相关论文: On Kinds of Indiscernibility in Logic and Metaphys…
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This…
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…
The dual character of invariance under transformations and definability by some operations has been used in classical work by for example Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves…
There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown…
The central focus is on clarifying the distinction between sets and proper classes. To this end we identify several categories of concepts (surveyable, definite, indefinite), and we attribute the classical set theoretic paradoxes to a…
We prove a category-theoretic independence theorem for four fundamental notions: meaning, object, name, and existence. Working in a Lawvere-style categorical semantics and in particular in toposes, we show that these notions occupy distinct…
The Univalence Principle is the statement that equivalent mathematical structures are indistinguishable. We prove a general version of this principle that applies to all set-based, categorical, and higher-categorical structures defined in a…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…
This article explores the following methodological principle for theory construction in physics: if an ontological theory predicts two scenarios that are ontologically distinct but empirically indiscernible, then this theory should be…
Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete…
The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of…
This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially…
When people share the same documents and observations yet reach different conclusions, the disagreement often shifts into a judgment that the other party is cognitively defective, irrational, or acting in bad faith. This paper argues that…
Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…