Foundational Ideas on Paradox Analysis

a paradox is a claim that seems strange, but has an argument to support it Consider: standing is more tiring than walking working out (say, doing yoga) is more restful than sitting around theres a person who is 21 years old, but has had only five birthdays there can be no barber (in some town) who shaves all and only those who do not shave themselves analysis is a method of investigation whereby one thing is broken down to reveal its constituent parts seeing what these parts are and how they make up the original whole is supposed to provide insight into that original thing conceptual analysis is the activity of analyzing concepts this activity reveals what have come to be known as the paradoxes of analysis a concept is the mental means whereby one recognizes and differentiates a certain kind of thing concepts are crucial to ones understanding the world, to dividing it up in certain ways and organizing it a conceptual framework is a system of concepts that characterizes how the world is (or, at least, is taken to be) concepts have traditionally been associated with certain expressions of ones language, with predicates like is a brother or with terms like cat what exactly concepts are is hard to say maybe mental images, set of conditions, an ability here is a simple example of conceptual analysis consider the term vixen or the predicate is a vixen one might propose to analyze the concept associated with these terms in the following way: a vixen is a female fox here: the concept of vixen is the analysandum, the thing to be analyzed the plural of analysandum is analysanda

here: the concept of female fox is the analysans, the thing providing the analysis the plural of analysans is analysantia the significance of analysis is that it reveals ones conceptual framework a concept is sometimes taken to be the meaning of a kind term or a predicate the idea of meaning is pretty complicated to get a sense of this, one might take the meaning of a predicate to be all the things that that predicate applies to, i.e., the extension of the predicate or one might take the meaning of a predicate to be the criterion (or rule) that determines what that predicate applies to, i.e., the intension of the predicate here, perhaps the intension can be thought of as a bunch of conditions this distinction is important, consider the term Ithere are various contenders for the meaning of this term a proposition is a non-linguistic, abstract, representational object the contentperhaps meaningof a declarative sentence, named in English by that- clauses, the primary bearer of truth or falsity e.g. that the tree is green, that my door is closed, that my desk is brown a propositional attitude is a way of taking a proposition e.g. belief, doubt, fear, hope a propositional attitude context is a linguistic expression of a subjects propositional attitude(s) e.g. Roxanne believes that the sun is shining Ashley fears that the pandemic will continue into next year expressions can be substituted salva veritate in a context if the substitution never changes the truth-value of the proposition expressed Consider: Superman = Clark Kent, two names for the same person, to wit, Superman and Clark Kent These expressions can be substituted salva veritate in some contexts, but not others For example, Superman picked up the car (True) Clark Kent picked up the car (True) Lois believed that Superman picked up the car (True) Lois believed that Clark Kent picked up the car (False)

Often, terms cannot be substituted salva veritate in propositional attitude contexts