|
14234
|
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
|
|
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').
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
|
|
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.
|
|
14237
|
We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
|
|
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.
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
|
|
A reaction:
[Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it.
|
|
14246
|
If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
|
|
Full Idea:
If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics.
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1)
|
|
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.
|
|
14247
|
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
|
|
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.
|
|
From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2)
|
|
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.
|
|
7903
|
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
|
|
Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
|
|
From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
|
|
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').
|
|
7600
|
The Buddha believed the gods would eventually disappear, and Nirvana was much higher [Buddha, by Armstrong,K]
|
|
Full Idea:
The Buddha believed implicitly in the gods because they were part of his cultural baggage, but they were involved in the cycle of rebirth, and would eventually disappear; the ultimate reality of Nirvana was higher than the gods.
|
|
From:
report of Buddha (Siddhartha Gautama) (reports [c.540 BCE]) by Karen Armstrong - A History of God Ch.1
|
|
A reaction:
We might connect this with Plato's Euthyphro question (Ideas 336 and 337), and the relationship between piety and morality on the one hand, and the gods on the other.
|
|
7601
|
Life is suffering, from which only compassion, gentleness, truth and sobriety can save us [Buddha]
|
|
Full Idea:
Buddha taught that the only release from 'dukkha' (the meaningless flux of suffering which is human life) is a life of compassion for all living beings, speaking and behaving gently, kindly and accurately, and refraining from all intoxicants.
|
|
From:
Buddha (Siddhartha Gautama) (reports [c.540 BCE], Ch.1), quoted by Karen Armstrong - A History of God Ch.1
|
|
A reaction:
Christians are inclined to give the impression that Jesus invented the idea of being nice, but it ain't so. The obvious thought is that the Buddha seems to be focusing on the individual, but this is actually a formula for a better community.
|