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All the ideas for 'Abstract Objects: a Case Study', 'On 'The Beginning of Philosophy'' and 'The Correspondence Theory of Truth'

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13 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is distinguished from other sciences by its complete lack of presuppositions [Feuerbach]
     Full Idea: Philosophy does not presuppose anything. It is precisely in this fact of non-presupposition that its beginning lies - a beginning by virtue of which it is set apart from all the other sciences.
     From: Ludwig Feuerbach (On 'The Beginning of Philosophy' [1841], p.135)
     A reaction: Most modern philosophers seem to laugh at such an idea, because everything is theory-laden, culture-laden, language-laden etc. As an aspiration I love it, and think good philosophers get quite close to the goal (which, I admit, is not fully attainable).
3. Truth / A. Truth Problems / 5. Truth Bearers
Must sentences make statements to qualify for truth? [O'Connor]
     Full Idea: Maybe a sentence is not a candidate for truth until it is used to make a statement.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.6)
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Beliefs must match facts, but also words must match beliefs [O'Connor]
     Full Idea: Our beliefs must claim a correspondence with facts, and then the verbal expression of the belief must correspond to the belief itself.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.4)
3. Truth / F. Semantic Truth / 2. Semantic Truth
The semantic theory requires sentences as truth-bearers, not propositions [O'Connor]
     Full Idea: The Semantic Theory of truth requires that sentences are truth-bearers (rather than statements, or propositions).
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.6)
What does 'true in English' mean? [O'Connor]
     Full Idea: We do not seem to have any use in ordinary discourse for phrases like 'true in English', 'false in German'.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], II.1)
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Logic seems to work for unasserted sentences [O'Connor]
     Full Idea: If sentences can have truth-values only when they occur as asserted, it would be impossible to have a truth-functional basis to logic.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.6)
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
     Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
     A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
     Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
     A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Events are fast changes which are of interest to us [O'Connor]
     Full Idea: The standard cases of events are physical changes which happen sufficiently fast to be observed as changes, and which are of sufficient interest to us to be noticed or commented on.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.7)
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
     Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
     Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We can't contemplate our beliefs until we have expressed them [O'Connor]
     Full Idea: It is only when beliefs are given some symbolic expression that they acquire the precision and stability that enables us to entertain them.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.5)
Without language our beliefs are particular and present [O'Connor]
     Full Idea: Without language we would be restricted to particular beliefs about the here and now.
     From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.8)