19 ideas
| 8877 | We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa] |
| Full Idea: Coherence involves the logical, explanatory and probabilistic relations among one's beliefs, but it could not do to attain a tightly iterrelated system by lopping off whatever beliefs refuse to fit. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.4) | |
| A reaction: This is clearly right, so the coherentist has to distinguish between lopping off a belief because it is inconvenient (fundamentalists rejecting textual contradictions), and lopping it off because it is wrong (chemists rejecting phlogiston). |
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| Full Idea: ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7) | |
| A reaction: If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them. |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| Full Idea: The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1) | |
| A reaction: My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff. |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| Full Idea: It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 8.1) | |
| A reaction: This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable. |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| Full Idea: There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth? |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| Full Idea: It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 5) | |
| A reaction: Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals. |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| Full Idea: The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 6.1) | |
| A reaction: Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done. |
| 8884 | The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa] |
| Full Idea: You could detect the absence of an eleven-dot pattern without having counted the dots, so your phenomenal concept of that array is not an arithmetical concept, and its content will not yield that its dots do indeed number eleven. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.3) | |
| A reaction: Sosa is discussing foundational epistemology, but this draws attention to the gulf that has to be leaped by structuralists. If eleven is not derived from the pattern, where does it come from? Presumably two eleven-dotters are needed, to map them. |
| 8878 | It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa] |
| Full Idea: I am quite flexible on epistemic terminology, and am even willing to grant that a supermarket door can 'know' that someone is approaching. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.6) | |
| A reaction: I take this amazing admission to be a hallmark of externalism. Sosa must extend this to thermostats. So flowers know the sun has come out. This is knowledge without belief. Could the door ever be 'wrong'? |
| 8880 | In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa] |
| Full Idea: In trying to reduce arithmetic to self-evident logical axioms, logicism is in sympathy with rationalism. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.7) | |
| A reaction: I have heard Frege called "the greatest of all rationalist philosophers". However, the apparent reduction of arithmetic to analytic truths played into the hands of logical positivists, who could then marginalise arithmetic. |
| 8881 | Most of our knowledge has insufficient sensory support [Sosa] |
| Full Idea: Almost nothing that one knows of history or geography or science has adequate sensory support, present or even recalled. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.7) | |
| A reaction: This seems a bit glib, and may be false. The main issue to which this refers is, of course, induction, which (almost by definition) is a supposedly empirical process which goes beyond the empirical evidence. |
| 8882 | Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa] |
| Full Idea: There is a difference between having just an indexical concept which one can apply to a perceptual characteristic (just saying 'this is thus'), and having a thicker perceptual concept of that characteristic. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.2) | |
| A reaction: Both of these, of course, would precede any categorial concepts that enabled one to identify the characteristic or the object. This is a ladder foundationalists must climb if they are to reach the cellar of basic beliefs. |
| 8883 | Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa] |
| Full Idea: Are foundationally justified beliefs perhaps those that result from attending to our experience and to features of it or in it? | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.3) | |
| A reaction: A promising suggestion. I do think our ideas acquire a different epistmological status once we have given them our full attention, though is that merely full consciousness, or full thoughtful evaluation? The latter I take to be what matters. Cf Idea 2414. |
| 8885 | Some features of a thought are known directly, but others must be inferred [Sosa] |
| Full Idea: Some intrinsic features of our thoughts are attributable to them directly, or foundationally, while others are attributable only based on counting or inference. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.5) | |
| A reaction: In practice the brain combines the two at a speed which makes the distinction impossible. I'll show you ten dot-patterns: you pick out the sixer. The foundationalist problem is that only those drained of meaning could be foundational. |
| 8876 | Much propositional knowledge cannot be formulated, as in recognising a face [Sosa] |
| Full Idea: Much of our propositional knowledge is not easily formulable, as when a witness looking at a police lineup may know what the culprit's face looks like. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.1) | |
| A reaction: This is actually a very helpful defence of foundationalism, because it shows that we will accept perceptual experiences as knowledge when they are not expressed as explicit propositions. Davidson (Idea 8801), for example, must deal with this difficulty. |
| 8879 | Fully comprehensive beliefs may not be knowledge [Sosa] |
| Full Idea: One's beliefs can be comprehensively coherent without amounting to knowledge. | |
| From: Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 6.6) | |
| A reaction: Beliefs that are fully foundational or reliably sourced may also fail to be knowledge. I take it that any epistemological theory must be fallibilist (Idea 6898). Rational coherentism will clearly be sensitive to error. |
| 11945 | In addition to laws, God must also create appropriate natures for things [Leibniz] |
| Full Idea: It isn't sufficient to say that God has made a general law, for in addition to the decree there has also to be a natural way of carrying it out. It is necessary, that is, that what happens should be explicable in terms of the God-given nature of things. | |
| From: Gottfried Leibniz (Letter to the Editor about Bayle [1698], p.205) | |
| A reaction: Thus Leibniz is an ancestor of scientific essentialism, but he was too frightened to take the next step, which is to see that once God has endowed the natures, he doesn't need to wield his laws as well. The natures will do the whole job. |
| 19348 | All that is real in motion is the force or power which produces change [Leibniz] |
| Full Idea: As for motion, what is real in it is force or power; that is to say, what there is in the present state which carries with it a change in the future. The rest is only phenomena and relations. | |
| From: Gottfried Leibniz (Letter to the Editor about Bayle [1698], §13) | |
| A reaction: This presumably contradicts Newton's concept of inertia, which allows constant motion without force. I always like a reference to powers. What is 'kinetic energy' in this context? |