Citations of:
Platonism in the Philosophy of Mathematics
In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (2009)
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Olszewski claims that the ChurchTuring thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turingcomputable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being right twice (...) 

Meinongians in general, and Routley in particular, subscribe to the principle of the independence of Sosein from Sein. In this paper, I put forward an interpretation of the independence principle that philosophers working outside the Meinongian tradition can accept. Drawing on recent work by Stephen Yablo and others on the notion of subject matter, I offer a new account of the notion of Sosein as a subject matter and argue that in some cases Sosein might be independent from Sein. The (...) 

***Platão ou Platonismo. Um tópico em dialética descendente***A ontologia dialética pode ser reconstruída percorrendo dois caminhos complementares. A via ascendente parte da influência da ontologia de Platão, mediada por Nicolau de Cusa, sobre Bertalanffy, o fundador da teoria de sistemas. Esta abordagem teórica, uma vez convergindo com o darwinismo, dará nascimento à teoria dos sistemas adaptativos complexos e logo se espalhará pelas diversas ciências, transmudandose de uma ontologia regional em parte relevante de uma nova ontologia geral. O caminho descendente, a (...) 

Many philosophers posit abstract entities – where something is abstract if it is acausal and lacks spatiotemporal location. Theories, types, characteristics, meanings, values and responsibilities are all good candidates for abstractness. Such things raise an epistemological puzzle: if they are abstract, then how can we have any epistemic access to how they are? If they are invisible, intangible and never make anything happen, then how can we ever discover anything about them? In this article, I critically examine epistemological objections to (...) 

A solution to the question "Why is there something rather than nothing?" is proposed that also entails a proposed solution to the question "Why does a thing exist?". In brief, I propose that a thing exists if it is a grouping. A grouping ties stuff together into a unit whole and, in so doing, defines what is contained within that new unit whole. The grouping is physically or mentally present and is visually seen as an edge, boundary, or enclosing surface (...) 

The platonism/nominalism debate in the philosophy of mathematics concerns the question whether numbers and other mathematical objects exist. Platonists believe the answer to be in the positive, nominalists in the negative. According to nonfactualists, the question is ‘moot’, in the sense that it lacks a correct answer. Elaborating on ideas from Stephen Yablo, this article articulates a nonfactualist position in the philosophy of mathematics and shows how the case for nonfactualism entails that standard arguments for rival positions fail. In particular, (...) 

Contemporary philosophers of mathematics are deadlocked between two alternative ontologies for numbers: Platonism and nominalism. According to contemporary mathematical Platonism, numbers are real abstract objects, i.e. particulars which are nonetheless “wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal.” While this view does justice to intuitions about numbers and mathematical semantics, it leaves unclear how we could ever learn anything by mathematical inquiry. Mathematical nominalism, by contrast, holds that numbers do not exist extramentally, which raises difficulties about how mathematical statements could be (...) 

The core idea of social constructivism in mathematics is that mathematical entities are social constructs that exist in virtue of social practices, similar to more familiar social entities like institutions and money. Julian C. Cole has presented an institutional version of social constructivism about mathematics based on John Searle’s theory of the construction of the social reality. In this paper, I consider what merits social constructivism has and examine how well Cole’s institutional account meets the challenge of accounting for the (...) 

Identity is ordinarily taken to be a relation defined on all and only objects. This consensus is challenged by Agustín Rayo, who seeks to develop an analogue of the identity sign that can be flanked by sentences. This paper is a critical exploration of the attempted generalization. First the desired generalization is clarified and analyzed. Then it is argued that there is no notion of content that does the desired philosophical job, namely ensure that necessarily equivalent sentences coincide in this (...) 

O desenvolvimento da filosofia acadêmica no Brasil é direcionada, entre vários fatores, pelas investigações dos diversos Grupos de Trabalho (GTs) da Associação Nacional de PósGraduação em Filosofia (ANPOF). Esses GTs se dividem de acordo com a temática investigada. O GT de Metafísica Analítica é relativamente novo e ainda tem poucos membros, mas os temas nele trabalhados são variados e todos centrais no debate metafísico contemporâneo internacional. A sua investigação se caracteriza pelo rigor lógico e conceitual com o qual aborda esses (...) 



Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the platonism–antiplatonism dispute and recent debates over (...) 

A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated  what is the truthmaker (...) 

Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an (...) 

