26 ideas
| 3695 | Philosophy is a priori if it is anything [Bonjour] |
| Full Idea: My conviction is that philosophy is a priori if it is anything. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], Pref) | |
| A reaction: How about knowledge of a posteriori necessities, such as the length of a metre, known by observation of the standard metre in Paris? |
| 3651 | Perceiving necessary connections is the essence of reasoning [Bonjour] |
| Full Idea: If one never in fact grasps any necessary connections between anything, it is hard to see what reasoning could possible amount to. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §4.3) |
| 3700 | Coherence can't be validated by appeal to coherence [Bonjour] |
| Full Idea: The epistemic authority of coherence cannot itself be established by appeal to coherence. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §3.7 n50) | |
| A reaction: The standard approach amongs modern philosophers (following, I think, Kripke) is to insist on 'intuition' as basic, despite all its problems. I have no better suggestion. |
| 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. |
| 3697 | The concept of possibility is prior to that of necessity [Bonjour] |
| Full Idea: While necessity and possibility are interdefinable concepts, it is the idea of a possible world or situation which is intuitively primary. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §1.3) |
| 3704 | Moderate rationalists believe in fallible a priori justification [Bonjour] |
| Full Idea: Moderate rationalism preserves a priori justification, but rejects the idea that it is infallible. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §4.1) |
| 3707 | Our rules of thought can only be judged by pure rational insight [Bonjour] |
| Full Idea: Criteria or rules do not somehow apply to themselves. They must be judged by the sort of rational insight or intuition that the rationalist is advocating. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §5.2) |
| 3696 | A priori justification requires understanding but no experience [Bonjour] |
| Full Idea: A proposition will count as being justified a priori as long as no appeal to experience is needed for the proposition to be justified - once it is understood. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §1.2) | |
| A reaction: Could you 'understand' that a square cannot be circular without appeal to experience? I'm losing faith in the pure a priori. |
| 3703 | You can't explain away a priori justification as analyticity, and you can't totally give it up [Bonjour] |
| Full Idea: Moderate empiricists try unsuccessfully to explain a priori justification by means of analyticity, and radical empiricist attempts to dispense with a priori justification end in nearly total scepticism. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §4.1) | |
| A reaction: My working theory is neither of the above. Because we can abstract from the physical world, we can directly see/experience generalised (and even necessary) truths about it. |
| 3706 | A priori justification can vary in degree [Bonjour] |
| Full Idea: A priori justification can vary in degree. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §4.5) | |
| A reaction: This idea, which I trace back at least to Russell, seems to me one of breakthrough ideas in modern thought. It means that a priori knowledge can be reconnected with a posteriori knowledge. |
| 3699 | The induction problem blocks any attempted proof of physical statements [Bonjour] |
| Full Idea: The attempt to prove physical statements on the basis of sensory evidence is defeated by the problem of induction. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §3.6) | |
| A reaction: This sounds like a logician's use of the word 'prove', which would be a pretty forlorn hope. Insofar as experience proves anything, fully sensing a chair proves its existence. |
| 3701 | Externalist theories of justification don't require believers to have reasons for their beliefs [Bonjour] |
| Full Idea: An externalist theory of epistemic justification or warrant need not involve the possession by the believer of anything like a reason for thinking that their belief is true. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §3.7) | |
| A reaction: That is the problem with externalism. If the believer does not have a reason, then why would they believe? Externalists are interesting on justification, but daft about belief. Why do I believe I know something, when I can't recall how I learnt it? |
| 3702 | Externalism means we have no reason to believe, which is strong scepticism [Bonjour] |
| Full Idea: If externalism is the final story, we have no reason to think that any of our beliefs are true, which amounts to a very strong and intuitively implausible version of scepticism. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §3.7) | |
| A reaction: A very good point. I may, like a cat, know many things, with good external support, but as soon as I ask sceptical questions, I sink without trace if I lack internal reasons. |
| 3709 | Induction must go beyond the evidence, in order to explain why the evidence occurred [Bonjour] |
| Full Idea: Inductive explanations must be conceived of as something stronger than mere Humean constant conjunction; …anything less than this will not explain why the inductive evidence occurred in the first place. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §7.7) |
| 3708 | All thought represents either properties or indexicals [Bonjour] |
| Full Idea: I assume that the contents of thought can be accounted for by appeal to just two general sorts of ingredient - properties (including relations) and indexicals. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §6.7) | |
| A reaction: I don't accept that relations are a type of properties. Since he does not include objects or substances, I take it that he considers objects to be bundles of properties. |
| 3698 | Indeterminacy of translation is actually indeterminacy of meaning and belief [Bonjour] |
| Full Idea: The thesis of the indeterminacy of translation would be better described as the thesis of the indeterminacy of meaning and belief. | |
| From: Laurence Bonjour (In Defence of Pure Reason [1998], §3.5) | |
| A reaction: Not necessarily. It is not incoherent to believe that the target people have a coherent and stable system of meaning and belief, but finding its translation indeterminate because it is holistic, and rooted in a way of life. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |