12 ideas
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| Full Idea: The result of joining Hume's Principle to second-order logic is a consistent system which is a foundation for arithmetic, in the sense that all the fundamental laws of arithmetic are derivable within it as theorems. This seems a vindication of logicism. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: The controversial part seems to be second-order logic, which Quine (for example) vigorously challenged. The contention against most attempts to improve Frege's logicism is that they thereby cease to be properly logical. |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| Full Idea: The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?) | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 3) | |
| A reaction: One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right. |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| Full Idea: It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 8) | |
| A reaction: It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading. |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| Full Idea: Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant. | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2) | |
| A reaction: Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting. |
| 5673 | If we have a pain, we are strongly aware of the bodily self [Cassam] |
| Full Idea: Since sensations such as pain generally present themselves as in some part of one's body, the bodily self seems to be anything but elusive in sensory awareness. | |
| From: Quassim Cassam (Introduction to 'Self-Knowledge' [1994], §I) | |
| A reaction: This strikes me as a really good observation. Whenever we do Hume's experiment in introspection, we tend to examine either pure sense experiences or abstract ideas. If we introspect a pain, we actually find the body at the centre of activity. |
| 5670 | Knowledge of thoughts covers both their existence and their contents [Cassam] |
| Full Idea: Our knowledge of our thoughts includes both our knowledge that we think and our knowledge of the contents of our thought. | |
| From: Quassim Cassam (Introduction to 'Self-Knowledge' [1994], §I) | |
| A reaction: This seems like a simple, self-evident and true distinction. We might question the first part, though. Knowledge involves the contents, but the fact that we think may be an inference from the contents, or even a fictional abstraction. Contents alone? |
| 5671 | Outer senses are as important as introspection in the acquisition of self-knowledge [Cassam] |
| Full Idea: It would be quite legitimate to claim that the outer senses are at least as important as introspection in the acquisition of self-knowledge. | |
| From: Quassim Cassam (Introduction to 'Self-Knowledge' [1994], §I) | |
| A reaction: It is interesting to speculate about the extent to which a 'mind in a void' could have a personal identity. Experiences tend to be 'mine' because of my body, which has a history and a space-time location. But this doesn't make identity entirely cultural. |
| 5672 | Is there a mode of self-awareness that isn't perception, and could it give self-knowledge? [Cassam] |
| Full Idea: The key questions are: can one be introspectively aware of oneself other than through an inner sense, and, if there is a non-perceptual mode of introspective self-awareness, can it be the ground or basis of one's self-knowledge? | |
| From: Quassim Cassam (Introduction to 'Self-Knowledge' [1994], §I) | |
| A reaction: Perception would involve a controlled attempt to experience a separate object. The other mode would presumably be more direct. The question boils down to 'is there an object which introspection can attempt to perceive?' Good question. |
| 5675 | Neither self-consciousness nor self-reference require self-knowledge [Cassam] |
| Full Idea: According to Kant, self-consciousness does not require self-knowledge, and it also appears that self-reference does not require self-knowledge. | |
| From: Quassim Cassam (Introduction to 'Self-Knowledge' [1994], §II) | |
| A reaction: Kant's point is that knowledge requires a stage of conceptualisation, which simple self-consciousness might not involve. The second point is that self-reference require no knowledge because error is impossible. Two nice points, and useful distinctions. |
| 5674 | We can't introspect ourselves as objects, because that would involve possible error [Cassam] |
| Full Idea: One can identify an object in a mirror as oneself, but that brings with it the possibility of misidentification, so since introspective awareness statements are immune to error, one is not introspectively aware of oneself as an object. | |
| From: Quassim Cassam (Introduction to 'Self-Knowledge' [1994], §I) | |
| A reaction: As a pure argument this looks weak. There could be two sorts of knowledge of objects, one admitting possible error, the other not. Introspecting pain appears to be awareness of oneself as an object. Planning my future needs my body. |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| Full Idea: An example of a first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines; a higher-order example (which refers to first-order predicates) defines 'equinumeral' in terms of one-to-one correlation (Hume's Principle). | |
| From: B Hale / C Wright (Logicism in the 21st Century [2007], 1) | |
| A reaction: [compressed] This is the way modern logicians now treat abstraction, but abstraction principles include the elusive concept of 'equivalence' of entities, which may be no more than that the same adjective ('parallel') can be applied to them. |
| 22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
| Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
| From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
| A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |