7 ideas
| 18281 | In mathematics everything is algorithm and nothing is meaning [Wittgenstein] |
| Full Idea: In mathematics everything is algorithm and nothing is meaning; even when it doesn't look like that because we seem to be using words to talk about mathematical things. | |
| From: Ludwig Wittgenstein (Philosophical Grammar [1932], p.468), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 13 'Constr' | |
| A reaction: I would have thought that an algorithm needs some raw material to work with. This leads to the idea that meaning arises from rules of usage. |
| 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) |
| 6606 | Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful" [Wittgenstein] |
| Full Idea: Suppose someone were to say: "Imagine this butterfly exactly as it is, but ugly instead of beautiful"?! | |
| From: Ludwig Wittgenstein (Philosophical Grammar [1932], §127), quoted by Robert Fogelin - Walking the Tightrope of Reason | |
| A reaction: This reminds us that the concept of supervenience was originally introduced in aesthetics. Beauty is supervenient on physical form. But "Imagine how someone else might look at this butterfly and think it was ugly". |
| 19739 | The maxim for suicide is committed to the value of life, and is thus contradictory [Kant] |
| Full Idea: If my maxim is to shorten my life if its continuance threatens more evil than pleasure ...it is seen that a system of nature by whose law the feeling intended to further life should actually destroy life would contradict itself, and could not subsist. | |
| From: Immanuel Kant (Lectures on Ethics [1780], 422:53) | |
| A reaction: [compressed] I take it this means that a potential suicide is assessing what is best for life, and is therefore implicitly committed to life. Not persuasive! Should we not terminate the life of a mass murderer in mid-crime? |