19 ideas
22002 | Wolff's version of Leibniz dominated mid-18th C German thought [Pinkard] |
Full Idea: The dominant philosophy of mid-eighteenth century Germany was Wolffianism, a codified and almost legalistically organised form of Leibnizian thought. | |
From: Terry Pinkard (German Philosophy 1760-1860 [2002], Intro) | |
A reaction: Kant grew up in this intellectual climate. |
22021 | Romantics explored beautiful subjectivity, and the re-enchantment of nature [Pinkard] |
Full Idea: Early Romanticism can be seen as the exploration of subjective interiority and as the re-enchantment of nature (as organic). Hegel said they had the idea of a 'beautiful soul', which (he said) either paralysed action, or made them smug. | |
From: Terry Pinkard (German Philosophy 1760-1860 [2002], 06) | |
A reaction: [compressed, inc Note 1] A major dilemma of life is the extent of our social engagement, because it makes life worthwhile, but pollutes the mind with continual conflicts. |
22010 | The combination of Kant and the French Revolution was an excited focus for German philosophy [Pinkard] |
Full Idea: After the French Revolution, philosophy suddenly became the key rallying point for an entire generation of German intellectuals, who had been reading Kant as the harbinger of a new order. | |
From: Terry Pinkard (German Philosophy 1760-1860 [2002], Pt II Intro) | |
A reaction: Kant was a harbinger because he offered an autonomous status to each individual, rather than being subservient to a social order. |
22036 | In Hegel's time naturalism was called 'Spinozism' [Pinkard] |
Full Idea: In Hegel's time the shorthand for the Naturalistic worldview was 'Spinozism'. | |
From: Terry Pinkard (German Philosophy 1760-1860 [2002], 10) | |
A reaction: Spinozism hit Germany like a bomb in 1786, when it was reported that the poet Hölderlin was a fan of Spinoza. |
13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
8751 | Only applicability raises arithmetic from a game to a science [Frege] |
Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
9891 | The first demand of logic is of a sharp boundary [Frege] |
Full Idea: The first demand of logic is of a sharp boundary. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
22048 | Idealism is the link between reason and freedom [Pinkard] |
Full Idea: Idealism was conceived as a link between reason and freedom. | |
From: Terry Pinkard (German Philosophy 1760-1860 [2002], 14 Conc) | |
A reaction: I'm beginning to see the Romantic era as the Age of Freedom, which followed the Age of Reason. This idea fits that picture nicely. Pinkard says that paradoxes resulted from the attemptl |
9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |