Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'fragments/reports' and 'De Re Aedificatoria'

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11 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason

1813	All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]
	Full Idea: Twelfth mode: all reasoning leads on to further reasoning, and this process goes on forever.
	From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10

1811	Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]
	Full Idea: Fifteenth mode: proofs often presuppose the thing to be proved.
	From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10

1815	Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]
	Full Idea: Fourteenth mode: reasoning requires arbitrary faith in preliminary hypotheses.
	From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10

1812	All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]
	Full Idea: Eleventh mode: all topics of discussion are full of uncertainty and contradiction.
	From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10

2. Reason / D. Definition / 2. Aims of Definition

10528	Definitions concern how we should speak, not how things are [Fine,K]
	Full Idea: Our concern in giving a definition is not to say how things are by to say how we wish to speak
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
	A reaction: This sounds like an acceptable piece of wisdom which arises out of analytical and linguistic philosophy. It puts a damper on the Socratic dream of using definition of reveal the nature of reality.

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

10529	If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
	Full Idea: Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
	A reaction: This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.

10530	Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
	Full Idea: The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
	A reaction: I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8850	Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]
	Full Idea: Agrippa's Trilemma offers three possible outcomes for a regress of justification: the chain goes on for ever (infinite); or the chain stops at an unjustified proposition (arbitrary); or the chain eventually includes the original proposition (circular).
	From: report of Agrippa (fragments/reports [c.60], §2) by Michael Williams - Without Immediate Justification §2
	A reaction: This summarises Ideas 1911, 1913 and 1914. Agrippa's Trilemma is now a standard starting point for modern discussions of foundations. Personally I reject 2, and am torn between 1 (+ social consensus) and 3 (with a benign, coherent circle).

13. Knowledge Criteria / E. Relativism / 1. Relativism

1814	Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]
	Full Idea: Thirteenth mode: everything is always perceived in relation to something else.
	From: report of Agrippa (fragments/reports [c.60]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.10

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

10527	An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
	Full Idea: If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
	From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
	A reaction: I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.

21. Aesthetics / A. Aesthetic Experience / 4. Beauty

18555	The beautiful is that from which nothing can be subtracted and to which nothing can be added [Alberti]
	Full Idea: The beautiful is that from which nothing can be taken away and to which nothing can be added but for the worse.
	From: Leon Battista Alberti (De Re Aedificatoria [1485]), quoted by Roger Scruton - Beauty: a very short introduction 9
	A reaction: Scruton rejects this Platonic tradition of beauty as organic wholeness, because you can't say how it would be 'worse' without invoking beauty, which makes it circular. Scruton appears to be correct.