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All the ideas for 'Substance and Individuation in Leibniz', 'Review of Husserl's 'Phil of Arithmetic'' and 'Knowledge by Acquaintance and Description-1'

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29 ideas

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

9821	A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett]
	Full Idea: Frege expressly denies that a correct definition need capture the sense of the expression it defines: it need only get the reference right.
	From: report of Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.3
	A reaction: This might hit up against the renate/cordate problem, of two co-extensive concepts, where the definition gets the extension right, but the intension wrong.

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

9585	Since every definition is an equation, one cannot define equality itself [Frege]
	Full Idea: Since every definition is an equation, one cannot define equality itself.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327)
	A reaction: This seems a particularly nice instance of the general rule that 'you have to start somewhere'. It is a nice test case for the nature of meaning to ask 'what do you understand when you understand equality?', given that you can't define it.

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation

17446	Counting rests on one-one correspondence, of numerals to objects [Frege]
	Full Idea: Counting rests itself on a one-one correlation, namely of numerals 1 to n and the objects.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]), quoted by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
	A reaction: Parsons observes that counting will establish a one-one correspondence, but that doesn't make it the aim of counting, and so Frege hasn't answered Husserl properly. Which of the two is conceptually prior? How do you decide.

9582	Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege]
	Full Idea: When Husserl says that sameness of number can be shown by one-one correlation, he forgets that this counting itself rests on a univocal one-one correlation, namely that between the numerals 1 to n and the objects of the set.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326)
	A reaction: This is the platonist talking. Neo-logicism is attempting to build numbers just from the one-one correlation of objects.

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

9586	In a number-statement, something is predicated of a concept [Frege]
	Full Idea: In a number-statement, something is predicated of a concept.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.328)
	A reaction: A succinct statement of Frege's theory of numbers. By my lights that would make numbers at least second-order abstractions.

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

9580	Our concepts recognise existing relations, they don't change them [Frege]
	Full Idea: The bringing of an object under a concept is merely the recognition of a relation which previously already obtained, [but in the abstractionist view] objects are essentially changed by the process, so that objects brought under a concept become similar.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324)
	A reaction: Frege's view would have to account for occasional misapplications of concepts, like taking a dolphin to be a fish, or falsely thinking there is someone in the cellar.

9589	Numbers are not real like the sea, but (crucially) they are still objective [Frege]
	Full Idea: The sea is something real and a number is not; but this does not prevent it from being something objective; and that is the important thing.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.337)
	A reaction: This seems a qualification of Frege's platonism. It is why people start talking about abstract items which 'subsist', instead of 'exist'. It shows Frege's motivation in all this, which is to secure logic and maths from the vagaries of psychology.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism

9577	The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege]
	Full Idea: The most naïve opinion of number is that it is something like a heap in which things are contained. The next most naïve view is the conception of number as the property of a heap, cleansing the objects of their particulars.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.323)
	A reaction: A hundred toothbrushes and a hundred sponges can be seen to contain the same number (by one-to-one mapping), without actually knowing what that number is. There is something numerical in the heap, even if the number is absent.

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction

9578	If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege]
	Full Idea: If an object is just presentation, we can pay less attention to a property and it disappears. By letting one characteristic after another disappear, we obtain concepts that are increasingly more abstract.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324)
	A reaction: Frege despises this view. Note there is scope in the despised view for degrees or levels of abstraction, defined in terms of number of properties ignored. Part of Frege's criticism is realist. He retains the object, while Husserl imagines it different.

8. Modes of Existence / A. Relations / 1. Nature of Relations

13076	Scholastics treat relations as two separate predicates of the relata [Cover/O'Leary-Hawthorne]
	Full Idea: The scholastics treated it as a step in the right explanatory direction to analyze a relational statement of the form 'aRb' into two subject-predicate statements, attributing different relational predicates to a and to b.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2.1)
	A reaction: The only alternative seems to be Russell's view of relations as pure universals, having a life of their own, quite apart from their relata. Or you could take them as properties of space, time (and powers?), external to the relata?

8. Modes of Existence / D. Universals / 2. Need for Universals

21710	We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does' [Russell]
	Full Idea: We are aware of the universal 'yellow'; this universal is the subject in such judgements as 'yellow differs from blue' or 'yellow resembles blue less than green does'.
	From: Bertrand Russell (Knowledge by Acquaintance and Description-1 [1911], 154), quoted by Bernard Linsky - Russell's Metaphysical Logic 2.3
	A reaction: This still seems one of the strongest examples in support of universals. You could hardly be talking about yellow tropes in such instances (even if the world does contain yellow tropes).

