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All the ideas for 'Function and Concept', 'Logical Investigations' and 'Abstraction Reconsidered'

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22 ideas

1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology is the science of essences - necessary universal structures for art, representation etc. [Husserl, by Polt]
     Full Idea: For Husserl, phenomenology must seek the essential aspects of phenomena - necessary, universal structures, such as the essence of art or the essence of representation. He sought a science of these essences.
     From: report of Edmund Husserl (Logical Investigations [1900]) by Richard Polt - Heidegger: an introduction 2 'Dilthey'
Bracketing subtracts entailments about external reality from beliefs [Husserl, by Putnam]
     Full Idea: In effect, the device of bracketing subtracts entailments from the ordinary belief locution (the entailments that refer to what is external to the thinker's mind).
     From: report of Edmund Husserl (Logical Investigations [1900]) by Hilary Putnam - Reason, Truth and History Ch.2
     A reaction: This seems to leave phenomenology as pure introspection, or as a phenomenalist description of sense-data. It is also a refusal to explain anything. That sounds quite appealing, like Keats's 'negative capability'.
Phenomenology aims to describe experience directly, rather than by its origins or causes [Husserl, by Mautner]
     Full Idea: Phenomenology, in Husserl, is an attempt to describe our experience directly, as it is, separately from its origins and development, independently of the causal explanations that historians, sociologists or psychologists might give.
     From: report of Edmund Husserl (Logical Investigations [1900]) by Thomas Mautner - Penguin Dictionary of Philosophy p.421
     A reaction: In this simple definition the concept sounds very like the modern popular use of the word 'deconstruction', though that is applied more commonly to cultural artifacts than to actual sense experience.
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
     Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic.
     From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2
     A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped.
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
     Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions.
     From: Gottlob Frege (Function and Concept [1891], p.38)
     A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions.
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [Frege]
     Full Idea: Functions of one argument are concepts; functions of two arguments are relations.
     From: Gottlob Frege (Function and Concept [1891], p.39)
     A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
     Full Idea: For an understanding of arithmetic the grasp of an operation's being performed 'so many times' is quite indispensable; and abstraction of a feature from groups of nuts cannot give us this grasp.
     From: Peter Geach (Abstraction Reconsidered [1983], p.170)
     A reaction: I end up defending the empirical approach to arithmetic because remarks like this are so patently false. Geach seems to think we arrive ready-made in the world, just raring to get on with some counting. He lacks the evolutionary perspective.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
     Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism.
     From: Gottlob Frege (Function and Concept [1891], p.30)
     A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
     Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'.
     From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism'
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
     Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property.
     From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2
     A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects.
9. Objects / A. Existence of Objects / 3. Objects in Thought
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
     Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place.
     From: Gottlob Frege (Function and Concept [1891], p.32)
     A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them.
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Husserl says we have intellectual intuitions (of categories), as well as of the senses [Husserl, by Velarde-Mayol]
     Full Idea: The novelty of Husserl is to describe that we have intellectual intuitions, intuitions of categories as we have intuitions of sense objects.
     From: report of Edmund Husserl (Logical Investigations [1900], II.VI.24) by Victor Velarde-Mayol - On Husserl 2.4.4
     A reaction: This is 'intuitions' in Kant's sense, of something like direct apprehensions. This idea is an axiom of phenomenology, because all mental life must be bracketed, and not just the sense experience part.
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible [Geach]
     Full Idea: If concepts were nothing but recognitional capacities, then it is unintelligible that I can judge that cats eat mice when neither of them are present.
     From: Peter Geach (Abstraction Reconsidered [1983], p.164)
     A reaction: Having observed the importance of recognition for the abstractionist (Idea 10731), he then seems to assume that there is nothing more to their concepts. Geach fails to grasp levels of abstraction, and cross-reference, and generalisation.
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
     Full Idea: For abstractionists, concepts are essentially capacities for recognizing recurrent features of the world.
     From: Peter Geach (Abstraction Reconsidered [1983], p.163)
     A reaction: Recognition certainly strikes me as central to thought (and revelatory of memory, since we continually recognise what we cannot actually recall). Geach dislikes this view, but I see it as crucial to an evolutionary view of thought.
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
     Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions.
     From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
     A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties.
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
     Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it.
     From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects
     A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status.
A concept is a function whose value is always a truth-value [Frege]
     Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part.
     From: Gottlob Frege (Function and Concept [1891], p.30)
     A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable.
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
     Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature.
     From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2
     A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity.
18. Thought / E. Abstraction / 8. Abstractionism Critique
The abstractionist cannot explain 'some' and 'not' [Geach]
     Full Idea: The abstractionist cannot give a logically coherent account of the features that are supposed to be reached by discriminative attention, corresponding to the words 'some' and 'not'.
     From: Peter Geach (Abstraction Reconsidered [1983], p.167)
     A reaction: I understand 'some' in terms of mereology, because that connects to experience, and 'not' I take to derive more from psychological experience than from the physical world, building on thwarted expectation, which even animals experience.
Only a judgement can distinguish 'striking' from 'being struck' [Geach]
     Full Idea: To understand the verb 'to strike' we must see that 'striking' and 'being struck' are different, but necessarily go together in event and thought; only in the context of a judgment can they be distinguished, when we think of both together.
     From: Peter Geach (Abstraction Reconsidered [1983], p.168)
     A reaction: Geach seems to have a strange notion that judgements are pure events which can precede all experience, and are the only ways we can come to understand experience. He needs to start from animals (or 'brutes', as he still calls them!).
19. Language / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
     Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false.
     From: Gottlob Frege (Function and Concept [1891], p.14)
     A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?'
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]
     Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept.
     From: Gottlob Frege (Function and Concept [1891], p.38 n)
     A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate.