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All the ideas for 'Mathematical Methods in Philosophy', 'Grounding Concepts' and 'The Blue and Brown Notebooks'

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28 ideas

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?
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.
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
     Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1)
     A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
     Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
     Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea.
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 / 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).
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
     Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting.
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.
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
     Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory.
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
     Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
     Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular).
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
     Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds.
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
     Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5)
     A reaction: They accept lots of successes in modelling necessity and time.
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 / 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'?
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
'I' is a subject in 'I am in pain' and an object in 'I am bleeding' [Wittgenstein, by McGinn]
     Full Idea: 'I' is used as a subject in 'I am in pain', ....and used as an object in 'I am bleeding'.
     From: report of Ludwig Wittgenstein (The Blue and Brown Notebooks [1936], pp. 66-7) by Colin McGinn - Subjective View: sec qualities and indexicals 4
     A reaction: How about 'my wound is painful'? Does that have the logical form of a conversation? This idea is incorrect. Shoemaker (1968) suggests that the subjective use is immune to error, unlike the object use.
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 / 6. Interpreting Language / b. Indeterminate translation
The doctrine of indeterminacy of translation seems implied by the later Wittgenstein [Wittgenstein, by Quine]
     Full Idea: Perhaps the doctrine of indeterminacy of translation will have little air of paradox for readers familiar with Wittgenstein's latter-day remarks on meaning.
     From: report of Ludwig Wittgenstein (The Blue and Brown Notebooks [1936], II.§16 n) by Willard Quine - Word and Object II.§16 n
     A reaction: This may be right, and I am inclined to link the names of Wittgenstein and Quine among those who led philosophy up a relativistic and sceptical cul-de-sac for many years. You can think too hard, you know.