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All the ideas for 'Mathematical Methods in Philosophy', 'Categories' and 'Problems of Knowledge'

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39 ideas

2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
We can't do philosophy without knowledge of types and categories [Ryle]
     Full Idea: We are in the dark about the nature of philosophical problems and methods if we are in the dark about types and categories.
     From: Gilbert Ryle (Categories [1938], p.189), quoted by Ofra Magidor - Category Mistakes 1.2
     A reaction: Magidor and others take this to be an assertion about language and logic, but I take it to be an assertion about reality. It is an early assertion of Schaffer's claim that ontology concerns the structure of existence, and not just what exists.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The only way to specify the corresponding fact is asserting the sentence [Williams,M]
     Full Idea: The trouble with appeal to facts in the correspondence theory is that, in general, we have no way of indicating what fact a sentence, when true, corresponds to other than asserting the sentence.
     From: Michael Williams (Problems of Knowledge [2001], Ch.12)
3. Truth / D. Coherence Truth / 1. Coherence Truth
Coherence needs positive links, not just absence of conflict [Williams,M]
     Full Idea: It is often claimed that coherence is more than 'absence of conflict' between beliefs; it also involves 'positive connections'.
     From: Michael Williams (Problems of Knowledge [2001], Ch.10)
Justification needs coherence, while truth might be ideal coherence [Williams,M]
     Full Idea: Contemporary coherence theorists are advancing a theory of justification, not of truth, …with those who argue that truth is also coherence explaining it in terms of ideal coherence, or coherence at the limit of enquiry.
     From: Michael Williams (Problems of Knowledge [2001], Ch.10)
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Deduction shows entailments, not what to believe [Williams,M]
     Full Idea: The rules of deduction are rules of entailment, not rules of inference. They tell us what follows from what, not what to believe on the basis of what.
     From: Michael Williams (Problems of Knowledge [2001], Ch.18)
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.
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.
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.
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We could never pin down how many beliefs we have [Williams,M]
     Full Idea: Asking how many beliefs I have is like asking how many drops of water there are in a bucket. If I believe my dog is in the garden, do I also believe he is not in the house, or in Siberia?
     From: Michael Williams (Problems of Knowledge [2001], Ch.11)
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Propositions make error possible, so basic experiential knowledge is impossible [Williams,M]
     Full Idea: Propositional content is inseparable from possible error. Therefore no judgement, however modest, is indubitable. So if basic experiential knowledge has to be indubitable, there is no such knowledge.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 8)
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Phenomenalism is a form of idealism [Williams,M]
     Full Idea: Phenomenalism is a form of idealism.
     From: Michael Williams (Problems of Knowledge [2001], Ch.12)
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Sense data avoid the danger of misrepresenting the world [Williams,M]
     Full Idea: The point of insisting on the absolute immediacy of sense data is that representation always seems to involve the possibility of misrepresentation.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 8)
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Sense data can't give us knowledge if they are non-propositional [Williams,M]
     Full Idea: Acquaintance with sense data is supposed to be a form of non-propositional knowledge, but how can something be non-propositional and yet knowledge?
     From: Michael Williams (Problems of Knowledge [2001], Ch. 8)
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Is it people who are justified, or propositions? [Williams,M]
     Full Idea: What exactly is supposed to be 'justified': a person's believing some particular proposition, or the proposition that he believes?
     From: Michael Williams (Problems of Knowledge [2001], Ch. 1)
     A reaction: A key distinction. See my comment on Idea 3752. What would justify a sign saying 'treasure buried here'? People can be justified in believing falsehoods. How could a false proposition be justified?
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
What works always takes precedence over theories [Williams,M]
     Full Idea: A theory that represents working practices as unworkable is a bad theory.
     From: Michael Williams (Problems of Knowledge [2001], Ch.13)
     A reaction: Good point. There's a lot of this about in epistemology, especially accusations of circularity or infinite regress, which (if true) don't somehow seem to worry the cove on the Clapham omnibus.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
Experience must be meaningful to act as foundations [Williams,M]
     Full Idea: If we are to treat experience as the foundation of knowledge, then experience must itself be understood to involve propositional content.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 8)
     A reaction: This sounds right, but since pure 'experience' obviously doesn't have propositional content, because it needs interpretation and evaluation, then this strategy won't work.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
Are empirical foundations judgements or experiences? [Williams,M]
     Full Idea: Empirical foundationists must decide whether knowledge ultimately rests on either beliefs or judgements about experience, or on the experiences or sensations themselves.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 8)
     A reaction: This clarifies the key issue very nicely, and I firmly vote for the former option. The simplest point is that error is possible about what sensations are taken to be of, so they won't do on their own.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Foundationalists are torn between adequacy and security [Williams,M]
     Full Idea: The foundationalists dilemma is to define a basis for knowledge modest enough to be secure but rich enough to be adequate.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 7)
     A reaction: ..And that is just what they are unable to do, precisely because adequate support would have to have enough content to be defeasibe or fallible.
Strong justification eliminates error, but also reduces our true beliefs [Williams,M]
     Full Idea: A strongly justificationist view of rationality may not be so rational; we want the truth, but avoiding all errors and maximising our number of true beliefs are not the same thing.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 7)
     A reaction: An interesting dilemma - to avoid all errors, believing nothing; to maximise true belief, believe everything. It is rational to follow intuition, guesses, and a wing and a prayer - once you are experienced and educated.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Why should diverse parts of our knowledge be connected? [Williams,M]
     Full Idea: Why should political theory ever have much to do with quantum physics, or pet care with parliamentary history?
