that all toddlers liked the nuggets served. If we looked at carefully at the protein content of this nugget with complete essential amino acid content, it is very possible to substitute the fulfillment of toddler protein requirements. Consumption of toddler protein according to needs will achieve optimal nutritional status, in other words, the problem of stunting can be prevented and dealt with. (shrink)

This essay offers an account of the truth conditions of sentences involving deontic modals like ‘ought’, designed to capture the difference between objective and subjective kinds of ‘ought’ This account resembles the classical semantics for deontic logic: according to this account, these truths conditions involve a function from the world of evaluation to a domain of worlds (equivalent to a so-called “modal base”), and an ordering of the worlds in such domains; this ordering of the worlds itself arises from two (...) further elements – a probability function and a value function – since this ordering ranks the worlds in accordance with the expected value of certain propositions that are true at those worlds. Thus, a proposition of the form ‘Ought (p)’ is true at a world of evaluation w if and only if p is true at all the top-ranked worlds in the domain assigned to w. This domain of worlds consists of metaphysically possible worlds, while the probability function is defined over a space of epistemically possible worlds (which may include metaphysically impossible worlds, such as worlds where Hesperus is not Phosphorus). Evidence is given that this account assigns the correct truth conditions to a wide range of sentences involving ‘ought’. Since these truth conditions involve both a domain of metaphysically possible worlds and a space of epistemically possible worlds, there are two corresponding kinds of conditional involving ‘ought’, depending on which space of worlds is restricted by the conditional. Finally, some objections that might be raised against this account are answered. (shrink)

Presented in this study is an analysis of the electronic properties of doped diamond calculated using the Vienna ab initio simulation package, employing density functional theory within the generalized-gradient approximation. The dopants studied here have been inserted substitutionally into a 64-atom diamond supercell and include the single-electron acceptors boron and aluminium, the single-electron donors nitrogen and phosphorus and the double-electron donors oxygen and sulphur. Co-doping of diamond with sulphur and boron has also been briefly examined. The doped supercells have (...) been relaxed, followed by calculation of electronic properties from the electronic density of states such as the indirect bandgap E g , the valence bandwidth and an examination of the acceptor and donor states in the bandgap. It is anticipated that this study will provide a useful comparison of the third- and fourth-row donors and acceptors in diamond. (shrink)

My aim in this paper is to connect naming and analyticity and to argue that, like “Hesperus is Hesperus”, “Hesperus is Phosphorus” is analytic. In the paper, I also discuss several other unexpected cases of analytic truth like “Aristotle existed”.

According to Pure Russellianism, if -/- (1) David believes that Hesperus is a planet -/- is true, -/- (2) David believes that Phosphorus is a planet -/- is also true. It is also usually thought, by friends and foes of Pure Russellianism alike, that on it, when (1) and (2) are true, -/- (3) David does not believe that Phosphorus is a planet -/- cannot but be false and because of this, many departed from Pure Russellianism. In this (...) paper, I will show that by relying on the very explanation Pure Russellianism is usually combined with to account for sentences such as (1) and (2) and by acknowledging the well-attested linguistic phenomenon of metalinguistic negation, even if (1) and (2) are true, it is not the case that on Pure Russellianism (3) cannot but be false. (shrink)

In Frege’s Puzzle, Nathan Salmon takes it to be obvious that the fact that names such as ‘Hesperus’ and ‘Phosphorus’ are coreferential is purely a matter of arbitrary linguistic convention, while the fact that Hesperus is Phosphorus is by no means a conventional matter. Salmon also takes these points to be ones to which Frege appeals in the opening paragraph of “On Sense and Reference,” and hence finds it ironic that these points undercut the theory of sense that (...) Frege develops in that paper. It is argued that the thesis that the coreferentiality of a pair of proper names is purely a matter of arbitrary linguistic convention is inconsistent with any plausible theory of reference. Salmon’s reading of Frege’s argument is also called into question. (shrink)

There is obviously tension between any view which claims that the object denoted is all that names and simple referring terms contribute to propositions expressed by sentences in which they appear and the apparent a posteriority of identity statements containing different but codesignative names. Frege solved the tension by adopting a description theory of names. The direct designation theorist cannot do the same, for that would amount to abandoning the theory. Instead, she has to provide one of two solutions; (a) (...) argue that although Hesperus is Hesperus and Hesperus is Phosphorus express the same proposition their epistemic status differs such that one’s justification of the proposition expressed by the former but not the latter is a priori, or (b) argue that both Hesperus is Hesperus and Hesperus is Phosphorus express a priori truths. I will argue for a version of option (a), and that while coreferential names can be freely substituted in simple belief contexts, they cannot be freely substituted in contexts involving justification. (shrink)

The permutation of basic atoms—nitrogen, hydrogen, oxygen, carbon and phosphorus―into the biomolecules DNA and RNA, subsequently evolved in cells and brains, defining the origin of life and intelligence, remains unexplained. Equally the origin of the genetic information and the intertwined nature of ‘hardware’ and ‘software’ involved in the evolution of bio-molecules and the cells are shrouded in mystery. This treatise aims at exploring individual and swarm behaviour patterns which potentially hint at as yet unknown biological principles. It reviews theories (...) of evolution with perspectives from the earth sciences, commencing with the earliest observed records of life. This is followed by reviews and discussion of the building blocks of life, marine and terrestrial communities, the arthropods, birds and finally humans. It is suggested that, further to the mutation/natural selection processes established by Darwin and Wallace, an understanding of the evolution of intelligence remains little understood. A directionality of evolutionary trajectories is evident, not least the purposeful thinking process of humans as well as animals. It is not clear how directional intelligence, manifested for example by the collective intelligence of arthropod colonies, has evolved from mutation/natural selection processes. Potential clues for the understanding of life and evolution are provided by Aristotle’s dictum of “the whole being greater than the sum of the parts”, Niels Bohr’s principle of quantum complementarity and George Ellis’ theory of top-down causality. Inherent in the question of the origin of life is an anthropocentric bias, related to the self-referential Anthropic Principle and theological paradigms of man’s supposed dominion over all other species. The Anthropic Principle, however, should be capable of being circumvented using the scientific falsification method, assuming universal verified constants of physics. The phenomenon of the human mastery of fire and the splitting of the atom, leading to the seventh major mass extinction of species, remains incomprehensible. (shrink)

To free Allen�s Creek from its ignominous confines within an aging, inadequate storm drain. To free Allen�s Creek from its status as a flooding disaster-in-waiting. To free Allen�s Creek from its role of contributing the heaviest concentration of phosphorus and other pollutants of any tributary of the Huron River in Washtenaw County. To free Allen�s Creek from its obscurity.

There is a traditional picture of belief, according to which someone's having a belief is that person's standing in a certain relation to an abstract object, a proposition. My dissertation examines the metaphysical demands that two problems for this picture of belief make on these abstract objects. The first problem comes to us from Frege's "On Sense and Reference," and the second concerns a certain sort of one's beliefs about oneself, which I call "indexical beliefs." ;Frege notes that someone can (...) believe that Hesperus is Hesperus without believing that Hesperus is Phosphorus. It is but a short step from Frege's observation to the claim that the sentence "A believes that Hesperus is Hesperus" could be true while "A believes that Hesperus is Phosphorus" is false. Quine has insisted that we cannot address this problem by taking either of these sentences to express a predication of the referent of both names, the planet Venus, as then both sentences would express the same predication of the same object, and this stands in evident tension with the fact that they can differ in truth value. In a recent response to Frege's problem, Mark Richard has taken exactly the route Quine has warned against. In my first chapter, I show that Richard's response is unsuccessful. I then consider the implications of the failure of his response on his proposed semantics for belief and the philosophical motivation he provides for it. I argue that his semantics for belief ascriptions stands in serious tension with its purported philosophical motivation. ;In the second and third chapters, I turn to the problem about indexical belief. The task of the second chapter is to identify this problem. To this end, I consider three of John Perry's arguments that the traditional picture of belief cannot accommodate indexical belief. I show that even if these arguments are sound, they give us no reason to think that the problem about indexical belief is in any way unique. I then suggest that there is a special problem about indexical belief, despite the failure of these three arguments to isolate it. Special difficulties attend an account of what it is to retain a tensed belief over time, and I suggest that the special problem about indexical belief is, in brief, a generalization of this problem about retention of tensed belief. ;In the third chapter, I raise the problem about indexical belief in a new way, as arising from a tension between several intuitively plausible claims about the relationship between beliefs and desires, on the one hand, and actions, on the other. This presentation of the problem brings out how the problem is special. I survey several solutions to this problem, including one due to Perry. I then argue that Perry's solution cannot characterize the specific kind of similarity between the beliefs of two different people who share an indexical belief. It allows too much to count as shared indexical belief. Thus Perry's solution inadequately addresses what I have suggested is the unique problem about indexical belief. Finally, I suggest that Frege's response to the problem I raise points the way towards an emendation of Perry's account that will enable it to suitably characterize the special way in which different people can share an indexical belief. (shrink)

In contrast to standard possible worlds semantics, possible worlds in a two-dimensional semantic framework play two kinds of roles, rather than just one. This allows the framework to assign two kinds of intensions to expressions, rather than just one. Its fruitful use in explicating modal operators and the meanings of referential expressions like indexicals has led to two-dimensional accounts that seek to revive the Fregean conception of meaning, or more specifically the descriptivist view of reference, which has fallen into disrepute (...) due to intense criticisms, most famously, by Saul Kripk’s seminal work Naming and Necessity (1972). This entry provides a critical overview of the two most prominent of such accounts, proposed by Frank Jackson and David Chalmers. Unfortunately, there is not space to describe either account in detail, so I rely largely on brief descriptions and plenty of references to primary and secondary sources. More importantly, I rely on focusing on how the accounts explain the phenomenon of necessary a posteriori identity that Kripke’s well-known examples (such as ‘Hesperus is Phosphorus’) have brought to light. Focusing on and structuring our discussions around this phenomenon is by no means just an expository convenience. These cases are of central importance in themselves. They epitomize a large part of the contribution of Naming and Necessity to the theory of reference. This is why section 2 outlines Kripke’s critique of the Fregean theory of referential expressions and section 3 explains rigid designation and identity statements. Section 4 discusses rigidification and the notion of a world considered as actual, leading to the introduction of two-dimensional functions in Section 5. I discuss, finally, Frank Jackson’s and David Chalmers’ two-dimensionalism in Sections 6 and 7. Section 8 makes a few critical remarks on Jackson’s handling of the semantic argument. I conclude (Section 8) by discussing the important distinction between semantics and metasemantics. (shrink)