Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Dialogue on human freedom and origin of evil' and 'Plural Quantification'

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15 ideas

2. Reason / D. Definition / 12. Paraphrase
'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
     Full Idea: The Geach-Kaplan sentence 'Some critics admire only one another' provably has no singular first-order paraphrase using only its predicates.
     From: Øystein Linnebo (Plural Quantification [2008], 1)
     A reaction: There seems to be a choice of either going second-order (picking out a property), or going plural (collectively quantifying), or maybe both.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
A pure logic is wholly general, purely formal, and directly known [Linnebo]
     Full Idea: The defining features of a pure logic are its absolute generality (the objects of discourse are irrelevant), and its formality (logical truths depend on form, not matter), and its cognitive primacy (no extra-logical understanding is needed to grasp it).
     From: Øystein Linnebo (Plural Quantification [2008], 3)
     A reaction: [compressed] This strikes me as very important. The above description seems to contain no ontological commitment at all, either to the existence of something, or to two things, or to numbers, or to a property. Pure logic seems to be 'if-thenism'.
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Second-order quantification and plural quantification are different [Linnebo]
     Full Idea: Second-order quantification and plural quantification are generally regarded as different forms of quantification.
     From: Øystein Linnebo (Plural Quantification [2008], 2)
Traditionally we eliminate plurals by quantifying over sets [Linnebo]
     Full Idea: The traditional view in analytic philosophy has been that all plural locutions should be paraphrased away by quantifying over sets, though Boolos and other objected that this is unnatural and unnecessary.
     From: Øystein Linnebo (Plural Quantification [2008], 5)
Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
     Full Idea: Plural quantification can be used to eliminate the commitment of science and common sense to complex objects. We can use plural quantification over mereological atoms arranged tablewise or chairwise.
     From: Øystein Linnebo (Plural Quantification [2008], 4.5)
     A reaction: [He cites Hossack and van Ingwagen]
Plural plurals are unnatural and need a first-level ontology [Linnebo]
     Full Idea: Higher-order plural quantification (plural plurals) is often rejected because plural quantification is supposedly ontological innocent, with no plural things to be plural, and because it is not found in ordinary English.
     From: Øystein Linnebo (Plural Quantification [2008], 2.4)
     A reaction: [Summary; he cites Boolos as a notable rejector] Linnebo observes that Icelandic contains a word 'tvennir' which means 'two pairs of'.
Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
     Full Idea: Plural quantification seems to offer ontological economy. We can pay the price of a mere first-order theory and then use plural quantification to get for free the corresponding monadic second-order theory, which would be an ontological bargain.
     From: Øystein Linnebo (Plural Quantification [2008], 4.4)
     A reaction: [He mentions Hellman's modal structuralism in mathematics]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Circles must be bounded, so cannot be infinite [Leibniz]
     Full Idea: An infinite circle is impossible, since any circle is bounded by its circumference.
     From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114)
     A reaction: This is interesting if one is asking what the essence of a circle must be. If is tempting to say merely that the radii must be equal, but can they have the length of some vast transfinite number? The circumference must be 2π bigger.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
     Full Idea: Some philosophers speak about a theory's 'ideological commitments' and not just about its 'ontological commitments'.
     From: Øystein Linnebo (Plural Quantification [2008], 5.4)
     A reaction: This is a third strategy for possibly evading one's ontological duty, along with fiddling with the words 'exist' or 'object'. An ideological commitment to something to which one is not actually ontologically committed conjures up stupidity and dogma.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Ordinary speakers posit objects without concern for ontology [Linnebo]
     Full Idea: Maybe ordinary speakers aren't very concerned about their ontological commitments, and sometimes find it convenient to posit objects.
     From: Øystein Linnebo (Plural Quantification [2008], 2.4)
     A reaction: I think this is the whole truth about the ontological commitment of ordinary language. We bring abstraction under control by pretending it is a world of physical objects. The 'left wing' in politics, 'dark deeds', a 'huge difference'.
16. Persons / F. Free Will / 6. Determinism / b. Fate
Sloth's Syllogism: either it can't happen, or it is inevitable without my effort [Leibniz]
     Full Idea: The ancient Sloth's Syllogism says that if something is foreseen and infallible, it will happen without my effort, and if it is not foreseen, it will not happen, even though I am able to do it.
     From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.113)
     A reaction: Presumable the foreseeing is to be done by the oracle, and not by the slothful person.
19. Language / C. Assigning Meanings / 3. Predicates
Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]
     Full Idea: The predicate 'is on the table' is 'distributive', since some things are on the table if each one is, whereas the predicate 'form a circle' is 'non-distributive', since it is not analytic that when some things form a circle, each one forms a circle.
     From: Øystein Linnebo (Plural Quantification [2008], 1.1)
     A reaction: The first predicate can have singular or plural subjects, but the second requires a plural subject? Hm. 'The rope forms a circle'. The second is example is not true, as well as not analytic.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
Evil is a negation of good, which arises from non-being [Leibniz]
     Full Idea: The cause of good is positive, but evil is a defect, that is, a privation or negation, and consequently, it arises from nothingness or nonbeing.
     From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114)
     A reaction: He goes on to illustrate his idea from mathematics. He is modifying Augustine's view that evil is an absence of good, by adding nonbeing as the driving force behind it. Doesn't sound very persuasive to me.
God only made sin possible because a much greater good can be derived from it [Leibniz]
     Full Idea: We must believe that God would not have allowed sin nor would he have created things he knows will sin, if he could not derive from them a good incomparably greater than the resulting evil.
     From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.115)
     A reaction: Why 'must' we believe this? Do we have to imagine all the genocides shrinking to insignificance once we grasp the wonderful goods that can be derived from them? The end justifies the means. Genocide is actually a good thing. Hm.