     From: Michael Williams (Problems of Knowledge [2001], Ch.11)
     A reaction: This hardly demolishes the coherence account of justification, since your views on pet care had better be coherent, for your pet's sake. It's a pity people can make their politics cohere with their ethics.
Coherence theory must give a foundational status to coherence itself [Williams,M]
     Full Idea: Coherence theory implicitly assigns the criteria of coherence a special status. …In so far as this status is assigned a priori, the coherence theory represents a rationalistic variant of foundationalism.
     From: Michael Williams (Problems of Knowledge [2001], Ch.11)
     A reaction: Nice move, to accuse coherence theorists of foundationalism! Wrong, though, because the a priori principles of coherence are not basic beliefs, but evolved pragmatic procedures (or something...).
13. Knowledge Criteria / C. External Justification / 1. External Justification
Externalism does not require knowing that you know [Williams,M]
     Full Idea: From an externalist point of view, knowing about one's reliability is not required for 'first-order' knowledge.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 2)
     A reaction: Ah. 'First-order knowledge' - what's that? What we used to call 'true belief', I would say. Adequate for animals, and a good guide to daily life, but uncritical and unjustifiable.
Externalism ignores the social aspect of knowledge [Williams,M]
     Full Idea: A problem with pure externalism is that it ignores the social dimension of knowledge.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 2)
     A reaction: This seems to be contradicted by Idea 3573, which allows a social dimension to agreement over what is reliable. I am inclined to take knowledge as an entirely social concept.
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
In the causal theory of knowledge the facts must cause the belief [Williams,M]
     Full Idea: According to Goldman's early causal theory of knowledge, my belief that p counts as knowledge if and only if it is caused by the fact that p. This is sufficient as well as necessary, and so does not involve justification.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 2)
     A reaction: I take his theory simply to be false because what causes a belief is not what justifies it. I expect my mother to ring; the phone rings; I 'know' it is my mother (and it is), because I strongly expect it.
How could there be causal relations to mathematical facts? [Williams,M]
     Full Idea: It is not clear what would even be meant by supposing that there are causal relations to mathematical facts.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 2)
     A reaction: I agree, though platonists seem to be willing to entertain the possibility that there are causal relations, for which no further explanation can be given. Better is knowledge without a causal relation.
Only a belief can justify a belief [Williams,M]
     Full Idea: Justification requires logical rather than causal connections. That is the point of the slogan that only a belief can justify a belief.
     From: Michael Williams (Problems of Knowledge [2001], Ch.10)
     A reaction: It seems better to talk of 'rational' connections, rather than 'logical' connections. It isn't 'logical' to believe that someone despises me because their lip is faintly curled.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Externalist reliability refers to a range of conventional conditions [Williams,M]
     Full Idea: The radical externalists' key notion is 'reliability', which is a normative condition governing adequate performance, involving reference to a range of conditions which we decide rather than discover.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 2)
     A reaction: If we can decide whether a source is reliable, we can also decide whether a reliable source has performed well on this occasion, and that will always take precedence.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Sometimes I ought to distrust sources which are actually reliable [Williams,M]
     Full Idea: I may reach a belief using a procedure that is in fact reliable, but which I ought to distrust.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 1)
     A reaction: The tramp on the park bench who gives good share tips. The clock that is finally working, but has been going haywire for weeks. Reliabilism is a bad theory.
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
We control our beliefs by virtue of how we enquire [Williams,M]
     Full Idea: We control our beliefs by virtue of how we enquire.
     From: Michael Williams (Problems of Knowledge [2001], Ch. 1)
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Scepticism just reveals our limited ability to explain things [Williams,M]
     Full Idea: All the sceptic's arguments show is that there are limits to our capacity to give reasons or cite evidence.
     From: Michael Williams (Problems of Knowledge [2001], Ch.13)
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M]
     Full Idea: The classical Five Modes of Scepticism are Discrepancy (people always disagree), Relativity ('according to you'), Infinity (infinite regress of questions), Assumption (ending in dogma) and Circularity (end up where you started).
     From: Michael Williams (Problems of Knowledge [2001], Ch. 5)
     A reaction: I take Relativity to be different from scepticism (because, roughly, it says there is nothing to know), and the others go with Agrippa's Trilemma of justification, which may have solutions.
14. Science / A. Basis of Science / 1. Observation
Seeing electrons in a cloud chamber requires theory [Williams,M]
     Full Idea: Armed with enough theory, we can see electrons in a cloud chamber.
     From: Michael Williams (Problems of Knowledge [2001], Ch.10)
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Foundationalists base meaning in words, coherentists base it in sentences [Williams,M]
     Full Idea: In the foundationalist picture the meaning of individual words (defined ostensively) is primary, and that of sentences is derivative. For coherentists sentences come first, with meaning understood functionally or inferentially.
     From: Michael Williams (Problems of Knowledge [2001], Ch.10)
     A reaction: Coherentism about language doesn't imply coherentism about justification. On language I vote for foundationalism, because I am impressed by the phenomenon of compositionality.