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14234
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If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
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Full Idea:
A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives').
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
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A reaction:
A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology.
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14237
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We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
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Full Idea:
Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
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A reaction:
[Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it.
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14246
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If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
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Full Idea:
If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1)
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A reaction:
Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application.
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14247
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Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
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Full Idea:
Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2)
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A reaction:
Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated.
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19451
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When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach]
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Full Idea:
When, submerged in deep reflection, you forget both yourself and your surroundings, is it you who controls reason, or is it rather reason that controls and absorbs you?
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From:
Ludwig Feuerbach (Introduction of 'Essence of Christianity' [1841], I)
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A reaction:
A delightful question, even if it looks like a false dichotomy. I'm not sure what to make of 'me', if my reason can be subtracted from it. Aquinas was one the same wavelength here.
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19450
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Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach]
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Full Idea:
Reason, love and power of will are perfections of man; they are his highest powers, his absolute essence in so far as he is man, the purpose of his existence. Man exists in order to think, love and will.
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From:
Ludwig Feuerbach (Introduction of 'Essence of Christianity' [1841], I)
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A reaction:
Feuerbach was a notable atheist, but adopts a religious style of language which modern atheists would find rather alien. Personally I love talk of ideals and perfections. Ideals have been discredited in modern times, but need a revival.
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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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19454
|
A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach]
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Full Idea:
The concept of God depends on the concepts of justice, kindness and wisdom - a God who is not kind, not just, and not wise is no God. But these concepts do not depend on the concept of God. That a quality is possessed by God does not make it divine.
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From:
Ludwig Feuerbach (Introduction of 'Essence of Christianity' [1841], II)
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A reaction:
This is part of Feuerbach's argument for atheism, but if you ask for the source of our human concepts of justice, kindness and wisdom, no one, I would have thought, could cite God for the role.
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19453
|
If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach]
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Full Idea:
If love, goodness, and personality are human determinations, the being which constitutes their source and ...their presupposition is also an anthropomorphism; so is the existence of God.
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From:
Ludwig Feuerbach (Introduction of 'Essence of Christianity' [1841], II)
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A reaction:
It is certainly a struggle for the imagination to grasp a being which is characterised by idealised versions of human virtues, and yet has an intrinsic nature which is utterly different from humanity.
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