38 ideas
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| Full Idea: In present-day mathematics, it is set theory that serves as the background theory in which other branches of mathematics are developed. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: [He cites Bourbaki as an authority for this] See Benacerraf for a famous difficulty here, when you actually try to derive an ontology from the mathematicians' working practices. |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| Full Idea: On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference. |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| Full Idea: One might meet the 'Van Inwagen Problem' by saying that the intrinsic properties of the object playing the role of 2 will differ from one model to another, so that no statement about the intrinsic properties of 'the' real numbers will make sense. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: There seems to be a potential confusion among opponents of structuralism between relations at the level of actual mathematical operations, and generalisations about relations, which are captured in the word 'patterns'. Call them 'meta-relations'? |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| Full Idea: It is to set theory that one turns for the very definition of 'structure', ...and this creates a problem of circularity if we try to impose a structuralist interpretation on set theory. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: This seems like a nice difficulty, especially if, like Shapiro, you wade in and try to give a formal account of structures and patterns. Resnik is more circumspect and vague. |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| Full Idea: Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions). | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general. |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| Full Idea: The 'Van Inwagen Problem' for structuralism is of explaining how a mathematical relation (such as set membership, or the ratios of an ellipse) can fit into one of the three scholastics types of relations: are they internal, external, or intrinsic? | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: The difficulty is that mathematical objects seem to need intrinsic properties to get any of these three versions off the ground (which was Russell's complaint against structures). |
| 14308 | We can bring dispositions into existence, as in creating an identifier [Dennett, by Mumford] |
| Full Idea: We can bring a real disposition into existence, as in Dennett's case of a piece of cardboard torn in half, so that two strangers can infallibly identify one another. | |
| From: report of Daniel C. Dennett (Consciousness Explained [1991], p.376) by Stephen Mumford - Dispositions 03.7 n37 | |
| A reaction: Presumably human artefacts in general qualify as sets of dispositions which we have created. |
| 7384 | Words are fixed by being attached to similarity clusters, without mention of 'essences' [Dennett] |
| Full Idea: We don't need 'essences' or 'criteria' to keep the meaning of our word from sliding all over the place; our words will stay put, quite firmly attached as if by gravity to the nearest similarity cluster. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 13.2) | |
| A reaction: Plausible, but essentialism (which may have been rejuventated by a modern theory of reference in language) is not about language. It is offering an explanation of why there are 'similarity clusters. Organisms are too complex to have pure essences. |
| 7374 | Light wavelengths entering the eye are only indirectly related to object colours [Dennett] |
| Full Idea: The wavelengths of the light entering the eye are only indirectly related to the colours we see objects to be. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 12.2) | |
| A reaction: This is obviously bad news for naïve realism, but I also take it as good support for the primary/secondary distinction. I just can't make sense of anyone claiming that colour exists anywhere else except in the brain. |
| 7369 | Brains are essentially anticipation machines [Dennett] |
| Full Idea: All brains are, in essence, anticipation machines. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 7.2) | |
| A reaction: This would necessarily, I take it, make them induction machines. So brains will only evolve in a world where induction is possible, which is one where there a lot of immediately apprehensible regularities. |
| 7393 | We can't draw a clear line between conscious and unconscious [Dennett] |
| Full Idea: Even in our own case, we cannot draw the line separating our conscious mental states from our unconscious mental states. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 14.2) | |
| A reaction: This strikes me as being a simple and self-evident truth, which anyone working on the brain takes for granted, but an awful lot of philosophers (stuck somewhere in the seventeenth century) can't seem to grasp. |
| 7367 | Perhaps the brain doesn't 'fill in' gaps in consciousness if no one is looking. [Dennett] |
| Full Idea: Perhaps the brain doesn't actually have to go to the trouble of "filling in" anything with "construction" - for no one is looking. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 5.4) | |
