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All the ideas for 'On the Question of Absolute Undecidability', 'Concepts' and 'The Enneads'

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45 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence]
     Full Idea: Philosophers who oppose conceptual analysis identify their approach as being 'naturalistic'. Philosophy is supposed to be continuous with science, and philosophical theories are to be defended on explanatory grounds, not by a priori intuitions.
     From: E Margolis/S Laurence (Concepts [2009], 5.2)
     A reaction: [They cite Papineau 1993, Devitt 1996 aand Kornblith 2002] I think there is a happy compromise here. I agree that any philosophical knowledge should be continuous with science, but we shouldn't prejudge how the analytic branch of science is done.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
     Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
     Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
     Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
     Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
     A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
     Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)
     A reaction: Each expansion brings a limitation, but then you can expand again.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
     Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Being is the product of pure intellect [Plotinus]
     Full Idea: Intellectual-Principle [Nous] by its intellective act establishes Being.
     From: Plotinus (The Enneads [c.245], 5.1.04)
     A reaction: This is a surprising view - that there is something which is prior to Being - but I take it to be Plotinus giving primacy to Plato's Form of the Good (a pure ideal), ahead of the One of Parmenides (which is Being).
The One does not exist, but is the source of all existence [Plotinus]
     Full Idea: The First is no member of existence, but can be the source of all.
     From: Plotinus (The Enneads [c.245], 5.1.07)
     A reaction: The First is the One, and this explicitly denies that it has Being. This answers the self-predication problem of Forms. Plato thought the Form of the Beautiful was beautiful, but it can't be (because of the regress). The source of existence can't exist.
The One is a principle which transcends Being [Plotinus]
     Full Idea: There exists a principle which transcends Being; this the One.
     From: Plotinus (The Enneads [c.245], 5.1.10)
     A reaction: The idea that the One transcends Being is the distinctive Plotinus doctrine. He defends the view that this was also the view of Anaxagoras, Empedocles and Plato.
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
Number determines individual being [Plotinus]
     Full Idea: Number is the determinant of individual being.
     From: Plotinus (The Enneads [c.245], 5.1.05)
     A reaction: You might have thought that number was the consequence of the individualities (or units) within being, but not so. You can't get more platonic than saying that the idealised numbers are the source of the particular units.
12. Knowledge Sources / D. Empiricism / 2. Associationism
Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence]
     Full Idea: A growing number of philosophers are attracted to modified forms of empiricism, emphasizing psychological relations between the conceptual system and perceptual and motor states, not semantic relations.
     From: E Margolis/S Laurence (Concepts [2009], 3.2)
     A reaction: I suddenly spot that this is what I have been drifting towards for some time! The focus is concept formation, where the philosophers need to join forces with the cognitive scientists.
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
If soul was like body, its parts would be separate, without communication [Plotinus]
     Full Idea: If the soul had the nature of the body, it would have isolated members each unaware of the condition of the other;..there would be a particular soul as a distinct entity to each local experience, so a multiplicity of souls would administer an individual.
     From: Plotinus (The Enneads [c.245], 4.2.2), quoted by R Martin / J Barresi - Introduction to 'Personal Identity' p.15
     A reaction: Of course, the modern 'modularity of mind' theory does suggest that we are run by a team, but a central co-ordinator is required, with a full communication network across the modules.
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus]
     Full Idea: The Soul maintains its unfailing movement; for not all that passes in the soul is, by that fact, perceptible; we know just as much as impinges on the faculty of the sense.
     From: Plotinus (The Enneads [c.245], 5.1.12)
     A reaction: This is a straightforward argument in favour of an unconscious aspect to the mind - and a rather good argument too. No one thinks that our minds ever stop working, even in sleep.
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
A person is the whole of their soul [Plotinus]
     Full Idea: Man is not merely a part (the higher part) of the Soul but the total.
     From: Plotinus (The Enneads [c.245], 5.1.12)
     A reaction: The soul is psuche, which includes the vegetative soul. The higher part is normally taken to be reason. This seems pretty close to John Locke's view of the matter.
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus]
     Full Idea: Our own soul is of that same ideal nature [as the oldest god of them all], so that to consider it, purified, freed from all accruement, is to recognise in ourselves which we have found soul to be, honourable above the body. For what is body but earth?
