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All the ideas for 'Reply to Fourth Objections', 'Grounding Concepts' and 'The Nature of Mathematics'

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26 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?
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy is an experimental science, resting on common experience [Peirce]
     Full Idea: Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], I)
     A reaction: The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce]
     Full Idea: It is an anacoluthon to say that a proposition is impossible because it is self-contradictory. It rather is thought so to appear self-contradictory because the ideal induction has shown it to be impossible.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
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 / C. Ontology of Logic / 3. If-Thenism
Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
     Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], II)
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 / a. Early logicism
Mathematics is close to logic, but is even more abstract [Peirce]
     Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV)
     A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities.
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 / 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 / B. Possibility / 1. Possibility
Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce]
     Full Idea: Many say everything is logically possible which involves no contradiction. In this sense two contradictory propositions may be severally possible. In the substantive sense, the contradictory of a possible proposition is impossible (if we were omniscient).
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
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 / D. Empiricism / 1. Empiricism
Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
     Full Idea: If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898])
     A reaction: Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience.
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The world is one of experience, but experiences are always located among our ideas [Peirce]
     Full Idea: The real world is the world of sensible experience, and it is part of the process of sensible experience to locate its facts in the world of ideas.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
     A reaction: This is the neatest demolition of the sharp dividing line between empiricism and rationalism that I have ever encountered.
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'?
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
The concept of mind excludes body, and vice versa [Descartes]
     Full Idea: The concept of body includes nothing at all which belongs to the mind, and the concept of mind includes nothing at all which belongs to the body.
     From: René Descartes (Reply to Fourth Objections [1641], 225)
     A reaction: A headache? Hunger? The mistake, I think, is to regard the mind as entirely conscious, thus creating a sharp boundary between two aspects of our lives. As shown by blindsight, I take many of my central mental operations to be pre- or non-conscious.
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.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Ethics is the science of aims [Peirce]
     Full Idea: Ethics is the science of aims.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], II)
     A reaction: Intriguing slogan. He is discussing the aims of logic. I think what he means is that ethics is the science of value. 'Science' may be optimistic, but I would sort of agree with his basic idea.