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All the ideas for 'Posthumous notes', 'The Theory of Epistemic Rationality' and 'Non-Monotonic Logic'

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12 ideas

2. Reason / E. Argument / 1. Argument
You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli]
     Full Idea: A 'rebut' of an argument establishes that its conclusion is not the case. An 'undercut' of the argument shows that the premises do not support that conclusion.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 3.2)
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli]
     Full Idea: The exceptional status of an object with respect to some default is more likely to spread to other objects if they share properties with that object that may play a role in explaining the exceptional status.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 4)
     A reaction: This is an example of the sort of rational behaviour we exhibit, and which a 'real life' logic would somehow need to capture. I would suggest the essentialist logic designed by Kit Fine as a first port of call.
4. Formal Logic / E. Nonclassical Logics / 12. Non-Monotonic Logic
We can rank a formula by the level of surprise if it were to hold [Antonelli]
     Full Idea: We can think of an 'ordinal ranking function' κ([φ)] as the level of surprise we would face were φ to hold, up to maximal surprise.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 3.5.2)
     A reaction: This suggests that Bayes's Theorem might be relevant to non-monotonic logic. This suggests that registering surprise would need to be an important feature of robot behaviour.
People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli]
     Full Idea: Test subjects seem to perform very poorly in various reasoning tests (Wason Selection, Suppression Task), suggesting logic has a subordinate role, but this may be using classical logic, where non-monotonic logics would be more appropriate.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 4)
     A reaction: Fred Sommers presents his Term Logic (based on Aristotle) as closer to how people actually reason. It is certainly crazy to infer that most people's everyday reasoning is irrational. Induction is highly rational; it's just not deductive.
Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli]
     Full Idea: In the Weakest Link Principle, an argument is preferred to another conflicting argument if its weakest defeasible link is stronger than the weakest defeasible link in the conflicting argument.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 2.1)
     A reaction: [He cites John Pollock 1991] This sounds like the elementary principle applied when choosing a rope by which to hang a large weight above your head. It gets non-monotonic logic off the ground - if you know how to evaluate 'weakest'.
Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli]
     Full Idea: Conservative core of non-monotonic logic:Reflexivity (p proves p), Cut (if p proves q, it proves their joint implications), Cautious Monotonicity, Left Logical Equivalence (equivalences have same consequences), Right Weakening (non-m preserves classical).
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 3.5.1)
     A reaction: [Highly compressed, and without symbols]
Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli]
     Full Idea: Most defeasible reasoning is externally dynamic, affected by the addition of further premises. But there is also an internal (or 'diachronic') dynamic, when further analysis reveals more about the given premises.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli]
     Full Idea: There is much discussion of whether Floating Conclusions should be derived, given that they were derived from two arguments which conflict with one another.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 2.3)
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
In classical logic the relation |= has Monotony built into its definition [Antonelli]
     Full Idea: In classical logic, Monotony follows immediately from the nature of the relation |=, for Γ |= φ holds precisely when φ is true on every interpretation on which all sentences in Γ are true.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
     A reaction: That is, semantic consequence (|=) is defined in terms of a sentence (φ) always being true if some other bunch of sentences (Γ) are true. Hence the addition of further sentences to Γ will make no difference - which is Monotony.
Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli]
     Full Idea: Basic Monotony: something stays proved if further premises are added. Cautious Monotony: the addition of something which has been proved makes no difference. Rational Monotony: it stays proved as long as the addition's negation hasn't been proved.
     From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
     A reaction: [A compressed and non-symbolic summary]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Transcendental philosophy is the subject becoming the originator of unified reality [Kant]
     Full Idea: Transcendental philosophy is the act of consciousness whereby the subject becomes the originator of itself and, thereby, of the whole object of technical-practical and moral-practical reason in one system - ordering all things in God
     From: Immanuel Kant (Posthumous notes [1799], 21:78, p.245), quoted by A.W. Moore - The Evolution of Modern Metaphysics 06 App
     A reaction: This is evidently Kant's last word on the matter (c.1799), and Moore says he was drifting close to Fichte's idealism, in which reality is actually (sort of) created by our own minds. Disappointing! God's role here is unclear.
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Rational internal belief is conviction that a proposition enhances a belief system [Foley, by Vahid]
     Full Idea: In Foley's subjective internalist account it is egocentrically rational for an agent to believe a proposition only if he would think on deep reflection that believing it is conducive to having an accurate and comprehensive belief system.
     From: report of Richard Foley (The Theory of Epistemic Rationality [1987], 2.1 B) by Hamid Vahid - Externalism/Internalism
     A reaction: I like this idea, because it indicates the link between internalism and coherence about justification. I don't think you can be an externalist coherence theorist for justification. [Reminder: Paul Thagard is the best writer on coherence].