     From: Plotinus (The Enneads [c.245], 5.1.02)
     A reaction: The strongest versions of substance dualism are religious in character, because the separateness of the mind elevates us above the grubby physical character of the world. I'm with Nietzsche on this one - this view is actually harmful to us.
The soul is outside of all of space, and has no connection to the bodily order [Plotinus]
     Full Idea: We may not seek any point in space in which to seat the soul; it must be set outside of all space; its distinct quality, its separateness, its immateriality, demand that it be a thing alone, untouched by all of the bodily order.
     From: Plotinus (The Enneads [c.245], 5.1.10)
     A reaction: You can't get more dualist than that. He doesn't seem bothered about the interaction problem. He likens such influence to the radiation of the sun, rather than to physical movement.
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence]
     Full Idea: It is claimed, on the basis of empirical research, that the type of body that an organism has profoundly affects it cognitive operations and the way it conceptualises the world. We can't assume that human minds could inhere in wildly different body types.
     From: E Margolis/S Laurence (Concepts [2009], 3.2)
     A reaction: Sounds interesting. They cite Lawrence Shapiro 2004. It needs a large effort of imagination to think how a snake or whale or albatross might conceptualise the world, in relation to their bodies.
18. Thought / B. Mechanics of Thought / 4. Language of Thought
Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence]
     Full Idea: The language of thought is taken to have subject/predicate form and include logical devices, such as quantifiers and variables.
     From: E Margolis/S Laurence (Concepts [2009], 1.1)
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence]
     Full Idea: The three main options for the ontological status of concepts are to identify them with mental representations, or with abilities, or with Fregean senses.
     From: E Margolis/S Laurence (Concepts [2009], 1)
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
A computer may have propositional attitudes without representations [Margolis/Laurence]
     Full Idea: It may be possible to have propositional attitudes without having the mental representations tokened in one's head. ...We may say a chess-playing computer thinks it should develop its queen early, though we know it has no representation with that content.
     From: E Margolis/S Laurence (Concepts [2009], 1.1)
     A reaction: [Thye cite Dennett - who talks of the 'intentional stance'] It is, of course, a moot point whether we would attribute a propositional attitude (such as belief) to a machine once we knew that it wasn't representing the relevant concepts.
Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence]
     Full Idea: A standard criticism is that the mental representation view of concepts creates just another item whose significance bears explaining. Either we have a vicious regress, or we might as well explain external language directly.
     From: E Margolis/S Laurence (Concepts [2009], 1.2)
     A reaction: [They cite Dummett, with Wittgenstein in the background] I don't agree, because I think that explanation of concepts only stops when it dovetails into biology.
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence]
     Full Idea: The view that concepts are abilities (e.g. found in Brandom, Dummett and Millikan) would say that the concept CAT amounts to the ability to discriminate cats from non-cats and to draw certain inferences about cats.
     From: E Margolis/S Laurence (Concepts [2009], 1.2)
     A reaction: Feels wrong. The concept is what makes these abilities possible, but it seems rather behaviourist to identify the concept with what is enabled by the concept. You might understand 'cat', but fail to recognise your first cat (though you might suspect it).
The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence]
     Full Idea: The abilities view of concepts, by its rejection of mental representation, is ill-equipped to explain the productivity of thought; and it can say little about mental processes.
     From: E Margolis/S Laurence (Concepts [2009], 1.2)
     A reaction: The latter point arises from its behaviouristic character, which just gives us a black box with some output of abilities. In avoiding a possible regress, it offers no explanation at all.
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence]
     Full Idea: The structures of concepts are invoked to explain typicality effects, reflective categorization, cognitive development, reference determination, and compositionality.
     From: E Margolis/S Laurence (Concepts [2009], 2.5)
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence]
     Full Idea: The classical theory is that a concept has a definitional structure in that it is composed of simpler concepts that express necessary and sufficient conditions for falling under the concept, the stock example being unmarried and a man for 'bachelor'.
     From: E Margolis/S Laurence (Concepts [2009], 2.1)
     A reaction: This is the background idea to philosophy as analysis, and it makes concepts essentially referential, in that they are defined by their ability to pick things out. There must be some degree of truth in the theory.
Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence]
     Full Idea: The classical view is challenged by the discovery that certain categories are taken to be more typical, with typicality widely correlating with other data. Apples are judged to be more typical of (and have more common features with) fruit than plums are.
     From: E Margolis/S Laurence (Concepts [2009], 2.1)
     A reaction: This discovery that people use prototypes in thinking has been the biggest idea to ever hit the philosophy of concepts, and simply cannot be ignored (as long as the research keeps reinforcing it, which I believe it does). The classical view might adapt.
The classical theory explains acquisition, categorization and reference [Margolis/Laurence]
     Full Idea: The appeal of the classical theory of concepts is that it offers unified treatments of concept acquisition (assembling constituents), categorization (check constituents against target), and reference determination (whether they apply).
     From: E Margolis/S Laurence (Concepts [2009], 2.1)
     A reaction: [See Idea 11128 for the theory] As so often, I find myself in sympathy with the traditional view which has been relegated to ignominy by our wonderful modern philosophers.
It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence]
     Full Idea: In the light of problems such as the definition of knowledge, many philosophers now take seriously the possibility that our concepts lack definitional structure.
     From: E Margolis/S Laurence (Concepts [2009], 2.1)
     A reaction: This challenges the classical view, that there are precise conditions for each concept. That view would obviously be in difficulties with atomic concepts, so our account of those might be applied all the way up.
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence]
     Full Idea: In the prototype theory of concepts, a lexical concept has probabilistic structure in that something falls under it if it satisfies a sufficient number of properties encoded by the constituents. It originates in Wittgenstein's 'family resemblance'.
     From: E Margolis/S Laurence (Concepts [2009], 2.2)
     A reaction: It would seem unlikely to be a matter of the 'number' of properties, and would have to involve some notion of what was essential to the prototype.
Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence]
     Full Idea: On the prototype theory, categorization is to be understood as a similarity comparison process, where similarity is computed as a function of the number of constituents that two concepts hold in common.
     From: E Margolis/S Laurence (Concepts [2009], 2.2)
     A reaction: Again it strikes me that 'computing' similarity by mere 'number' of shared constituents won't do, as there is a prior judgement about which constituents really matter, or are essential. That may even be hard-wired.
People don't just categorise by apparent similarities [Margolis/Laurence]
     Full Idea: When it comes to more reflexive judgements, people go beyond the outcome of a similarity comparison. Even children say that a dog surgically altered to look like a raccoon is still a dog.
     From: E Margolis/S Laurence (Concepts [2009], 2.2)
     A reaction: We can defend the theory by not underestimating people so much. Most categorisation is done on superficial grounds, but even children know there may be hidden similarities (behind the mask, under the bonnet) which are more important.
Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence]
     Full Idea: An objection to the prototype view concerns compositionality. A complex concept often has emergent properties, as when it seems that 'pet fish' encodes for brightly coloured, which has no basis in the prototypes for 'pet' or 'fish'.
     From: E Margolis/S Laurence (Concepts [2009], 2.2)
     A reaction: I would take 'pet fish' to work like a database query. 'Fish' has a very vague prototype, and then 'pet fish' narrows the search to fish which are appropriate to be pets. We might say that the prototype is refined, or the Mk 2 prototype appears.
Many complex concepts obviously have no prototype [Margolis/Laurence]
     Full Idea: Many patently complex concepts don't even have a prototype structure, such as 'Chairs that were purchased on a Wednesday'.
     From: E Margolis/S Laurence (Concepts [2009], 2.2)
     A reaction: [The example seems to be from Fodor] I disagree. If we accept the notion of 'refining' the prototype (see Idea 11135), then the compositionality of the expression will produce a genuine but very unusual prototype.
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence]
     Full Idea: The theory theory of concepts says that terms are related as in a scientific theory, and that categorization resembles theorising. It is generally assumed that scientific terms are interdefined so that content is determined by its role in the theory.
     From: E Margolis/S Laurence (Concepts [2009], 2.3)
     A reaction: I never like this sort of account. What are the characteristics of the thing which enable it to fulfil its role? You haven't defined a car when you've said it gets you from A to B.
The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence]
     Full Idea: A problem with the theory theory of concepts is that it is holistic, saying a concept is determined by its role, not by its constituents. It then seems difficult for different people to possess the same concepts (or even the same person, over time).
