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All the ideas for 'Foundations of Geometry', 'Modern Philosophy:introduction and survey' and 'Grounding Concepts'

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50 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
Philosophy aims to provide a theory of everything [Scruton]
     Full Idea: Philosophy studies everything: it tries to provide a theory of the whole of things.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 1.2)
     A reaction: Good, but you can't avoid value-judgements about which things are important; philosophers place more value on moral theories than on theories about glacier movement. There is a tension in philosophy between human and eternal concerns.
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
If p entails q, then p is sufficient for q, and q is necessary for p [Scruton]
     Full Idea: If p entails q, then p is sufficient for q, and q is necessary for p.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 15.7)
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Examining concepts can recover information obtained through the senses [Jenkins]
     Full Idea: My idea is that conceptual examination might be a way of recovering information previously obtained through the senses.
     From: Carrie Jenkins (Grounding Concepts [2008], 4.8)
     A reaction: Now you're talking! This is really interesting conceptual analysis, rather than the sort of stamp-collecting approach to analsis practised by the duller sort of philosopher. But why bother with conceptual examination, when you have senses?
2. Reason / E. Argument / 4. Open Question
We may define 'good' correctly, but then ask whether the application of the definition is good [Scruton]
     Full Idea: The 'open question' argument is clearly invalid. A question remains open just so long as our ignorance permits. …It may be an open question whether promoting happiness is good, even though this is what 'good' means.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 20.1)
     A reaction: A nice objection. Like small children, we can keep asking questions forever. Whether there is a question to be asked about a thing is not a property of that thing, but of us who ask it.
3. Truth / A. Truth Problems / 1. Truth
A true proposition is consistent with every other true proposition [Scruton]
     Full Idea: A true proposition is consistent with every other true proposition: no truth is contradicted by another.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 9.1)
     A reaction: Interesting. It resembles the rule that if you always tell the truth you don't need to remember what you said. Close to the heart of the concept of truth. Coherence and correspondence.
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins]
     Full Idea: Instead of considering only a proposition's 'correspondence to the facts', we should also consider the correspondence between parts of the proposition and parts of the world (a 'correspondence-as-congruence' view).
     From: Carrie Jenkins (Grounding Concepts [2008], Final - Branching)
     A reaction: This is something like Russell's Othello example (1912), except that the parts there, with relations seemed to add up to the whole proposition. For Jenkins, presumably parts might correspond, but the whole proposition fail to.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
The pragmatist does not really have a theory of truth [Scruton]
     Full Idea: The pragmatist does not really have a theory of truth.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 9.4)
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
     Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry.
     From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2
     A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]
     Full Idea: Could someone have a perfect intellectual acquaintance with numbers, but be incapable of counting a flock of sheep?
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.6)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
     Full Idea: We might arrive to the concept of infinity by composing concepts of negation and finiteness.
     From: Carrie Jenkins (Grounding Concepts [2008], 5.3)
     A reaction: Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
     Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions.
     From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1
     A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries.
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
     Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised.
     From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2
     A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy.
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
     Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms.
     From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3
     A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
     Full Idea: The indispensability of arithmetical concepts is evidence that they do in fact accurately represent features of the independent world.
     From: Carrie Jenkins (Grounding Concepts [2008], Intro)
     A reaction: This seems to me to be by far the best account of the matter. So why is the world so arithmetical? Dunno, mate; ask someone else.
Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
     Full Idea: I propose that arithmetical truths are known through an examination of our own arithmetical concepts; that basic arithmetical concepts map the arithmetical structure of the world; that the map obtains in virtue of our normal sensory apparatus.
     From: Carrie Jenkins (Grounding Concepts [2008], Pref)
     A reaction: She defends the nice but unusual position that arithmetical knowledge is both a priori and empirical (so that those two notions are not, as usually thought, opposed). I am a big Carrie Jenkins fan.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
     Full Idea: A problem for the neo-Fregeans is that it has not proved easy to establish that Hume's Principle is analytic or definitive in the required sense.
     From: Carrie Jenkins (Grounding Concepts [2008], 4.3)
     A reaction: It is also asked how we would know the principle, if it is indeed analytic or definitional (Jenkins p.119).
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton]
     Full Idea: If there can be unprovable truths of mathematics, then mathematics cannot be reduced to the proofs whereby we construct it.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.7)
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
We can learn about the world by studying the grounding of our concepts [Jenkins]
     Full Idea: What concept grounding does for us is ensure that our concepts, like the results of our empirical tests, can be treated as a source of information about the independent world.
     From: Carrie Jenkins (Grounding Concepts [2008], 4.4)
     A reaction: Presumably we learn our concepts hand-in-hand with experience, so learning our concepts is itself learning about the world. Later checking of concepts and their relations largely confirms what we already knew?
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG]
     Full Idea: Dependence comes in essential, modal, explanatory, conceptual, metaphysical and constitutive forms.
     From: report of Carrie Jenkins (Grounding Concepts [2008], 1.2) by PG - Db (ideas)
     A reaction: You'll have to look up Jenkins for the details.
