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10007
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Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
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Full Idea:
Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
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A reaction:
This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008.
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10002
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'2 + 2 = 4' can be read as either singular or plural [Hofweber]
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Full Idea:
There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four').
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1)
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A reaction:
Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers.
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9998
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What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
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Full Idea:
There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related?
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1)
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A reaction:
A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first?
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10003
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Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
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Full Idea:
Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2)
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A reaction:
His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects.
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10008
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Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
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Full Idea:
I argue for an internalist conception of arithmetic. Arithmetic is not about a domain of entities, not even quantified entities. Quantifiers over natural numbers occur in their inferential-role reading in which they merely generalize over the instances.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
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A reaction:
Hofweber offers the hope that modern semantics can disentangle the confusions in platonist arithmetic. Very interesting. The fear is that after digging into the semantics for twenty years, you find the same old problems re-emerging at a lower level.
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10005
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Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
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Full Idea:
That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2)
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A reaction:
This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them.
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10000
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We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
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Full Idea:
Determiner uses of number words may disappear on analysis. This is inspired by Russell's elimination of the word 'the'. The number becomes blocks of first-order quantifiers at the level of semantic representation.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2)
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A reaction:
[compressed] The proposal comes from platonists, who argue that numbers cannot be analysed away if they are objects. Hofweber says the analogy with Russell is wrong, as 'the' can't occur in different syntactic positions, the way number words can.
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10006
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First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
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Full Idea:
Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
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A reaction:
This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting.
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8147
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We have an apparent and a true self; only the second one exists, and we must seek to know it [Anon (Upan)]
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Full Idea:
There are two selves, the apparent self, and the real Self. Of these it is the real Self (Atman), and he alone, who must be felt as truly existing. To the man who has felt him as truly existing he reveals his innermost nature.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Katha')
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A reaction:
A central Hindu doctrine against which Buddhism rebelled, by denying the self altogether. I prefer the Hindu view. A desire to abandon the self just seems to be a desire for death. Knowledge of our essential self is more interesting. But see Idea 2932!
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8155
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Without speech we cannot know right/wrong, true/false, good/bad, or pleasant/unpleasant [Anon (Upan)]
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Full Idea:
If there were no speech, neither right nor wrong would be known, neither the true nor the false, neither the good nor the bad, neither the pleasant nor the unpleasant.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Chandogya')
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A reaction:
This could stand as the epigraph for the whole of modern philosophy of language. However, the text goes on to say that mind is higher than speech. The test question is the mental capabilities of animals. Do they 'know' pleasure, or truth?
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8153
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By knowing one piece of clay or gold, you know all of clay or gold [Anon (Upan)]
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Full Idea:
By knowing one lump of clay, all things made of clay are known; by knowing a nugget of gold, all things made of gold are known.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Chandogya')
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A reaction:
I can't think of a better basic definition of a natural kind. There is an inductive assumption, of course, which hits trouble when you meet fool's gold, or two different sorts of jade. But the concept of a natural kind is no more than this.
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8154
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Originally there must have been just Existence, which could not come from non-existence [Anon (Upan)]
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Full Idea:
In the beginning there was Existence, One only, without a second. Some say that in the beginning there was non-existence only, and that out of that the universe was born. But how could such a thing be? How could existence be born of non-existence?
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Chandogya')
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A reaction:
A very rare instance of an argument in the Upanishads, arising out of a disagreement. The monotheistic religions have preferred to make God the eternal element, presumably because that raises his status, but is also explains the start as a decision.
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8148
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Brahma, supreme god and protector of the universe, arose from the ocean of existence [Anon (Upan)]
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Full Idea:
Out of the infinite ocean of existence arose Brahma, first-born and foremost among the gods. From him sprang the universe, and he became its protector.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Mundaka')
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A reaction:
Brahma does not have eternal (or necessary) existence. Could Brahma cease to exist? I suppose we cannot ask what caused the appearance of Brahma? Is it part of a plan, or just luck, or some sort of necessity?
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8152
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Earth, food, fire, sun are all forms of Brahman [Anon (Upan)]
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Full Idea:
Earth, food, fire, sun - all these that you worship - are forms of Brahman.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Chandogya')
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A reaction:
In 'Taittiriya' food is named as the "chief of all things". Pantheism seems to arise from a desire that one's god should have every conceivable good, so in addition to power and knowledge, your god must keep you warm and healthy.
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8156
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The gods are not worshipped for their own sake, but for the sake of the Self [Anon (Upan)]
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Full Idea:
It is not for the sake of the gods, my beloved, that the gods are worshipped, but for the sake of the Self (Atman).
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Brihadaranyaka')
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A reaction:
There is an uneasy selfish streak in all religions, which conflicts with their exhorations to altruism, and to the love of the gods. It also occurs in the exhortation of Socrates to be virtuous. 'Pure' altruism seems only to arise in the 18th century.
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8157
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A man with desires is continually reborn, until his desires are stilled [Anon (Upan)]
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Full Idea:
A man acts according to desires; after death he reaps the harvest of his deeds, and returns again to the world of action. Thus he who has desires continues subject to rebirth, but he in who desire is stilled suffers no rebirth.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Brihadaranyaka')
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A reaction:
I greatly prefer the Stoic idea (Idea 3066) that we should live according to nature, to this perverse longing to completely destroy our own nature and become something we are not. Play the cards you are dealt, which include desires.
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8150
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The immortal Self and the sad individual self are like two golden birds perched on one tree [Anon (Upan)]
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Full Idea:
Like two birds of golden plumage, the individual self and the immortal Self perch on the branches of the same tree. The individual self, deluded by forgetfulness of his identity with the divine self, bewildered by his ego, grieves and is sad.
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From:
Anon (Upan) (The Upanishads [c.950 BCE], 'Mundaka')
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A reaction:
Hinduism gives a much clearer and bolder picture of the soul than Christianity does. I don't see much consolation in the immortality of the wonderful Self, if my individual self is doomed to misery and extinction. Which one is me?
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