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8698
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Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
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Full Idea:
The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
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From:
report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
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A reaction:
Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?
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10263
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Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
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Full Idea:
The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
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From:
comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
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A reaction:
I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?
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24071
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Markets are transparent, with known prices and activity, and minimal profits [Davies,W]
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Full Idea:
Markets are characterised by transparency. Prices are public, and all relevant activity is visible to everyone. And because of competition, profits are minimal, little more than a 'wage' for the seller.
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From:
William Davies (Review of 'The Price is Wrong' by B.Christophers [2024], 24-04-04)
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A reaction:
This account, from Braudel, is to distinguish markets from capitalism.
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24073
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Capitalists use their exceptional power to impose their own rules, and make the state their ally [Davies,W]
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Full Idea:
Capitalists exploit their unrivalled control over time and space in order to impose their rules on everyone else. …It triumphed late, only becoming dominant in the 19th century, when it had conscripted the state as its ally.
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From:
William Davies (Review of 'The Price is Wrong' by B.Christophers [2024], 24-04-04)
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A reaction:
This so very much makes sense of the modern world. Nowadays capitalists are so wealthy that the state has largely become their pawn, rather than their ally. Populist leaders are their puppets (and are well rewarded).
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24070
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Economies have material, economic and capitalist layers [Davies,W]
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Full Idea:
Braudel's economic history has three layers. At the bottom is material life of consumption, production, reproduction. Next is economic life of markets, of equals in exchange and competition. Top is capitalism, of opacity, monopoly, power, high profits.
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From:
William Davies (Review of 'The Price is Wrong' by B.Christophers [2024], 24-04-04)
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A reaction:
The point Davies emphasises here is the sharp distinction between the market economy and capitalism.
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24074
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Capitalism must mainly rely either on the labour market, or on the financial markets [Davies,W]
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Full Idea:
According to Marxists, the one market capitalism cannot do without is the labour market, which creates saleable things. Others, influenced by Keynes, emphasise financial markets, where pieces of paper change hands on expectation of their value.
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From:
William Davies (Review of 'The Price is Wrong' by B.Christophers [2024], 24-04-04)
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A reaction:
Modern Britain fits the Keynesian account much better, given its low production, and very active (until recently) London financial market.
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24072
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Capitalism is the anti-market, with opacity, monopolies, powers, exceptional profits and wealth [Davies,W]
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Full Idea:
Braudel sees capitalism as the 'anti-market': a world of opacity, monopoly, concentration of power and wealth, and the exceptional profits that can be achieved only by escaping the norms of 'economic life'.
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From:
William Davies (Review of 'The Price is Wrong' by B.Christophers [2024], 24-04-04)
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A reaction:
Given all the talk about the wonders of the 'free market' from right-wingers, this passage came as a revelation to me. Capitalists all dream of a monopoly, which is precisely the destruction of a market.
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19384
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Space and time are the order of all possibilities, and don't just relate to what is actual [Leibniz]
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Full Idea:
Space and time taken together constitute the order of possibilities of the one entire universe, so that these orders relate not only to what actually is, but also to anything that could be put in its place.
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From:
Gottfried Leibniz (Reply to 'Rorarius' 2nd ed [1702], GP iv 568), quoted by Richard T.W. Arthur - Leibniz 7 'Space and Time'
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A reaction:
A very nice idea. Rather like the 'space of reasons', where all rational thought must exist, space and time are the 'space of existence and action'. Their concepts involve more than relations between what actually exists.
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