Combining Texts

All the ideas for 'The Philosopher's Toolkit', 'The Structure of Objects' and 'The Foundations of Mathematics'

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48 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
The Principle of Sufficient Reason does not presuppose that all explanations will be causal explanations [Baggini /Fosl]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
You cannot rationally deny the principle of non-contradiction, because all reasoning requires it [Baggini /Fosl]
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic aims at unified truth, unlike analysis, which divides into parts [Baggini /Fosl]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl]
In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
4. Formal Logic / G. Formal Mereology / 1. Mereology
The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Some questions concern mathematical entities, rather than whole structures [Koslicki]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
8. Modes of Existence / A. Relations / 3. Structural Relations
Structures have positions, constituent types and number, and some invariable parts [Koslicki]
8. Modes of Existence / B. Properties / 6. Categorical Properties
'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki]
If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki]
Statue and clay differ in modal and temporal properties, and in constitution [Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
There are at least six versions of constitution being identity [Koslicki]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
For three-dimensionalist parthood must be a three-place relation, including times [Koslicki]
The parts may be the same type as the whole, like a building made of buildings [Koslicki]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki]
Wholes are entities distinct from their parts, and have different properties [Koslicki]
Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki]
9. Objects / F. Identity among Objects / 3. Relative Identity
If identity is based on 'true of X' instead of 'property of X' we get the Masked Man fallacy ('I know X but not Y') [Baggini /Fosl, by PG]
9. Objects / F. Identity among Objects / 4. Type Identity
'I have the same car as you' is fine; 'I have the same fiancée as you' is not so good [Baggini /Fosl]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects [Baggini /Fosl]
10. Modality / A. Necessity / 3. Types of Necessity
Is 'events have causes' analytic a priori, synthetic a posteriori, or synthetic a priori? [Baggini /Fosl]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
I just confront the evidence, and let it act on me [Ramsey]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
'A priori' does not concern how you learn a proposition, but how you show whether it is true or false [Baggini /Fosl]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
Basic beliefs are self-evident, or sensual, or intuitive, or revealed, or guaranteed [Baggini /Fosl]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
14. Science / A. Basis of Science / 6. Falsification
A proposition such as 'some swans are purple' cannot be falsified, only verified [Baggini /Fosl]
14. Science / C. Induction / 1. Induction
The problem of induction is how to justify our belief in the uniformity of nature [Baggini /Fosl]
14. Science / C. Induction / 4. Reason in Induction
How can an argument be good induction, but poor deduction? [Baggini /Fosl]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
Abduction aims at simplicity, testability, coherence and comprehensiveness [Baggini /Fosl]
To see if an explanation is the best, it is necessary to investigate the alternative explanations [Baggini /Fosl]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Consistency is the cornerstone of rationality [Baggini /Fosl]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
Natural kinds support inductive inferences, from previous samples to the next one [Koslicki]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
Should vernacular classifications ever be counted as natural kind terms? [Koslicki]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
There are apparently no scientific laws concerning biological species [Koslicki]