| A reaction: This a very nice point, because claims that the mind fills in in various psychological visual tests always has the presupposition of a person (or homunculus?) which is overseeing the visual experiences. |
| 7394 | Conscious events can only be explained in terms of unconscious events [Dennett] |
| Full Idea: Only a theory that explained conscious events in terms of unconscious events could explain consciousness at all. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 14.4) | |
| A reaction: This sounds undeniable, so it seems to force a choice between reductive physicalism and mysterianism. Personally I think there must be an explanation in terms of non-conscious events, even if humans are too thick to understand it. |
| 7391 | We can know a lot of what it is like to be a bat, and nothing important is unknown [Dennett] |
| Full Idea: There is at least a lot that we can know about what it is like to be a bat, and Nagel has not given us a reason to believe there is anything interesting or theoretically important that is inaccessible to us. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 14.2) | |
| A reaction: I agree. If you really wanted to identify with the phenomenology of bathood, you could spend a lot of time in underground caves whistling with your torch turned off. I can't, of course, be a bat, but then I can't be my self of yesterday. |
| 7387 | "Qualia" can be replaced by complex dispositional brain states [Dennett] |
| Full Idea: "Qualia" can be replaced by complex dispositional states of the brain. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 14.1) | |
| A reaction: 'Dispositional' reveals Dennett's behaviourist roots (he was a pupil of Ryle). Fodor is right that physicalism cannot just hide behind the word "complexity". That said, the combination of complexity and speed might add up to physical 'qualia'. |
| 7376 | We can't assume that dispositions will remain normal when qualia have been inverted [Dennett] |
| Full Idea: The goal of the experiment was to describe a case in which it was obvious that the qualia would be inverted while the reactive dispositions would be normalized. But the assumption that one could just tell is question-begging. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 12.4) | |
| A reaction: It certainly seems simple and plausible that if we inverted our experience of traffic light colours, no difference in driver behaviour would be seen. However, my example, of a conversation in a gallery of abstract art, seems more problematic. |
| 7372 | In peripheral vision we see objects without their details, so blindsight is not that special [Dennett] |
| Full Idea: If a playing card is held in peripheral vision, we can see the card without being able to identify its colours or its shapes. That's normal sight, not blindsight, so we should be reluctant on those grounds to deny visual experience to blindsight subjects. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 11.4) | |
| A reaction: This is an important point in Dennett's war against the traditional all-or-nothing view of mental events. Nevertheless, blindsight subjects deny all mental experience, while picking up information, and peripheral vision never seems like that. |
| 7373 | Blindsight subjects glean very paltry information [Dennett] |
| Full Idea: Discussions of blindsight have tended to ignore just how paltry the information is that blindsight subjects glean from their blind fields. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 11.4) | |
| A reaction: This is a bit unfair, because blindsight has mainly pointed to interesting speculations (e.g. Idea 2953). Nevertheless, if blindsight with very high information content is actually totally impossible, the speculations ought to be curtailed. |
| 7385 | People accept blurred boundaries in many things, but insist self is All or Nothing [Dennett] |
| Full Idea: Many people are comfortable taking the pragmatic approach to night/day, living/nonliving and mammal/premammal, but get anxious about the same attitude to having a self and not having a self. It must be All or Nothing, and One to a Customer. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 13.2) | |
| A reaction: Personally I think I believe in the existence of the self, but I also agree with Dennett. I greatly admire his campaign against All or Nothing thinking, which is a relic from an earlier age. A partial self could result from infancy or brain damage. |
| 7383 | The psychological self is an abstraction, not a thing in the brain [Dennett] |
| Full Idea: Like the biological self, the psychological or narrative self is an abstraction, not a thing in the brain. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 13.1) | |
| A reaction: Does Dennett have empirical evidence for this claim? It seems to me perfectly possible that there is a real thing called the 'self', and it is the central controller of the brain (involving propriotreptic awareness, understanding, and will). |
| 7386 | Selves are not soul-pearls, but artefacts of social processes [Dennett] |
| Full Idea: Selves are not independently existing soul-pearls, but artefacts of the social processes that create us, and, like other such artefacts, subject to sudden shifts in status. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 13.2) | |
| A reaction: "Soul-pearls" is a nice phrase for the Cartesian view, but there can something between soul-pearls and social constructs. Personally I think the self is a development of the propriotreptic (body) awareness that even the smallest animals must possess. |
