2008 | Guidebook to Wittgenstein's Tractatus |
Intro | p.14 | 23460 | To count, we must distinguish things, and have a series with successors in it |
Full Idea: Distinguishing between things is not enough for counting. …We need the crucial extra notion of a successor in a series of a certain kind. | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro) | |||
A reaction: This is the thinking that led to the Dedekind-Peano axioms for arithmetic. E.g. each series member can only have one successor. There is an unformalisable assumption that the series can then be applied to the things. |
Intro.2 | p.7 | 23449 | Interpreting a text is representing it as making sense |
Full Idea: Interpreting a text is a matter of making sense of it. And to make sense of a text is to represent it as making sense. | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro.2) | |||
A reaction: 'Making sense' is obviously not a very precise or determinate concept. It is probably better to say that the process is 'trying' to make sense of the text, because most texts don't totally make sense. |
Intro.5 | p.14 | 23451 | Counting needs to distinguish things, and also needs the concept of a successor in a series |
Full Idea: Just distinguishing things is not enough for counting (and hence arithmetic). We need the crucial extra notion of the successor in a series of some kind. | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro.5) | |||
A reaction: This is a step towards the Peano Axioms of arithmetic. The successors could be fingers and toes, taken in a conventional order, and matched one-to-one to the objects. 'My right big toe of cows' means 16 cows (but non-verbally). |
Intro.5 | p.15 | 23452 | Discriminating things for counting implies concepts of identity and distinctness |
Full Idea: The discrimination of things for counting needs to bring with it the notion of identity (and, correlatively, distinctness). | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], Intro.5) | |||
A reaction: Morris is exploring how practices like counting might reveal necessary truths about the world. |
3D | p.133 | 23484 | Bipolarity adds to Bivalence the capacity for both truth values |
Full Idea: According to the Principle of Bipolarity, every meaningful sentence must be capable both of being true and of being false. It is not enough merely that every sentence must be either true or false (which is Bivalence). | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 3D) | |||
A reaction: It is said that early Wittgenstein endorses this. That is, in addition to being true, the sentence must be capable of falsehood (and vice versa). This seems to be flirting with the verification principle. I presume it is 'affirmative' sentences. |
4.5 | p.36 | 23491 | There must exist a general form of propositions, which are predictabe. It is: such and such is the case |
Full Idea: The existence of a general propositional form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i.e. constructed). The general form of the proposition is: Such and such is the case. | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 4.5) | |||
A reaction: [last bit in Ogden translation] LW eventually expresses this symbolically. We could just say a proposition is an assertion. This strikes as either a rather empty claim, or an unfounded one. |
5C | p.218 | 23494 | Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite |
Full Idea: There are two problems with defining the quantifiers in terms of conjunction and disjunction. The general statements are unspecific, and do not say which things have the properties, and also they can't range over infinite objects. | |||
From: Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 5C) | |||
A reaction: That is, the universal quantifier is lots of ands, and the existential is lots of ors. If there only existed finite objects, then naming them all would be universal, and the infinite wouldn't be needed. |