9978
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Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
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Full Idea:
The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], IV)
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A reaction:
The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant.
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9986
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The null set was doubted, because numbering seemed to require 'units' [Tait]
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Full Idea:
The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets).
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], IX)
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A reaction:
This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely!
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9984
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We can have a series with identical members [Tait]
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Full Idea:
Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)?
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], VII)
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A reaction:
The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature?
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11115
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'All horses' either picks out the horses, or the things which are horses [Jubien]
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Full Idea:
Two ways to see 'all horses are animals' are as picking out all the horses (so that it is a 'horse-quantifier'), ..or as ranging over lots of things in addition to horses, with 'horses' then restricting the things to those that satisfy 'is a horse'.
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From:
Michael Jubien (Analyzing Modality [2007], 2)
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A reaction:
Jubien says this gives you two different metaphysical views, of a world of horses etc., or a world of things which 'are horses'. I vote for the first one, as the second seems to invoke an implausible categorical property ('being a horse'). Cf Idea 11116.
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9982
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Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
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Full Idea:
Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], V)
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A reaction:
[compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set.
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9985
|
Abstraction may concern the individuation of the set itself, not its elements [Tait]
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Full Idea:
A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], VIII)
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A reaction:
If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm.
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9980
|
If abstraction produces power sets, their identity should imply identity of the originals [Tait]
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Full Idea:
If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects.
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From:
William W. Tait (Frege versus Cantor and Dedekind [1996], V)
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A reaction:
An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features.
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7339
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Because human life is what is sacred, Mosaic law has no death penalty for property violations [Johnson,P]
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Full Idea:
Where other codes provided the death penalty for offences against property, in Mosaic law no property offence is capital; human life is too sacred, where the rights of property alone are violated.
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From:
Paul Johnson (The History of the Jews [1987], Pt I)
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A reaction:
We still preserve this idea in our law, and also in our culture, where we are keen to insist that catastrophes like earthquakes or major fires are measured almost entirely by the loss of life, not the loss of property. I approve.
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7353
|
The Pharisees undermined slavery, by giving slaves responsibility and status in law courts [Johnson,P]
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Full Idea:
It is no accident that slavery among Jews disappeared with the rise of the Pharisees, as they insisted that all were equal before God in a court. Masters were no longer responsible for actions of slaves, so a slave had status, and slavery could not work.
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From:
Paul Johnson (The History of the Jews [1987], Pt II)
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A reaction:
As in seventeenth century England, the rise of social freedom comes from religious sources, not social sources. A slave has status in the transcendent world of souls, despite being a nobody in the physical world.
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7340
|
Mosaic law was the first to embody the rule of law, and equality before the law [Johnson,P]
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Full Idea:
Mosaic law meant that God ruled through his laws, and since all were equally subject to the law, the system was the first to embody the double merits of the rule of law and equality before the law.
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From:
Paul Johnson (The History of the Jews [1987], Pt I)
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A reaction:
If this is correct, it seems to be a hugely important step, combined with Idea 1659, that revenge should be the action of a the state, not of the individual. They are the few simple and essential keys to civilization.
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7338
|
Man's life is sacred, because it is made in God's image [Johnson,P]
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Full Idea:
In Mosaic theology, man is made in God's image, and so his life is not just valuable, it is sacred.
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From:
Paul Johnson (The History of the Jews [1987], Pt I)
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A reaction:
The obvious question is what exactly is meant by "in God's image". Physically, spiritually, intellectually, morally? I am guessing that the original idea was intellectual, because we are the only rational animal. The others seem unlikely, or arrogant.
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7355
|
The Torah pre-existed creation, and was its blueprint [Johnson,P]
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Full Idea:
The Torah was not just a book about God. It pre-existed creation, in the same way as God did. In fact, it was the blueprint of creation.
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From:
Paul Johnson (The History of the Jews [1987], Pt III)
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A reaction:
You can only become a 'people of the book' (which Moslems resented in Judaism, and then emulated) if you give this stupendously high status to your book. Hence Christian fundamentalism makes sense, with its emphasis on the divinity of the Bible.
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7336
|
A key moment is the idea of a single moral God, who imposes his morality on humanity [Johnson,P]
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Full Idea:
The discovery of monotheism, and not just of monotheism but of a sole, omnipotent God actuated by ethical principles and seeking methodically to impose them on human beings, is one of the greatest turning-points in history, perhaps the greatest of all.
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From:
Paul Johnson (The History of the Jews [1987], Pt I)
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A reaction:
'Discovery' begs some questions, but when put like this you realise what a remarkable event it was. It is a good candidate for the most influential idea ever, even if large chunks of humanity, especially in the orient, never took to monotheism.
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7341
|
Sampson illustrates the idea that religious heroes often begin as outlaws and semi-criminals [Johnson,P]
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Full Idea:
Sampson is the outstanding example of the point which the Book of Judges makes again and again, that the Lord and society are often served by semi-criminal types, outlaws and misfits, who become folk-heroes and then religious heroes.
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From:
Paul Johnson (The History of the Jews [1987], Pt I)
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A reaction:
This illustrates nicely Nietzsche's claim, that the jews were responsible for his 'inversion of values', in which aristocratic virtues are downgraded, and the virtues of a good slave are elevated (though Sampson may not show that point so well!).
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7344
|
Judaism involves circumcision, Sabbath, Passover, Pentecost, Tabernacles, New Year, and Atonement [Johnson,P]
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Full Idea:
The practices of Judaism developed during their Exile: circumcision, the Sabbath, the Passover (founding of the nation), Pentecost (giving of the laws), the Tabernacles, the New Year, and the Day of Atonement.
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From:
Paul Johnson (The History of the Jews [1987], Pt II)
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A reaction:
These were the elements of ritual created to replace the existence of a physically located state. An astonishing achievement, not even remotely achieved by any other state that was driven off its lands. A culture is an idea, not a country.
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7347
|
Zoroastrians believed in one eternal beneficent being, Creator through the holy spirit [Johnson,P]
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Full Idea:
Cyrus the Great was a Zoroastrian, believing in one, eternal, beneficent being, 'Creator of all things through the holy spirit'.
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From:
Paul Johnson (The History of the Jews [1987], Pt II)
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A reaction:
Is this the actual origin of monotheism, or did they absorb this idea from the Jews? The interesting bit is the fact that the supreme being (called Marduk) is 'beneficent', which one doesn't associate with these remote and supposed pagans.
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7349
|
Immortality based on judgement of merit was developed by the Egyptians (not the Jews) [Johnson,P]
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Full Idea:
The idea of judgement at death and immortality on the basis of merit were developed in Egypt before 1000 BCE. It is not Jewish because it was not in the Torah, and the Sadducees, who stuck to their texts, seemed to have denied the afterlife completely.
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From:
Paul Johnson (The History of the Jews [1987], Pt II)
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A reaction:
This is the idea considered crucial to religion by Immanuel Kant (Idea 1455), who should be declared an honorary Egyptian. To me the idea that only the good go to heaven sounds like sadly wishful thinking - a fictional consolation for an unhappy life.
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