9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation

13102	If you individuate things by their origin, you still have to individuate the origins themselves [Cover/O'Leary-Hawthorne]
	Full Idea: If we go for the necessity-of-origins view, A and B are different if the origin of A is different from the origin of B. But one is left with the further question 'When is the origin of A distinct from the origin of B?'
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1)
	A reaction: There may be an answer to this, in a regress of origins that support one another, but in the end the objection is obviously good. You can't begin to refer to an 'origin' if you can't identify anything in the first place.

13103	Numerical difference is a symmetrical notion, unlike proper individuation [Cover/O'Leary-Hawthorne]
	Full Idea: Scholastics distinguished criteria of numerical difference from questions of individuation proper, since numerical difference is a symmetrical notion.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1)
	A reaction: This apparently old-fashioned point appears to be conclusively correct. Modern thinkers, though, aren't comfortable with proper individuation, because they don't believe in concepts like 'essence' and 'substance' that are needed for the job.

9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity

13104	Haecceity as property, or as colourless thisness, or as singleton set [Cover/O'Leary-Hawthorne]
	Full Idea: There is a contemporary property construal of haecceities, ...and a Scotistic construal as primitive, 'colourless' thisnesses which, unlike singleton-set haecceities, are aimed to do some explanatory work.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.4)
	A reaction: [He associates the contemporary account with David Kaplan] I suppose I would say that individuation is done by properties, but not by some single property, so I take it that I don't believe in haecceities at all. What individuates a haecceity?

9. Objects / B. Unity of Objects / 2. Substance / a. Substance

13100	Maybe 'substance' is more of a mass-noun than a count-noun [Cover/O'Leary-Hawthorne]
	Full Idea: We could think of 'substance' on the model of a mass noun, rather than a count noun.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.3)
	A reaction: They offer this to help Leibniz out of a mess, but I think he would be appalled. The proposal seems close to 'prime matter' in Aristotle, which never quite does the job required of it. The idea is nice, though, and should be taken seriously.

9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance

13068	We can ask for the nature of substance, about type of substance, and about individual substances [Cover/O'Leary-Hawthorne]
	Full Idea: In the 'blueprint' approach to substance, we confront at least three questions: What is it for a thing to be an individual substance? What is it for a thing to be the kind of substance that it is? What is it to be that very individual substance?
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.1)
	A reaction: My working view is that the answer to the first question is that substance is essence, that the second question is overrated and parasitic on the third, and that the third is the key question, and also reduces to essence.

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

13069	The general assumption is that substances cannot possibly be non-substances [Cover/O'Leary-Hawthorne]
	Full Idea: There is a widespread assumption, now and in the past, that substances are essentially substances: nothing is actually a substance but possibly a non-substance.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.2)
	A reaction: It seems to me that they clearly mean, in this context, that substances are 'necessarily' substances, not that they are 'essentially' substances. I would just say that substances are essences, and leave the necessity question open.

9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties

13072	Modern essences are sets of essential predicate-functions [Cover/O'Leary-Hawthorne]
	Full Idea: The modern view of essence is that the essence of a particular thing is given by the set of predicate-functions essential to it, and the essence of any kind is given by the set of predicate-functions essential to every possible member of that kind.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.2.2)
	A reaction: Thus the modern view has elided the meanings of 'essential' and 'necessary' when talking of properties. They are said to be 'functions' from possible worlds to individuals. The old view (and mine) demands real essences, not necessary properties.

17080	Modern essentialists express essence as functions from worlds to extensions for predicates [Cover/O'Leary-Hawthorne]
	Full Idea: The modern essentialist gives the same metaphysical treatment to every grammatical predicate - by associating a function from worlds to extensions for each.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 2.2)
	A reaction: I take this to mean that essentialism is the view that if some predicate attaches to an object then that predicate is essential if there is an extension of that predicate in all possible worlds. In English, essential predicates are necessary predicates.

9. Objects / E. Objects over Time / 12. Origin as Essential

13101	Necessity-of-origin won't distinguish ex nihilo creations, or things sharing an origin [Cover/O'Leary-Hawthorne]
	Full Idea: A necessity-of-origins approach cannot work to distinguish things that come into being genuinely ex nihilo, and cannot work to distinguish things sharing a single origin.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 7.4.1)
	A reaction: Since I am deeply suspicious of essentiality or necessity of origin (and they are not, I presume, the same thing) I like these two. Twins have always bothered me with the second case (where order of birth seems irrelevant).