7. Existence / E. Categories / 4. Category Realism
The concepts we have to use for categorising are ones which map the real world well [Jenkins]
     Full Idea: Concepts which are indispensably useful for categorising, understanding, explaining, and predicting our sensory input are likely to be ones which map the structure of that input well.
     From: Carrie Jenkins (Grounding Concepts [2008], 4.6)
     A reaction: Anti-realists about classification seem to think that we just invent an array of concepts, and then start classifying with them. The truth seems to be that the actual classes of worldly thing have generated our concepts.
8. Modes of Existence / B. Properties / 12. Denial of Properties
If possible worlds are needed to define properties, maybe we should abandon properties [Scruton]
     Full Idea: If the only way of defining properties involves quantifying over possible worlds, this could be taken as another reason for abandoning properties altogether.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.4)
10. Modality / A. Necessity / 11. Denial of Necessity
Hume assumes that necessity can only be de dicto, not de re [Scruton]
     Full Idea: It was one of the assumptions of Hume's empiricism that all necessities are de dicto: i.e. they are artefacts of language.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 13.5)
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
The conceivable can't be a test of the possible, if there are things which are possible but inconceivable [Scruton]
     Full Idea: If there are things which are possible but inconceivable, we must abandon the view, which has had a considerable following since Descartes, that the conceivable is a test of the possible.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 25)
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Epistemology is about the justification of belief, not the definition of knowledge [Scruton]
     Full Idea: In my view the concept of knowledge is of no very great interest in epistemology, which actually concerns the justification of belief.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 22)
     A reaction: I think this is an excellent thought. I see knowledge as slippery, and partially contextual, and I don't care whether someone precisely 'knows' something. I just want to know why they believe it.
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
In the Cogito argument consciousness develops into self-consciousness [Scruton]
     Full Idea: In the course of the argument the first person has acquired a character; he is not merely conscious, but self-conscious.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 4)
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
Maybe our knowledge of truth and causation is synthetic a priori [Scruton]
     Full Idea: 'Every event has a cause' and 'truth is correspondence to facts' are candidates for being synthetic a priori knowledge.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 13.2)
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins]
     Full Idea: Examining accurate concepts can help us acquire true beliefs about the world, examining justified concepts can help us acquire justified beliefs about the world, and examining grounded concepts can help us acquire knowledge of it.
     From: Carrie Jenkins (Grounding Concepts [2008], 4.4)
     A reaction: This summarises Jenkins's empirical account of concepts, and I love it all to bits. I feel that contemporary philosophy is beginning to produce a coherent naturalistic worldview which can replace religion. Bar the rituals. We can have priests...
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
Touch only seems to reveal primary qualities [Scruton]
     Full Idea: Touch seems to deliver a purely primary-quality account of the world.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 24)
     A reaction: Interesting, though a little over-confident. It seems occasionally possible for touch to be an illusion.
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
We only conceive of primary qualities as attached to secondary qualities [Scruton]
     Full Idea: Bradley argued that we cannot conceive of primary qualities except as attached to secondary qualities.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 10.1)
If primary and secondary qualities are distinct, what has the secondary qualities? [Scruton]
     Full Idea: If primary and secondary qualities are distinct, what do secondary qualities inhere in?
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], Ch.10 n)
     A reaction: What is the problem? A pin causes me pain, but I know the pain isn't in the pin. It is the same with colour. It is a mental property, if you like, triggered by a wavelength of radiation.
12. Knowledge Sources / B. Perception / 3. Representation
The representational theory says perceptual states are intentional states [Scruton]
     Full Idea: The representational theory is the unsurprising view that perceptual states are intentional, like beliefs, emotions and desires.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 23.3)
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins]
     Full Idea: The mere reliability of intuition is not a satisfactory ground for saying it is a source of knowledge - we need to know why it is reliable to understand whether it can be a source of knowledge.
     From: Carrie Jenkins (Grounding Concepts [2008], 6.5)
     A reaction: My theory is that intuition is simply believing things for reasons which we have either forgotten, or (more likely) reasons which are too complex or subtle to be articulated. Intuition feels rational, because it is rational. Updated view of mind needed.
13. Knowledge Criteria / C. External Justification / 1. External Justification
Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins]
     Full Idea: I propose that knowledge is true belief which can be well explained .....just by citing the proposition believed.
     From: Carrie Jenkins (Grounding Concepts [2008], 3.1)
     A reaction: I don't find this appealing, and my reservation about Jenkins's book is her reliabilist, externalist epistemology. I would add an internalist coherentist epistemology to her very nice theory. 'I believe there are fairies at the bottom of my garden'?
