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All the ideas for 'Intensional Logic', 'Reflections on Value' and 'On the General Idea of Proof Theory'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
All thought about values is philosophical, and thought about anything else is not philosophy [Weil]
     Full Idea: All reflections bearing on the notion of value and on the hierarchy of values is philosophical; all efforts of thought bearing on anything other than value are, if one examines them closely, foreign to philosophy.
     From: Simone Weil (Reflections on Value [1941], p.30)
     A reaction: If nothing else proves that Weil is a platonist, this does. She, of course, has a transcendent and religious view of values, whereas I just see them as concepts which embody what is important. That said, I'm not far off agreeing with this.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy aims to change the soul, not to accumulate knowledge [Weil]
     Full Idea: Philosophy does not consist in accumulating knowledge, as science does, but in changing the whole soul.
     From: Simone Weil (Reflections on Value [1941], p.33)
     A reaction: I agree, roughly. In the sense that philosophy is a much more personal matter than any pure pursuit of knowledge, such as geology. Though a life in geology could change your soul. Not just any old change, of course….
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Systems are not unique to each philosopher. The platonist tradition is old and continuous [Weil]
     Full Idea: People believe that every philosopher has a system that contradicts all the others! But there is a tradition, genuinely philosophical, that is as old as humanity itself. …Plato is the most perfect representative of this tradition.
     From: Simone Weil (Reflections on Value [1941], p.33)
     A reaction: I see roughly two traditions. If you believe in transcendence you follow Plato, like Simone. If you are a naturalist (like me) you follow Aristotle. A third tradition might be much more sceptical.
3. Truth / A. Truth Problems / 1. Truth
Truth is a value of thought [Weil]
     Full Idea: Truth is a value of thought. The word 'truth' cannot have any other meaning.
     From: Simone Weil (Reflections on Value [1941], p.32)
     A reaction: This makes a nice change from truth being a mere predicate. I would call truth the criterion of success in thought, and that counts as a value, so she is right.
4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
If terms change their designations in different states, they are functions from states to objects [Fitting]
     Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects.
     From: Melvin Fitting (Intensional Logic [2007], 3)
     A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough.
Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
     Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects.
     From: Melvin Fitting (Intensional Logic [2007], 3.3)
4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting]
     Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear.
     From: Melvin Fitting (Intensional Logic [2007], 3.6.1)
     A reaction: [He cites Fagin and Halpern 1988 for this]
4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
Justication logics make explicit the reasons for mathematical truth in proofs [Fitting]
     Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity.
     From: Melvin Fitting (Intensional Logic [2007], 3.6.1)
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Classical logic is deliberately extensional, in order to model mathematics [Fitting]
     Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics.
     From: Melvin Fitting (Intensional Logic [2007], §1)
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
     Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments.
     From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2)
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ-abstraction disambiguates the scope of modal operators [Fitting]
     Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □.
     From: Melvin Fitting (Intensional Logic [2007], §3.3)
     A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
     Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things.
     From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1)
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Definite descriptions pick out different objects in different possible worlds [Fitting]
     Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally.
     From: Melvin Fitting (Intensional Logic [2007], 3.4)
     A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others.
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
Ends, unlike means, cannot be defined, which is why people tend to pursue means [Weil]
     Full Idea: Everything that can be taken as an end cannot be defined. Means, such as power and money, are easily defined, and that is why people orient themselves exclusively towards the acquisition of means.
     From: Simone Weil (Reflections on Value [1941], p.31)
     A reaction: Nice, but too neat, because so many activities can be treated either as means or as ends, and often as both. It makes sense that people pursue what is clear to them.
22. Metaethics / B. Value / 2. Values / a. Normativity
Minds essentially and always strive towards value [Weil]
     Full Idea: For the mind essentially and always, in whatever manner it is disposed, strives towards value.
     From: Simone Weil (Reflections on Value [1941], p.31)
     A reaction: A typically platonist thought. If you accept my view that values identify what is important, the thought is plausible. We might distinguish between what the mind pointlessly entertains, and what it 'strives' for.