Combining Texts

All the ideas for 'fragments/reports', 'Parts of Classes' and 'Problems of Knowledge'

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66 ideas

3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The only way to specify the corresponding fact is asserting the sentence [Williams,M]
3. Truth / D. Coherence Truth / 1. Coherence Truth
Coherence needs positive links, not just absence of conflict [Williams,M]
Justification needs coherence, while truth might be ideal coherence [Williams,M]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Sets are mereological sums of the singletons of their members [Lewis, by Armstrong]
We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
Classes divide into subclasses in many ways, but into members in only one way [Lewis]
A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis]
We can accept the null set, but there is no null class of anything [Lewis]
There are four main reasons for asserting that there is an empty set [Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
If we don't understand the singleton, then we don't understand classes [Lewis]
We can replace the membership relation with the member-singleton relation (plus mereology) [Lewis]
If singleton membership is external, why is an object a member of one rather than another? [Lewis]
Maybe singletons have a structure, of a thing and a lasso? [Lewis]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Set theory has some unofficial axioms, generalisations about how to understand it [Lewis]
Set theory reduces to a mereological theory with singletons as the only atoms [Lewis, by MacBride]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
If singletons are where their members are, then so are all sets [Lewis]
A huge part of Reality is only accepted as existing if you have accepted set theory [Lewis]
Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Deduction shows entailments, not what to believe [Williams,M]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural quantification lacks a complete axiom system [Lewis]
I like plural quantification, but am not convinced of its connection with second-order logic [Lewis]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Zermelo's model of arithmetic is distinctive because it rests on a primitive of set theory [Lewis]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Giving up classes means giving up successful mathematics because of dubious philosophy [Lewis]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
To be a structuralist, you quantify over relations [Lewis]
7. Existence / A. Nature of Existence / 2. Types of Existence
Existence doesn't come in degrees; once asserted, it can't then be qualified [Lewis]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
We have no idea of a third sort of thing, that isn't an individual, a class, or their mixture [Lewis]
Atomless gunk is an individual whose parts all have further proper parts [Lewis]
8. Modes of Existence / B. Properties / 11. Properties as Sets
A property is any class of possibilia [Lewis]
9. Objects / C. Structure of Objects / 5. Composition of an Object
The many are many and the one is one, so they can't be identical [Lewis]
Lewis affirms 'composition as identity' - that an object is no more than its parts [Lewis, by Merricks]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
In mereology no two things consist of the same atoms [Lewis]
Trout-turkeys exist, despite lacking cohesion, natural joints and united causal power [Lewis]
Given cats, a fusion of cats adds nothing further to reality [Lewis]
The one has different truths from the many; it is one rather than many, one rather than six [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Lewis only uses fusions to create unities, but fusions notoriously flatten our distinctions [Oliver/Smiley on Lewis]
A commitment to cat-fusions is not a further commitment; it is them and they are it [Lewis]
Lewis prefers giving up singletons to giving up sums [Lewis, by Fine,K]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We could never pin down how many beliefs we have [Williams,M]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Propositions make error possible, so basic experiential knowledge is impossible [Williams,M]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Phenomenalism is a form of idealism [Williams,M]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
Some say qualities are parts of things - as repeatable universals, or as particulars [Lewis]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Sense data avoid the danger of misrepresenting the world [Williams,M]
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]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Is it people who are justified, or propositions? [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
What works always takes precedence over theories [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
Experience must be meaningful to act as foundations [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
Are empirical foundations judgements or experiences? [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Foundationalists are torn between adequacy and security [Williams,M]
Strong justification eliminates error, but also reduces our true beliefs [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Why should diverse parts of our knowledge be connected? [Williams,M]
Coherence theory must give a foundational status to coherence itself [Williams,M]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Externalism does not require knowing that you know [Williams,M]
Externalism ignores the social aspect of knowledge [Williams,M]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
In the causal theory of knowledge the facts must cause the belief [Williams,M]
How could there be causal relations to mathematical facts? [Williams,M]
Only a belief can justify a belief [Williams,M]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Externalist reliability refers to a range of conventional conditions [Williams,M]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Sometimes I ought to distrust sources which are actually reliable [Williams,M]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
We control our beliefs by virtue of how we enquire [Williams,M]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Scepticism just reveals our limited ability to explain things [Williams,M]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M]
14. Science / A. Basis of Science / 1. Observation
Seeing electrons in a cloud chamber requires theory [Williams,M]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Foundationalists base meaning in words, coherentists base it in sentences [Williams,M]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]