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
My belief that it will rain tomorrow can't be caused by its raining tomorrow [Scruton]
     Full Idea: It is impossible that my present belief that it will rain tomorrow is caused by its raining tomorrow.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 22.4)
     A reaction: This doesn't demolish a causal account of belief. It would be very surprising if I were to believe it was going to rain tomorrow for no cause whatsoever. That would be irrational.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Logical positivism avoids scepticism, by closing the gap between evidence and conclusion [Scruton]
     Full Idea: If the evidence for p is q, and that is the only evidence there is or can be, then 'p' means q. Hence there is no gap between evidence and conclusion, and the sceptical problem does not arise.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 3.2)
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Why should you believe someone who says there are no truths? [Scruton]
     Full Idea: A writer who says that there are no truths, or that all truth is 'merely relative', is asking you not to believe him. So don't.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 1.1)
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Every event having a cause, and every event being determined by its cause, are not the same [Scruton]
     Full Idea: To say that every event has a cause is one thing; to say that every event is determined by its cause is quite another thing.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 17.1)
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
The very concept of a substance denies the possibility of mutual interaction and dependence [Scruton]
     Full Idea: It is often held to be a consequence of the rationalist conception of substance, that separate substances cannot interact (since causal interaction is a form of mutual dependence).
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], Ch.16 n)
     A reaction: Yes, substances seem incapable of interaction, just as Leibniz argues that perfections could never interact. They are too pure.
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
The physical effect of world on brain explains the concepts we possess [Jenkins]
     Full Idea: I think the physical effects of the world on the brain explain our possessing the concepts we do.
     From: Carrie Jenkins (Grounding Concepts [2008], 8.2)
     A reaction: A nice slogan for a thought which strikes me as exactly right.
Grounded concepts are trustworthy maps of the world [Jenkins]
     Full Idea: Grounded concepts are like trustworthy on-board maps of the independent world.
     From: Carrie Jenkins (Grounding Concepts [2008], Intro)
     A reaction: You'll probably need more than one concept for it to qualify as a 'map', but I like this idea a lot. The world, rather than we ourselves, creates our concepts. The opposite of the view of Geach in 'Mental Acts'.
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins]
     Full Idea: I find an updated verificationism plausible, in which we say something meaningful just in case we employ only concepts whose possession could be justified or disjustified by sensory input.
     From: Carrie Jenkins (Grounding Concepts [2008], 5.6)
     A reaction: Wow! This is the first time I have ever had the slightest sympathy for verificationism. It saves my favourite problem case - of wild but meaningful speculation, for example about the contents of another universe. A very nice idea.
19. Language / C. Assigning Meanings / 2. Semantics
Success semantics explains representation in terms of success in action [Jenkins]
     Full Idea: Success semantics is the attempt to understand mental representation by thinking about the ways in which representing the world can lead to success in action.
     From: Carrie Jenkins (Grounding Concepts [2008], 6.3)
     A reaction: I take this to be what is also known as 'teleological semantics'. It sounds to me as if this might help to explain success in action, but isn't going to explain the representations that result in the success.
19. Language / E. Analyticity / 1. Analytic Propositions
'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins]
     Full Idea: 'Analytic' might mean conceptually true, or true in virtue of meaning, or where the predicate is contained in the subject, or for sentences which define something, or where meaning is sufficient for the truth.
     From: Carrie Jenkins (Grounding Concepts [2008], 4.3)
     A reaction: The second one says meaning grounds the truth, where the last one says meaning entails the truth.
19. Language / F. Communication / 4. Private Language
Wittgenstein makes it impossible to build foundations from something that is totally private [Scruton]
     Full Idea: Wittgenstein's point is that if I search for foundations in what can only be known to me, then the belief that I have discovered those foundations will also fall victim to Descartes' demon.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 5.3)
     A reaction: Why should foundations based in wider society or a language community fare any better? Getting a lot of people to agree won't trouble the demon too much. Flat earthers.
23. Ethics / B. Contract Ethics / 5. Free Rider
Any social theory of morality has the problem of the 'free rider', who only pretends to join in [Scruton]
     Full Idea: Any attempt to provide a social justification of morality runs the risk of the 'free rider' - one who pretends to play the game in order to enjoy the fruits of it.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 20.6)
23. Ethics / D. Deontological Ethics / 2. Duty
Membership is the greatest source of obligation [Scruton]
     Full Idea: Membership is the greatest source of obligation.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 11.2)
     A reaction: An interesting and rather Aristotelian idea. The alternative is individual debt or obligation.
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
The categorical imperative is not just individual, but can be used for negotiations between strangers [Scruton]
     Full Idea: The categorical imperative is also an instrument of negotiation and compromise between strangers, through which they can rise out of enmity and confront each other as equals.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 20.6)
26. Natural Theory / C. Causation / 1. Causation
'Cause' used to just mean any valid explanation [Scruton]
     Full Idea: Traditionally (before Leibniz and Spinoza) the world 'cause' signified any valid explanation.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 14)
27. Natural Reality / C. Space / 4. Substantival Space
Measuring space requires no movement while I do it [Scruton]
     Full Idea: I can measure the length of something only if I know that it has not moved between the moment when I locate one end of it and the moment when I locate the other.
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 25.3)
     A reaction: A nice example of how even simple propositions have many presuppositions.
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
'Existence' is not a predicate of 'man', but of the concept of man, saying it has at least one instance [Scruton]
     Full Idea: When I say that a man exists, Frege argues, I do not predicate existence of a man, but rather of the concept man: I say the concept has at least one instance (and existence is a predicate of predicates).
     From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.2)