Combining Texts

All the ideas for 'fragments/reports', 'Logicism, Some Considerations (PhD)' and 'Fact, Fiction and Forecast (4th ed)'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

10 ideas

5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention

12394	If the result is bad, we change the rule; if we like the rule, we reject the result [Goodman]
	Full Idea: A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend.
	From: Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954], p.64)
	A reaction: This is clearly in tune with Quine's assertion that logic is potentially revisable, and the idea is pragmatist in spirit. It is hard to deny that intuitions about what makes a good argument control our logic. I say the world controls our intuitions.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

13412	Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
	Full Idea: Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
	A reaction: Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.

13413	We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
	Full Idea: Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
	A reaction: This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

13411	If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
	Full Idea: If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
	A reaction: It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

13415	An adequate account of a number must relate it to its series [Benacerraf]
	Full Idea: No account of an individual number is adequate unless it relates that number to the series of which it is a member.
	From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169)
	A reaction: Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism.

8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions

14292	Dispositions seem more ethereal than behaviour; a non-occult account of them would be nice [Goodman]
	Full Idea: Dispositions of a thing are as important to us as overt behaviour, but they strike us by comparison as rather ethereal. So we are moved to enquire whether we can bring them down to earth, and explain disposition terms without reference to occult powers.
	From: Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954], II.3)
	A reaction: Mumford quotes this at the start of his book on dispositions, as his agenda. I suspect that the 'occult' aspect crept in because dispositions were based on powers, and the dominant view was that these were the immediate work of God.

13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention

1556	By nature people are close to one another, but culture drives them apart [Hippias]
	Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature.
	From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8

14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem

18749	Goodman argued that the confirmation relation can never be formalised [Goodman, by Horsten/Pettigrew]
	Full Idea: Goodman constructed arguments that purported to show that a satisfactory syntactic analysis of the confirmation relation can never be found. In response, philosophers of science tried to model it in probabilistic terms.
	From: report of Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 4
	A reaction: I take this idea to say that Bayesianism was developed in response to the grue problem. This is an interesting light on 'grue', which never bothered me much. The point is it scuppered formal attempts to model induction.

17646	Goodman showed that every sound inductive argument has an unsound one of the same form [Goodman, by Putnam]
	Full Idea: Goodman has shown that no purely formal criterion can distinguish arguments that are intuitively sound inductive arguments for unsound ones: for every sound one there is an unsound one of the same form. The predicates in the argument make the difference.
	From: report of Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954]) by Hilary Putnam - Why there isn't a ready-made world 'Causation'
	A reaction: This is to swallow grue whole. I think a bit more chewing is called for. By this date Putnam strikes me as a crazy relativist who has lost his grip on the world. Note the word 'formal' - but Putnam seems to think the argument is important.

26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities

4794	We don't use laws to make predictions, we call things laws if we make predictions with them [Goodman]
	Full Idea: Rather than a sentence being used for prediction because it is a law, it is called a law because it is used for prediction.
	From: Nelson Goodman (Fact, Fiction and Forecast (4th ed) [1954], p.21), quoted by Stathis Psillos - Causation and Explanation §5.4
	A reaction: This smacks of dodgy pragmatism, and sounds deeply wrong. The perception of a law has to be prior to making the prediction. Why do we make the prediction, if we haven't spotted a law. Goodman is mesmerised by language instead of reality.