Combining Texts

All the ideas for 'The Problem of Empty Names', 'Varieties of Ontological Dependence' and 'Remarks on the Foundations of Mathematics'

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11 ideas

2. Reason / D. Definition / 4. Real Definition
Real definitions don't just single out a thing; they must also explain its essence [Koslicki]
     Full Idea: A statement expressing a real definition must also accomplish more than simply to offer two different ways of singling out the same entity, since the definiens must also be explanatory of the essential nature of the definiendum.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4)
     A reaction: This is why Aristotelian definitions are not just short lexicographical definitions, but may be quite length. Effectively, a definition IS an explanation.
3. Truth / H. Deflationary Truth / 1. Redundant Truth
'It is true that this follows' means simply: this follows [Wittgenstein]
     Full Idea: The proposition: "It is true that this follows from that" means simply: this follows from that.
     From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6
     A reaction: Presumably this remark is simply expressing Wittgenstein's later agreement with the well-known view of Ramsey. Early Wittgenstein had endorsed a correspondence view of truth.
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
     Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible.
     From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4
     A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
     Full Idea: Being the successor of the successor of 0 is more explanatory than being predecessor of 3 of the nature of 2, since it mirrors more closely the method by which 2 is constructed from a basic entity, 0, and a relation (successor) taken as primitive.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4)
     A reaction: This assumes numbers are 'constructed', which they are in the axiomatised system of Peano Arithmetic, but presumably the numbers were given in ordinary experience before 'construction' occurred to anyone. Nevertheless, I really like this.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Two and one making three has the necessity of logical inference [Wittgenstein]
     Full Idea: "But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference? - Yes! it is the same.
     From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6
     A reaction: This need not be a full commitment to logicism - only to the fact that the inferential procedures in mathematics are the same as those of logic. Mathematics could still have further non-logical ingredients. Indeed, I think it probably does.
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
     Full Idea: The relata of the grounding relation are typically taken to be facts or propositions, while the relata of ontological dependence ...are objects and their characteristics, activities, constituents and so on.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.5 n25)
     A reaction: Interesting. Good riddance to propositions here, but this seems a bit unfair to facts, since I take facts to be in the world. Audi's concept of 'worldly facts' is what we need here.
9. Objects / D. Essence of Objects / 2. Types of Essence
Modern views want essences just to individuate things across worlds and times [Koslicki]
     Full Idea: According to the approach of Plantinga, Forbes and Mackie, the primary job of essences is to individuate the entities whose essences they are across worlds and times at which these entities exist.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4 n13)
     A reaction: A helpful simplification of what is going on. I wish those authors would just say this one their first pages. They all get in a right tangle, because individuation is either too easy, or hopeless. 'Tracking' is a good word for this game.
9. Objects / D. Essence of Objects / 4. Essence as Definition
For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
     Full Idea: Fine assumes that essences can be identified with collections of propositions that are true in virtue of the identity of a particular object, or objects. ...There is not, on this approach, much of a distinction between essences and real definitions.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4)
     A reaction: This won't do, because the essence of a physical object is not a set of propositions, it is some aspects of the object itself, which are described in a definition. Koslicki notes that psuché is an essence, and the soul is hardly a set of propositions!
We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki]
     Full Idea: To make room for a less propositional conception of essence than that assumed by Fine, I urge that we distinguish more firmly between essences and real definitions (which state these essences in the form of propositions).
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.6)
     A reaction: Yes. The idea that essence is just a verbal or conceptual entity would be utterly abhorrent to Aristotle (a hero for Fine), and it is anathema to me too. We intend essences to be in the world (even if we are deceived about that). They explain!
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
A good explanation captures the real-world dependence among the phenomena [Koslicki]
     Full Idea: It is plausible to think that an explanation, when successful, captures or represents (by argument, or a why? question) an underlying real-world relation of dependence which obtains among the phenomena cited.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.6)
     A reaction: She cites causal dependence as an example. I'm incline to think that 'grounding' is a better word for the target of good explanations than is 'dependence' (which can, surely, be mutual, where ground has the directionality needed for explanation).
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]
     Full Idea: In 'feature dependence', the ontologically dependent entity may be thought of as the result of a process of abstraction which takes the 'bearer' as its starting point and arrives at the abstracted entity by blocking out all the irrelevant features.
     From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.6)
     A reaction: She seems unaware that this is traditional abstraction, found in Aristotle, and a commonplace of thought until Frege got his evil hands on abstraction and stole it for other purposes. I'm a fan.