Ideas from 'Logical Pluralism' by JC Beall / G Restall [2006], by Theme Structure

[found in 'Logical Pluralism' by Beall,J/Restall,G [OUP 2006,978-0-19-928841-0]].

green numbers give full details    |     back to texts     |     expand these ideas

3. Truth / A. Truth Problems / 1. Truth
Some truths have true negations
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
A truthmaker is an object which entails a sentence
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
It's 'relevantly' valid if all those situations make it true
Excluded middle must be true for some situation, not for all situations
Relevant consequence says invalidity is the conclusion not being 'in' the premises
Relevant logic does not abandon classical logic
Relevant logic may reject transitivity
A doesn't imply A - that would be circular
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic terms aren't existential; classical is non-empty, with referring names
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic studies consequence; logical truths are consequences of everything, or nothing
Syllogisms are only logic when they use variables, and not concrete terms
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The view of logic as knowing a body of truths looks out-of-date
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Logic studies arguments, not formal languages; this involves interpretations
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
The model theory of classical predicate logic is mathematics
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
There are several different consequence relations
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
A sentence follows from others if they always model it
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truth is much more important if mathematics rests on it, as logicism claims
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
Preface Paradox affirms and denies the conjunction of propositions in the book
10. Modality / A. Necessity / 3. Types of Necessity
Relevant necessity is always true for some situation (not all situations)
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Judgement is always predicating a property of a subject
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
We can rest truth-conditions on situations, rather than on possible worlds
19. Language / D. Propositions / 1. Propositions
Propositions commit to content, and not to any way of spelling it out