11 ideas
10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
14759 | A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad] |
Full Idea: A thing is simply a long event, throughout the course of which there is either qualitative similarity or continuous qualitative change, together with a characteristic spatio-temporal unity. | |
From: C.D. Broad (Scientific Thought [1923], 10 'Duration') | |
A reaction: At least he is trying to give some sort of principle that links the stages of the event together. |
11842 | If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad] |
Full Idea: We call a lightning flash or a motor accident an event, but refuse to apply this to the cliffs of Dover. ...But quantitative differences (of time) give no good grounds for calling one bit of history an event, and refusing the name to another bit. | |
From: C.D. Broad (Scientific Thought [1923], p.54), quoted by David Wiggins - Sameness and Substance Renewed 2.3 n13 | |
A reaction: Wiggins calls this proposal a 'terrible absurdity', but it seems to me to demand attention. There is a case to be made for a 'process' to be the fundamental category of our ontology, with stable physical objects seen in that light. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
8160 | The present and past exist, but the future does not [Broad, by Dummett] |
Full Idea: Not only the present but also the past exist, but the future (so long as it is the future) does not. | |
From: report of C.D. Broad (Scientific Thought [1923]) by Michael Dummett - Thought and Reality 1 | |
A reaction: This is quite appealing, and seems right if you believe that every truth has a truthmaker, and that there are no truths about the future. And yet the whole misery of people dying is that they cease to exist. |
14609 | We could say present and past exist, but not future, so that each event adds to the total history [Broad] |
Full Idea: One theory accepts the reality of the present and the past, but holds that the future is simply nothing at all. Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. | |
From: C.D. Broad (Scientific Thought [1923], II) | |
A reaction: This is now known as Broad's 'Growing Block' view of time. It is tempting to say that neither past nor future exist, but it seems undeniable that statements about the past can be wholly true, unlike those about the future. |
22933 | We imagine the present as a spotlight, moving across events from past to future [Broad] |
Full Idea: We imagine presentness moving, like the spot of light from a policeman's bulls eye traversing the fronts of houses in a street. What is illuminated is present, what was illuminated is past, and what is not yet illuminated is the future. | |
From: C.D. Broad (Scientific Thought [1923], II) | |
A reaction: This is the 'moving spotlight' compromise theory, which retains the B-series eternal sequence of ordered events, but adds the A-series privileged present moment. Le Poidevin says Broad represents time twice over. |