     From: E Margolis/S Laurence (Concepts [2009], 2.3)
     A reaction: This seems a good objection to any holistic account of concepts or meaning - spotted by Plato in motivating his theory of Forms, to give the necessary stability to communication.
18. Thought / D. Concepts / 4. Structure of Concepts / g. Conceptual atomism
Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence]
     Full Idea: According to conceptual atomism, lexical concepts have no semantic structure, and the content of a concept isn't determined by its relation to other concepts but by its relations to the world.
     From: E Margolis/S Laurence (Concepts [2009], 2.4)
     A reaction: [They cite Fodor 1998 and Millikan 2000] I like the sound of that, because I take the creation of concepts to be (in the first instance) a response to the world, not a response to other concepts.
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
People can formulate new concepts which are only named later [Margolis/Laurence]
     Full Idea: People seem to be able to formulate novel concepts which are left to be named later; the concept comes first, the name second.
     From: E Margolis/S Laurence (Concepts [2009], 4.2)
     A reaction: [This seems to have empirical support, and he cites Pinker 1994] I do not find this remotely surprising, since I presume that human concepts are a continuous kind with animal concepts, including non-conscious concepts (why not?).
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus]
     Full Idea: Since there is a Soul which reasons upon the right and good - for reasoning is an enquiry into the rightness and goodness of this rather than that - there must exist some pemanent Right, the source and foundation of this reasoning in our soul.
     From: Plotinus (The Enneads [c.245], 5.1.11)
     A reaction: This is pretty close the Kant's concept of 'the moral order within me', and Plotinus even sees it as rational. Presumably this right is 'permanent' because the revelatlons of reason about it are necessary truths.
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach]
     Full Idea: Ecstasy or rapture is for the neo-Platonist the highest psychological state of man.
     From: report of Plotinus (The Enneads [c.245]) by Ludwig Feuerbach - Principles of Philosophy of the Future §29
     A reaction: See Bernini's statue of St Theresa. Personally I find this very unappealing because of its utter irrationality, but what is the 'highest' human psychological state? Doing mental arithmetic? Doing what is morally right? Dignity under pressure?
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
How can multiple existence arise from the unified One? [Plotinus]
     Full Idea: The problem endlessly debated is how, from such a unity as we have declared the One to be, does anything at all come into substantial existence, any multiplicity, dyad or number?
     From: Plotinus (The Enneads [c.245], 5.1.06)
     A reaction: This was precisely Aristotle's objection to the One of Parmenides, and especially the problem of the source of movement (which Plotinus also notices).
Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus]
     Full Idea: The soul is an utterance [logos] and act of the Intellectual-Principle [Nous], as that is an utterance and act of the One.
     From: Plotinus (The Enneads [c.245], 5.1.06)
     A reaction: Being only comes into the picture at the secondary Nous stage. Nous is the closest to the modern concept of God.
Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus]
     Full Idea: Given this immobility of the Supreme ...what happened then? It must be a circumradiation, which may be compared to the brilliant light encircling the sun and ceaselessly generating from that unchanging substance,
     From: Plotinus (The Enneads [c.245], 5.1.06)
     A reaction: This is the answer given to the problem raised in Idea 21814. The sun produces energy, without apparent movement. Not an answer that will satisfy a physicist, but an interesting answer.
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus]
     Full Idea: Soul is the author of all living things, ...it has breathed life into them all, whatever is nourished by earth and sea, the divine stars in the sky; ...it is the principle distinct from all of these to which it gives law and movement and life.
     From: Plotinus (The Enneads [c.245], 5.1.02)
     A reaction: This seems to derive from Anaxagoras, who is mentioned by Plotinus. The soul he refers to his not the same as our concept of God. Note the word 'law', which I am guessing is nomos. Not, I think, modern laws of nature, but closer to guidelines.
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus]
     Full Idea: Soul, for all the worth we have shown to belong to it, is yet a secondary, an image of the Intellectual-Principle [Nous]; reason uttered is an image of reason stored within the soul, and similarly soul is an utterance of the Intellectual-Principle.
     From: Plotinus (The Enneads [c.245], 5.1.03)
     A reaction: It then turns out that Nous is secondary to the One, so there is a hierarchy of Being (which only enters at the Nous stage).