| 7381 | We tell stories about ourselves, to protect, control and define who we are [Dennett] |
| Full Idea: Our fundamental tactic of self-protection, self-control and self-definition is telling stories, and more particularly concocting and controlling the story we tell others - and ourselves - about who we are. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 13.1) | |
| A reaction: This seems to suggest that there is someone who wants to protect themselves, and who wants to tell the stories, and does tell the stories. No one can deny the existence of this autobiographical element in our own identity. |
| 7382 | We spin narratives about ourselves, and the audience posits a centre of gravity for them [Dennett] |
| Full Idea: The effect of our string of personal narratives is to encourage the audience to (try to) posit a unified agent whose words they are, about whom they are: in short, to posit a centre of narrative gravity. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 13.1) | |
| A reaction: What would be the evolutionary advantage of getting the audience to posit a non-existent self, instead of a complex brain? It might be simpler than that, since we say of a bird "it wants to do x". What is "it"? Some simple thing, like a will. |
| 7370 | The brain is controlled by shifting coalitions, guided by good purposeful habits [Dennett] |
| Full Idea: Who's in charge of the brain? First one coalition and then another, shifting in ways that are not chaotic thanks to good meta-habits that tend to entrain coherent, purposeful sequences rather than an interminable helter-skelter power grab. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 8.1) | |
| A reaction: This is probably the best anti-ego account available. Dennett offers our sense of self as a fictional autobiography, but the sense of a single real controller is very powerful. If I jump at a noise, I feel that 'I' have lost control of myself. |
| 7379 | If an epiphenomenon has no physical effects, it has to be undetectable [Dennett] |
| Full Idea: Psychologists mean a by-product by an 'epiphenomenon', ...but the philosophical meaning is too strong: it yields a concept of no utility whatsoever. Since x has no physical effects (according to the definition), no instrument can detect it. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 12.5) | |
| A reaction: Well said! This has always been my half-formulated intuition about the claim that the mind (or anything) might be totally epiphenomenal. All a thing such as the reflection on a lake can be is irrelevant to the functioning of that specified system. |
| 7365 | Dualism wallows in mystery, and to accept it is to give up [Dennett] |
| Full Idea: Given the way dualism wallows in mystery, accepting dualism is giving up. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 2.4) | |
| A reaction: Some things, of course, might be inherently mysterious to us, and we might as well give up. The big dualist mystery is the explanation of how such different substances can interact. How do two physical substances manage to interact? |
| 7371 | All functionalism is 'homuncular', of one grain size or another [Dennett] |
| Full Idea: All varieties of functionalism can be viewed as 'homuncular' functionalism of one grain size or another. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 9.2) | |
| A reaction: This seems right, as any huge and complex mechanism (like a moon rocket) will be made up of some main systems, then sub-systems, then sub-sub-sub.... This assumes that there are one or two overarching purposes, which there are in people. |
| 7380 | Visual experience is composed of neural activity, which we find pleasing [Dennett] |
| Full Idea: All visual experience is composed of activities of neural circuits whose very activity is innately pleasing to us. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 12.6) | |
| A reaction: This is the nearest I can find to Dennett saying something eliminativist. It seems to beg the question of who 'us' refers to, and what is being pleased, and how it is 'pleased' by these neural circuits. The Hard Question? |
| 7366 | It is arbitrary to say which moment of brain processing is conscious [Dennett] |
| Full Idea: If one wants to settle on some moment of processing in the brain as the moment of consciousness, this has to be arbitrary. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 5.3) | |
| A reaction: Seems eliminativist, as it implies that all that is really going on is 'processing'. But there are two senses of 'arbitrary' - that calling it consciousness is arbitrary (wrong), or thinking that mind doesn't move abruptly into consciousness (right). |
| 7368 | Originally there were no reasons, purposes or functions; since there were no interests, there were only causes [Dennett] |
| Full Idea: In the beginning there were no reasons; there were only causes. Nothing had a purpose, nothing had so much as a function; there was no teleology in the world at all. The explanation is simple: there was nothing that had interests. | |
| From: Daniel C. Dennett (Consciousness Explained [1991], 7.2) | |
| A reaction: It seems reasonable to talk of functions even if the fledgling 'interests' are unconscious, as in a leaf. Is a process leading to an end an 'interest'? What are the 'interests' of a person who is about to commit suicide? |