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9987
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An aggregate in which order does not matter I call a 'set' [Bolzano]
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Full Idea:
An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'.
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From:
Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX
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A reaction:
The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate.
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11175
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Logical concepts rest on certain inferences, not on facts about implications [Fine,K]
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Full Idea:
The nature of the logical concepts is given, not by certain logical truths, but by certain logical inferences. What properly belongs to disjunction is the inference from p to (p or q), rather than the fact that p implies (p or q).
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From:
Kit Fine (Senses of Essence [1995], §3)
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A reaction:
Does this mean that Fine is wickedly starting with the psychology, rather than with the pure truth of the connection? Frege is shuddering. This view seems to imply that the truth table for 'or' is secondary.
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11176
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The property of Property Abstraction says any suitable condition must imply a property [Fine,K]
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Full Idea:
According to the principle of Property Abstraction, there is, for any suitable condition, a property that is possessed by an object just in case it conforms to the condition. This is usually taken to be a second-order logical truth.
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From:
Kit Fine (Senses of Essence [1995], §4)
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A reaction:
Fine objects that it is implied that if Socrates is essentially a man, then he essentially has the property of being a man. Like Fine, I think this conclusion is distasteful. A classification is not a property, at least the way most people use 'property'.
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11173
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Being a man is a consequence of his essence, not constitutive of it [Fine,K]
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Full Idea:
If we distinguish 'constitutive' from 'consequential' essence, ..then the essence of Socrates will, in part, be constituted by his being a man. But being a man (or a mountain) will merely be consequential upon, and not constitutive of, his essence.
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From:
Kit Fine (Senses of Essence [1995], §3)
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A reaction:
Yes yes yes. I think it is absurd to say that the class to which something belongs is part of its essential nature, given that it presumably can only belong to the class if it already has a certain essential nature. What did Frankenstein construct?
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11179
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If there are alternative definitions, then we have three possibilities for essence [Fine,K]
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Full Idea:
If there are alternative definitions for an essence, we must distinguish three notions. There is the essence as the manifold (the combined definitions), or as the range of alternative definitions (with component essences), or there is the common essence.
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From:
Kit Fine (Senses of Essence [1995], §8)
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A reaction:
Fine opts for the third alternative (what the definitions all have in common) as the best account. He says (p.68) 'definitive' properties come from one definition, and 'essential' properties from every possible definition.
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14014
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Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]
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Full Idea:
Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
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From:
Hermann Minkowski (Space and Time [1908], Intro)
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A reaction:
Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality
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