32 ideas
| 8797 | The negation of all my beliefs about my current headache would be fully coherent [Sosa] |
| Full Idea: If I have a headache, I could have a set of beliefs that I do not have a headache, that I am not in pain, that no one is in pain, and so on. The resulting system of beliefs would cohere as fully as does my actual system of beliefs. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §9) | |
| A reaction: I think this is a misunderstanding of coherentism. Beliefs are not to be formulated through a process of coherence, but are evaluated that way. A belief that I have headache just arrives; I then see that its denial is incoherent, so I accept it. |
| 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). |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| Full Idea: The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: They charge that this leads to circularity, as Infinity depends on the empty set. |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| Full Idea: Some authors need to be told loud and clear: if there is an empty set, it is something, not nothing. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: I'm inclined to think of a null set as a pair of brackets, so maybe that puts it into a metalanguage. |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| Full Idea: The empty set is said to be useful to express non-existence, but saying 'there are no Us', or ¬∃xUx are no less concise, and certainly less roundabout. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| Full Idea: Suppose we introduce Ω not as a term standing for a supposed empty set, but as a paradigm of an empty term, not standing for anything. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: This proposal, which they go on to explore, seems to mean that Ω (i.e. the traditional empty set symbol) is no longer part of set theory but is part of semantics. |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| Full Idea: Thomason says with no unit sets we couldn't call {1,2}∩{2,3} a set - but so what? Why shouldn't the intersection be the number 2? However, we then have to distinguish three different cases of intersection (common subset or member, or disjoint). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 2.2) |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
| A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
| A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |
| 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. |
| 8443 | Mereological essentialism says an entity must have exactly those parts [Sosa] |
| Full Idea: Mereological essentialism says that nothing else could have been the unique entity composed of certain parts except the very thing that is composed of those parts. | |
| From: Ernest Sosa (Varieties of Causation [1980], 2) | |
| A reaction: This sounds initially implausible. It means the ship of Theseus ceases to be that ship if you change a single nail of it. Whether we say that seems optional, but if we do, it leads to the collaps of all our normal understanding of identity. |
| 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. |
| 8794 | There are very few really obvious truths, and not much can be proved from them [Sosa] |
| Full Idea: Radical foundationalism suffers from two weaknesses: there are not so many perfectly obvious truths as Descartes thought; and if we restrict ourselves to what it truly obvious, very little supposed common sense knowledge can be proved. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §3) | |
| A reaction: It is striking how few examples can ever be found of self-evident a priori truths. However, if there are self-evident truths about direct experience (pace Descartes), that would give us more than enough. |
| 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. |
| 8796 | A single belief can trail two regresses, one terminating and one not [Sosa] |
| Full Idea: A single belief can trail at once regresses of both sorts: one terminating and one not. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §6) | |
| A reaction: This makes foundationalism possible, while admitting the existence of regresses. It is a good point, and triumphalist anti-foundationalists can't just point out a regress and then smugly troop off to the pub. |
| 8799 | If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa] |
| Full Idea: If a mental state is not propositional, then how can it possibly serve as a foundation for belief? How can one infer or justify anything on the basis of a state that, having no propositional content, must be logically dumb? | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §11) | |
| A reaction: This may be the best objection to foundationalism. McDowell tries to argue that conceptual content is inherent in perception, thus giving the beginnings of inbuilt propositional content. But an organism awash with bare experiences knows nothing. |
| 8795 | Mental states cannot be foundational if they are not immune to error [Sosa] |
| Full Idea: If a mental state provides no guarantee against error, then it cannot serve as a foundation for knowledge. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §4) | |
| A reaction: That assumes that knowledge entails certainty, which I am sure it should not. On a fallibilist account, a foundation could be incredibly secure, despite a barely imaginable scenario in which it turned out to be false. |
| 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. |
| 8798 | Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa] |
| Full Idea: Visual experience is recognized as both the cause and the justification of our visual beliefs. But these are not wholly independent. Presumably the justification that something is red derives partly from the fact that it originates in visual experience. | |
| From: Ernest Sosa (The Raft and the Pyramid [1980], §10) | |
| A reaction: Yes, but the fact that certain visual experiences originate in dreams is taken as grounds for denying their truth, not affirming it. So why do we distinguish them? I am thinking that only in the 'space of reasons' can a cause become a justification. |
| 8326 | Science has shown that causal relations are just transfers of energy or momentum [Fair, by Sosa/Tooley] |
| Full Idea: Basic causal relations can, as a consequence of our scientific knowledge, be identified with certain physicalistic [sic] relations between objects that can be characterized in terms of transference of either energy or momentum between objects. | |
| From: report of David Fair (Causation and the Flow of Energy [1979]) by E Sosa / M Tooley - Introduction to 'Causation' §1 | |
| A reaction: Presumably a transfer of momentum is a transfer of energy. If only anyone had the foggiest idea what energy actually is, we'd be doing well. What is energy made of? 'No identity without substance', I say. I like Fair's idea. |
| 10379 | Fair shifted his view to talk of counterfactuals about energy flow [Fair, by Schaffer,J] |
| Full Idea: Fair, who originated the energy flow view of causation, moved to a view that understands connection in terms of counterfactuals about energy flow. | |
| From: report of David Fair (Causation and the Flow of Energy [1979]) by Jonathan Schaffer - The Metaphysics of Causation 2.1.2 | |
| A reaction: David Fair was a pupil of David Lewis, the king of the counterfactual view. To me that sounds like a disappointing move, but it is hard to think that a mere flow of energy through space would amount to causation. Cause must work back from an effect. |
| 8442 | What law would explain causation in the case of causing a table to come into existence? [Sosa] |
| Full Idea: If I fasten a board onto a tree stump, causing a table to come into existence, ...what law of nature or, even, what quasi-law or law-like principle could possibly play in such a case of generation the role required by nomological accounts? | |
| From: Ernest Sosa (Varieties of Causation [1980], 1) | |
| A reaction: A very nice question. The nomological account is at its strongest when rocks fall off walls or magnets attract, but all sorts of other caused events seem too messy or complex or original to fit the story. |
| 8445 | The necessitated is not always a result or consequence of the necessitator [Sosa] |
| Full Idea: The necessitated is not always a result or consequence of the necessitator. If p-and-q is a fact, then this necessitates that p, but the fact that p need not be a result or consequence of the fact that p-and-q. | |
| From: Ernest Sosa (Varieties of Causation [1980], p.242) | |
| A reaction: This is obviously correct, and needs to be borne in mind when considering necessary causation. It is not enough to produce a piece of logic; something in the link from cause to effect must be demonstrated to be necessary. |
| 8444 | Where is the necessary causation in the three people being tall making everybody tall? [Sosa] |
| Full Idea: It is not clear how to analyse the form of necessary causation found in the only three people in the room being tall causing everybody in the room to be tall. | |
| From: Ernest Sosa (Varieties of Causation [1980], 5) | |
| A reaction: I would want to challenge this as a case of causation. There are no events or processes involved. It seems that a situation described in one way can also be described in another. |