25 ideas
| 21901 | 'Difference' refers to that which eludes capture [Deleuze, by May] |
| Full Idea: 'Difference' is a term which Deleuze uses to refer to that which eludes capture. | |
| From: report of Gilles Deleuze (Difference and Repetition [1968]) by Todd May - Gilles Deleuze 3.03 | |
| A reaction: Presumably its ancestor is Kant's noumenon. This is one of his concepts used to 'palpate' our ossified conceptual scheme. |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| Full Idea: The axiom of choice has a troubled history, but is now standard in mathematics. It could be replaced with a principle of comprehension for functions), or one could omit the variables ranging over functions. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], n 3) |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| Full Idea: Early study of first-order logic revealed a number of important features. Gödel showed that there is a complete, sound and effective deductive system. It follows that it is Compact, and there are also the downward and upward Löwenheim-Skolem Theorems. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| Full Idea: Some authors argue that second-order logic (with standard semantics) is not logic at all, but is a rather obscure form of mathematics. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| Full Idea: If the goal of logical study is to present a canon of inference, a calculus which codifies correct inference patterns, then second-order logic is a non-starter. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be because it is not 'complete'. However, moves like plural quantification seem aimed at capturing ordinary language inferences, so the difficulty is only that there isn't a precise 'calculus'. |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| Full Idea: Informally, logical consequence is sometimes defined in terms of the meanings of a certain collection of terms, the so-called 'logical terminology'. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be a compositional account, where we build a full account from an account of the atomic bits, perhaps presented as truth-tables. |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| Full Idea: Second-order variables can range over properties, sets, or relations on the items in the domain-of-discourse, or over functions from the domain itself. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| Full Idea: Upward Löwenheim-Skolem: if a set of first-order formulas is satisfied by a domain of at least the natural numbers, then it is satisfied by a model of at least some infinite cardinal. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| Full Idea: Both of the Löwenheim-Skolem Theorems fail for second-order languages with a standard semantics | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.3.2) |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorem is usually taken as a sort of defect (often thought to be inevitable) of the first-order logic. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: [He is quoting Wang 1974 p.154] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| Full Idea: Downward Löwenheim-Skolem: a finite or denumerable set of first-order formulas that is satisfied by a model whose domain is infinite is satisfied in a model whose domain is the natural numbers | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| Full Idea: Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) | |
| A reaction: [he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point? |
| 21902 | 'Being' is univocal, but its subject matter is actually 'difference' [Deleuze] |
| Full Idea: Being is said in a single and same sense of everything of which it is said, but that of which it is said differs: it is said of difference itself. | |
| From: Gilles Deleuze (Difference and Repetition [1968], p.36), quoted by Todd May - Gilles Deleuze 3.03 | |
| A reaction: This is an attempt to express the Heraclitean view of reality, as process, movement, multiplicity - something which always eludes our attempts to pin it down. |
| 21908 | Ontology can be continual creation, not to know being, but to probe the unknowable [Deleuze] |
| Full Idea: Ontology can be an ontology of difference ....where what is there is not the same old things but a process of continual creation, an ontology that does not seek to reduce being to the knowable, but widens thought to palpate the unknowable. | |
| From: Gilles Deleuze (Difference and Repetition [1968]), quoted by Todd May - Gilles Deleuze 5.05 | |
| A reaction: I'm inclined to think that the first duty of ontology is to face up to the knowable. I'm not sure that probing the unknowable, with no success or prospect of it, is a good way to spend a life. Probing ('palpating') can sometimes discover things. |
| 21903 | Ontology does not tell what there is; it is just a strange adventure [Deleuze, by May] |
| Full Idea: In Deleuze's hands ontology is not a matter of telling us what there is, but of taking us on strange adventures. | |
| From: report of Gilles Deleuze (Difference and Repetition [1968]) by Todd May - Gilles Deleuze 3.03 | |
| A reaction: Presumably you only indulge in the strange adventure because you have no idea how to specify what there is. This sounds like the essence of post-modernism, in which life is just a game. |
| 21904 | Being is a problem to be engaged, not solved, and needs a new mode of thinking [Deleuze, by May] |
| Full Idea: In Deleuze, Being is not a puzzle to be solved but a problem to be engaged. It is to be engaged by a thought that moves as comfortably among problems as it does among solutions, as fluidly among differences as it does among identities. | |
| From: report of Gilles Deleuze (Difference and Repetition [1968]) by Todd May - Gilles Deleuze 4.01 | |
| A reaction: This sounds like what I've always known as 'negative capability' (thanks to Keats). Is philosophy just a hobby, like playing darts? It seems that the aim of the process is 'liberation', about which I would like to know more. |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| Full Idea: In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.2.1) | |
| A reaction: Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties. |
| 22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
| Full Idea: Augustine says bodies don't form images in our spirit; our spirit does that itself with amazing quickness. ...So the appearances under which mind knows things aren't drawn from the things themselves. | |
| From: report of Augustine (works [c.415]) by Thomas Aquinas - Quodlibeta 8.2.1 | |
| A reaction: This is Augustine's theory of 'illumination' - that God creates experience within us. His theory was soon discarded by the early scholastics. |
| 22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
| Full Idea: Instead of supposing that what we know can be abstracted from sensible particulars that instantiate such knowledge, Augustine insists that our mind is so constituted as to see 'intelligible realities' directly by inner illumination. | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.74 | |
| A reaction: His 'theory of illumination'. This seems to be a sort of super-rationalism. This doesn't make clear the role of sensations. Surely he doesn't thing that we just bypass them? |
| 22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
| Full Idea: The modern concept of the will is often said to originate with Augustine. | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.74 | |
| A reaction: I'm beginning to think that this is the source of the trouble. How can a thing be intrinsically free? Surely freedom is always a contextual concept? |
| 4348 | Love, and do what you will [Augustine] |
| Full Idea: Love, and do what you will. | |
| From: Augustine (works [c.415]) | |
| A reaction: This sounds libertarian, but Augustine had a stern concept of what love required. It nicely captures one of the essential ideas of virtue ethics. |
| 7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
| Full Idea: Augustine claimed that the pagan schools between them had produced nearly three hundred different definitions of the highest good. | |
| From: report of Augustine (works [c.415]) by A.C. Grayling - What is Good? Ch.5 | |
| A reaction: I would expect the right definition to be in there somewhere, but no doubt Augustine's definition made it 301. Perhaps the biggest problem of human life is that (as with the Kennedy assassination) proliferating stories obscure the true story. |
| 22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
| Full Idea: Augustine insisted that 'ought' does not, in any straightforward way, imply 'can' - which distinguishes him from most modern ethicists. | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.74 | |
| A reaction: Not unreasonable. I ought to help my ailing friend who lives abroad, but I haven't the time or money to do it. We can experience impossibilities as duties. Impossibilities are just excuses. Augustine is opposing the Pelagian heresy. |
| 22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
| Full Idea: Augustine did the most to define Christian heresy. The three most prominent were Donatism, Pelagianism (that humans are perfectible), and Manicheism (that good and evil are equally basic metaphysical realities). | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.73 | |
| A reaction: Manicheans had presumably been studying Empedocles. (I suppose it's too late to identify Christianity as a heresy?). |
| 19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |
| Full Idea: Augustine solution to the problem of evil was to say that, strictly speaking, evil does not exist. Human beings are not part evil and part good, but rather just a limited amount of goodness. | |
| From: report of Augustine (works [c.415]) by Franklin Perkins - Leibniz: Guide for the Perplexed 2.III | |
| A reaction: Augustine was rebelling against Manicheanism, which he espoused when young, which proposed a good and an evil force. An apathetic slob seems devoid of goodness, but is not evil. It takes extra effort to perform active evil. |