Combining Texts

All the ideas for 'Logical Consequence', 'On the Question of Absolute Undecidability' and 'Introduction to the Philosophy of Religion'

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27 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690 Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691 Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689 A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696 A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10692 Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
28. God / A. Divine Nature / 5. God and Time
20712 God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
20701 Can God be good, if he has not maximised goodness? [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
20702 The goodness of God may be a higher form than the goodness of moral agents [Davies,B]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
20703 How could God have obligations? What law could possibly impose them? [Davies,B]
28. God / B. Proving God / 1. Proof of God
20694 'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
20706 A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
20707 The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
20708 If God is an orderly being, he cannot be the explanation of order [Davies,B]
28. God / B. Proving God / 3. Proofs of Evidence / d. Religious Experience
20710 Maybe an abnormal state of mind is needed to experience God? [Davies,B]
20711 A believer can experience the world as infused with God [Davies,B]
20709 The experiences of God are inconsistent, not universal, and untestable [Davies,B]
29. Religion / D. Religious Issues / 1. Religious Commitment / b. Religious Meaning
20697 One does not need a full understanding of God in order to speak of God [Davies,B]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
20699 Paradise would not contain some virtues, such as courage [Davies,B]