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All the ideas for 'Issues of Pragmaticism', 'Mathematics without Numbers' and 'The Emergence of Probability'

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12 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Gassendi is the first great empiricist philosopher [Hacking]
     Full Idea: Gassendi is the first in the great line of empiricist philosophers that gradually came to dominate European thought.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.5)
     A reaction: Epicurus, of course, was clearly an empiricist. British readers should note that Gassendi was not British.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
     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.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
     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'?
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
     Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
     A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
     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.
     From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
     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?
10. Modality / B. Possibility / 6. Probability
Probability was fully explained between 1654 and 1812 [Hacking]
     Full Idea: There is hardly any history of probability to record before Pascal (1654), and the whole subject is very well understood after Laplace (1812).
     From: Ian Hacking (The Emergence of Probability [1975], Ch.1)
     A reaction: An interesting little pointer on the question of whether the human race is close to exhausting all the available intellectual problems. What then?
Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking]
     Full Idea: Probability has two aspects: the degree of belief warranted by evidence, and the tendency displayed by some chance device to produce stable relative frequencies. These are the epistemological and statistical aspects of the subject.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.1)
     A reaction: The most basic distinction in the subject. Later (p.124) he suggests that the statistical form (known as 'aleatory' probability) is de re, and the other is de dicto.
Epistemological probability based either on logical implications or coherent judgments [Hacking]
     Full Idea: Epistemological probability is torn between Keynes etc saying it depends on the strength of logical implication, and Ramsey etc saying it is personal judgement which is subject to strong rules of internal coherence.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.2)
     A reaction: See Idea 7449 for epistemological probability. My immediate intuition is that the Ramsey approach sounds much more plausible. In real life there are too many fine-grained particulars involved for straight implication to settle a probability.
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
In the medieval view, only deduction counted as true evidence [Hacking]
     Full Idea: In the medieval view, evidence short of deduction was not really evidence at all.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.3)
     A reaction: Hacking says the modern concept of evidence comes with probability in the 17th century. That might make it one of the most important ideas ever thought of, allowing us to abandon certainties and live our lives in a more questioning way.
Formerly evidence came from people; the new idea was that things provided evidence [Hacking]
     Full Idea: In the medieval view, people provided the evidence of testimony and of authority. What was lacking was the seventeenth century idea of the evidence provided by things.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.4)
     A reaction: A most intriguing distinction, which seems to imply a huge shift in world-view. The culmination of this is Peirce's pragmatism, in Idea 6948, of which I strongly approve.
14. Science / A. Basis of Science / 3. Experiment
An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG]
     Full Idea: An experiment is a test (if T, then E implies R, so try E, and if R follows, T seems right), an adventure (no theory, but try things), a diagnosis (reading the signs), or a dissection (taking apart).
     From: report of Ian Hacking (The Emergence of Probability [1975], Ch.4) by PG - Db (ideas)
     A reaction: A nice analysis. The Greeks did diagnosis, then the alchemists tried adventures, then Vesalius began dissections, then the followers of Bacon concentrated on the test, setting up controlled conditions. 'If you don't believe it, try it yourself'.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking]
     Full Idea: Mathematics is the model for reasoning about necessary truths, but jurisprudence must be our model when we deliberate about contingencies.
     From: Ian Hacking (The Emergence of Probability [1975], Ch.10)
     A reaction: Interesting. Certainly huge thinking, especially since the Romans, has gone into the law, and creating rules of evidence. Maybe all philosophers should study law and mathematics?
19. Language / A. Nature of Meaning / 1. Meaning
The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce]
     Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol.
     From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1
     A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are.