18 ideas
| 9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
| Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
| A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |
| 19115 | 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) |
| 19119 | 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. |
| 19111 | 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) |
| 19114 | 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) |
| 19113 | 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'. |
| 19116 | 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] |
| 19117 | 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. |
| 19118 | 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. |
| 19110 | 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. |
| 19112 | 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] |
| 14933 | Scientific properties are defined by the laws that embody them [Psillos, by Ladyman/Ross] |
| Full Idea: For Psillos, properties in mature science are defined by the laws in which they feature. | |
| From: report of Stathis Psillos (Scientific Realism [1999]) by J Ladyman / D Ross - Every Thing Must Go 3.5 | |
| A reaction: This is a perfect example of the Humean approach getting everything the wrong way round. Laws are not primitives from which we derive our account of nature - they are generalisations built up from the behaviour of prior properties. |
| 9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
| Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
| A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified. |
| 9342 | Understanding needs a priori commitment [Horwich] |
| Full Idea: Understanding is itself based on a priori commitment. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
| A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional. |
| 9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
| Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
| A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it. |
| 9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
| Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
| A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge. |
| 9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
| Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9) | |
| A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate. |
| 9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
| Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11) | |
| A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away. |