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8242
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Philosophy aims at what is interesting, remarkable or important - not at knowledge or truth [Deleuze/Guattari]
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Full Idea:
Philosophy does not consist in knowing, and is not inspired by truth. Rather, it is categories like Interesting, Remarkable, or Important that determine success or failure.
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From:
G Deleuze / F Guattari (What is Philosophy? [1991], 1.3)
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A reaction:
Speak for yourself. I wonder what the criteria are for 'Interesting' or 'Important'. They can't seriously count 'remarkable' as a criterion of philosophical success, can they? There can be remarkable stupidity.
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8223
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The plague of philosophy is those who criticise without creating, and defend dead concepts [Deleuze/Guattari]
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Full Idea:
Those who criticise without creating, those who are content to defend the vanished concept without being able to give it the forces it needs to return to life, are the plague of philosophy.
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From:
G Deleuze / F Guattari (What is Philosophy? [1991], 1.1)
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A reaction:
This seems to be the continental view of analytical philosophy, that it is pathetically conservative. I would offer MacIntyre as a response, who gives a beautiful analysis of why the super-modern view is dead. The French are hopelessly romantic.
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8224
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'Eris' is the divinity of conflict, the opposite of Philia, the god of friendship [Deleuze/Guattari]
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Full Idea:
'Eris' is the Greek divinity of discord, conflict, and strife, the complementary opposite of Philia, the divinity of union and friendship.
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From:
G Deleuze / F Guattari (What is Philosophy? [1991], 1.2 n)
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A reaction:
Are these actual gods? This interestingly implies that the wonders of dialectic and Socrates' elenchus are simply aspects of friendship, which was elevated by Epicurus to the highest good. The Greeks just wanted wonderful friends and fine speeches.
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10170
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While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
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Full Idea:
While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
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A reaction:
[The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
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10175
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Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
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Full Idea:
In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
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A reaction:
It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types.
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10164
|
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
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Full Idea:
A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
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A reaction:
This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'!
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10167
|
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
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Full Idea:
Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
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A reaction:
In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent.
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10169
|
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
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Full Idea:
Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
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A reaction:
The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight?
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10179
|
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
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Full Idea:
The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6)
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A reaction:
This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start.
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10182
|
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
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Full Idea:
There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9)
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A reaction:
I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind?
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10168
|
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
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Full Idea:
Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3)
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A reaction:
[very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations.
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10178
|
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
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Full Idea:
It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
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A reaction:
[compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent.
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10177
|
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
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Full Idea:
Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out.
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From:
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
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A reaction:
I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra.
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7558
|
Substances mirror God or the universe, each from its own viewpoint [Leibniz]
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Full Idea:
Each substance is like a whole world, and like a mirror of God, or indeed of the whole universe, which each one expresses in its own fashion.
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From:
Gottfried Leibniz (Discourse on Metaphysics [1686]), quoted by Nicholas Jolley - Leibniz Intro
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A reaction:
Leibniz isn't a pantheist, so he does not identify God with the universe, so it is a bit revealing that substance could reflect either one or the other, and he doesn't seem to care which. In the end, for all the sophistication, he just made it up.
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13088
|
Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz]
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Full Idea:
The subject-term must always include the predicate-term, in such a way that the man who understood the notion of the subject perfectly would also judge that the predicate belongs to it.
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From:
Gottfried Leibniz (Discourse on Metaphysics [1686], §8)
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A reaction:
Sounds as if every sentence is analytic, but he doesn't mean that. He does, oddly, mean that if we fully understand the name 'Alexander', we understand his complete history, which is a bit silly, I'm afraid. Even God doesn't learn things just from names.
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5024
|
Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz]
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Full Idea:
It is always false to say that all our notions come from the so-called external senses, for the notion I have of myself and of my thoughts, and consequently of being, substance, action, identity, and many others, come from an internal experience.
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From:
Gottfried Leibniz (Discourse on Metaphysics [1686], §27)
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A reaction:
Of course, an empiricist like Hume would not deny this, as he bases his views on 'experience' (including anger, for example), not just 'sense experience'. But Hume, famously, said he has no experience of a Self, so can't get started on Leibniz's journey.
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8222
|
Concepts are superior because they make us more aware, and change our thinking [Deleuze/Guattari]
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Full Idea:
If one concept is 'better' than an earlier one, it is because it makes us aware of new variations and unknown resonances, it carries out unforeseen cuttings-out, it brings forth an Event that surveys (survole) us.
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From:
G Deleuze / F Guattari (What is Philosophy? [1991], 1.1)
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A reaction:
I don't get much of that, but it is certainly in tune with the Kuhn/Feyerabend idea that what science can generate is fresh visions, rather than precisely expanded truths. Personally I consider it dangerous nonsense, but I thought I ought to pass it on.
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5027
|
If a person's memories became totally those of the King of China, he would be the King of China [Leibniz]
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Full Idea:
If someone were suddenly to become the King of China, forgetting what he has been, as if born anew, is this not as if he were annihilated, and a King of China created in his place at the same moment?
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From:
Gottfried Leibniz (Discourse on Metaphysics [1686], §34)
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A reaction:
Strikingly, this clearly endorse the view of the empiricist Locke. It is a view about the continuity of the self, not its essence, but Descartes must have turned in his grave when he read this. When this 'King of China' introspects his self, what is it?
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5023
|
Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz]
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Full Idea:
We must distinguish between what is certain and what is necessary; everyone agrees that future contingents are certain, since God foresees them, but it is not thereby admitted that they are necessary.
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From:
Gottfried Leibniz (Discourse on Metaphysics [1686], §13)
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A reaction:
An interesting point, since there is presumably a difference between God foreseeing that future squares will have four corners, and His foreseeing the next war. It seems to me, though, that 'certainty' is bad enough news for free will, without necessity.
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8248
|
Phenomenology says thought is part of the world [Deleuze/Guattari]
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Full Idea:
According to phenomenology, thought depends on man's relations with the world - with which the brain is necessarily in agreement because it is drawn from these relations.
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From:
G Deleuze / F Guattari (What is Philosophy? [1991], Conclusion)
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A reaction:
The development of externalist views of mind, arising from the Twin Earth idea, seems to provide a link to continental philosophy, where similar ideas are found in Husserl, Sartre and Merleau-Ponty. So study science, psychology, or sociology?
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8245
|
The logical attitude tries to turn concepts into functions, when they are really forms or forces [Deleuze/Guattari]
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Full Idea:
Logic is reductionist not accidentally, but essentially and necessarily: following the route marked out by Frege and Russell, it wants to turn the concept into a function (...when actually a concept is a form, or a force).
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From:
G Deleuze / F Guattari (What is Philosophy? [1991], 2.6)
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A reaction:
[Last part on p.144] I'm not sure that I understand 'form or force', but the idea that concepts are mere functions is like describing something as 'transport', without saying whether it is bus/bike/train.. Is a concept a vision, or a tool?
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