display all the ideas for this combination of texts
5 ideas
| 10048 | There is no clear boundary between the logical and the non-logical [Tarski] |
| Full Idea: No objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms, the logical and the non-logical. | |
| From: Alfred Tarski (works [1936]), quoted by Alan Musgrave - Logicism Revisited §3 | |
| A reaction: Musgrave is pointing out that this is bad news if you want to 'reduce' something like arithmetic to logic. 'Logic' is a vague object. |
| 10694 | Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall] |
| Full Idea: Tarski's 1936 definition of logical consequence is that in any model in which the premises are true, the conclusion is true too (so that no model can make the conclusion false). | |
| From: report of Alfred Tarski (works [1936]) by JC Beall / G Restall - Logical Consequence 3 | |
| A reaction: So the general idea is that a logical consequence is distinguished by being unstoppable. Sounds good. But then we have monotonic and non-monotonic logics, which (I'm guessing) embody different notions of consequence. |
| 10479 | Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W] |
| Full Idea: Tarski's definition of logical consequence (1936) is that in a fully interpreted formal language an argument is valid iff under any allowed interpretation of its nonlogical symbols, if the premises are true then so is the conclusion. | |
| From: report of Alfred Tarski (works [1936]) by Wilfrid Hodges - Model Theory 3 | |
| A reaction: The idea that you can only make these claims 'under an interpretation' seems to have had a huge influence on later philosophical thinking. |
| 8447 | In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege] |
| Full Idea: The reference of 'Etna' cannot be Mount Etna itself, because each piece of frozen lava which is part of Mount Etna would then also be part of the thought that Etna is higher than Vesuvius. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.43) | |
| A reaction: This seems to be a straight challenge to Kripke's baptismal account of reference. I think I side with Kripke. Frege is allergic to psychological accounts, but the mind only has the capacity to think of the aspect of Etna that is relevant. |
| 8448 | Any object can have many different names, each with a distinct sense [Frege] |
| Full Idea: An object can be determined in different ways, and every one of these ways of determining it can give rise to a special name, and these different names then have different senses. | |
| From: Gottlob Frege (Letters to Jourdain [1910], p.44) | |
| A reaction: This seems right. No name is an entirely neutral designator. Imagine asking a death-camp survivor their name, and they give you their prison number. Sense clearly intrudes into names. But picking out the object is what really matters. |