10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity

13081	Even extreme modal realists might allow transworld identity for abstract objects [Cover/O'Leary-Hawthorne]
	Full Idea: It might be suggested that even the extreme modal realist can countenance transworld identity for abstract objects.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 3.2.2 n46)
	A reaction: This may sound right for uncontroversial or well-defined abstracta such as numbers and circles, but even 'or' is ambiguous, and heaven knows what the transworld identity of 'democracy' is!

12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems

8854	My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M on Russell]
	Full Idea: My 'acquaintance' with sense-data is nothing like my knowing New York.
	From: comment on Bertrand Russell (Knowledge by Acquaintance and Description-1 [1911]) by Michael Williams - Without Immediate Justification §4
	A reaction: This pinpoints a nice difficulty for Russell. Williams may misrepresent Russell's account of acquaintance, but that is probably because Russell is unclear, or uncertain. The problem is when Russell claims that his acquaintance gives knowledge.

14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence

13071	We can go beyond mere causal explanations if we believe in an 'order of being' [Cover/O'Leary-Hawthorne]
	Full Idea: The philosopher comfortable with an 'order of being' has richer resources to make sense of the 'in virtue of' relation than that provided only by causal relations between states of affairs, positing in addition other sorts of explanatory relationships.
	From: Cover,J/O'Leary-Hawthorne,J (Substance and Individuation in Leibniz [1999], 1.1.2)
	A reaction: This might best be characterised as 'ontological dependence', and could be seen as a non-causal but fundamental explanatory relationship, and not one that has to depend on a theistic world view.

18. Thought / A. Modes of Thought / 1. Thought

9581	Many people have the same thought, which is the component, not the private presentation [Frege]
	Full Idea: The same thought can be grasped by many people. The components of a thought, and even more so the things themselves, must be distinguished from the presentations which in the soul accompany the grasping of a thought.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.325)
	A reaction: This is the basic realisation, also found in Russell, of how so much confusion has crept into philosophy, in Berkeley, for example. Frege starts down the road which leads to the externalist view of content.

18. Thought / E. Abstraction / 3. Abstracta by Ignoring

9579	Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege]
	Full Idea: If from a black cat and a white cat we disregard colour, then posture, then location, ..we finally derive something which is completely without restrictions on content; but what is derived from the objects does differ, although it is not easy to say how.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324)
	A reaction: This is a key objection to abstractionism for Frege - we are counting two cats, not two substrata of essential catness, or whatever. But what makes a cat countable? (Key question!) It isn't its colour, or posture or location.

9587	How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege]
	Full Idea: Inattention is a very strong lye which must not be too concentrated, or it dissolves everything (such as the connection between the objects), but must not be too weak, to produce sufficient change. Personally I cannot find the proper dilution.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.330)
	A reaction: We may sympathise with the lack of precision here (frustrating for a logician), but it is not difficult to say of a baseball defence 'just concentrate on the relations, and ignore the individuals who implement it'. You retain basic baseball skills.

18. Thought / E. Abstraction / 8. Abstractionism Critique

9588	Number-abstraction somehow makes things identical without changing them! [Frege]
	Full Idea: Number-abstraction simply has the wonderful and very fruitful property of making things absolutely the same as one another without altering them. Something like this is possible only in the psychological wash-tub.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.332)
	A reaction: Frege can be awfully sarcastic. I don't really see his difficulty. For mathematics we only need to know what is countable about an object - we don't need to know how many hairs there are on the cat, only that it has identity.

19. Language / A. Nature of Meaning / 2. Meaning as Mental

9583	Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege]
	Full Idea: The psychological logicians are concerned with the sense of the words and with the presentations, which they do not distinguish from the sense; but the mathematicians are concerned with the matter itself, with the reference of the words.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326)
	A reaction: This is helpful for showing the point of his sense/reference distinction; it is part of his campaign against psychologism, by showing that there is a non-psychological component to language - the reference, where it meets the public world.

9584	Identity baffles psychologists, since A and B must be presented differently to identify them [Frege]
	Full Idea: The relation of sameness remains puzzling to a psychological logician. They cannot say 'A is the same as B', because that requires distinguishing A from B, so that these would have to be different presentations.
	From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327)
	A reaction: This is why Frege needed the concept of reference, so that identity could be outside the mind (as in Hesperus = Phosophorus). Think about an electron; now think about a different electron.