19 ideas
| 19441 | All philosophies presuppose their historical moment, and arise from it [Feuerbach] |
| Full Idea: Every philosophy originates as a manifestation of its time; its origin presupposes its historical time. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.59) | |
| A reaction: There seems to be widespread agreement among continental philosophers about this idea, whereas analytic philosophers largely ignore, and treat Plato as if he were a current professor in Chicago. |
| 19442 | I don't study Plato for his own sake; the primary aim is always understanding [Feuerbach] |
| Full Idea: Plato in writing is only a means for me; that which is primary and a priori, that which is the ground to which all is ultimately referred, is understanding. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.63) | |
| A reaction: It always seems to that the main aim of philosophy is understanding - which is why its central activity is explanation. |
| 19445 | A dialectician has to be his own opponent [Feuerbach] |
| Full Idea: A thinker is a dialectician only insofar as he is his own opponent. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.72) | |
| A reaction: Quite an inspirational slogan for beginners in philosophy. How many non-philosophers are willing to be their own opponent. In law courts and the House of Commons we assign the roles to separate persons. Hence rhetoric replaces reason? |
| 19444 | Each proposition has an antithesis, and truth exists as its refutation [Feuerbach] |
| Full Idea: Every intellectual determination has its antithesis, its contradiction. Truth exists not in unity with, but in refutation of its opposite. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.72) | |
| A reaction: This appears to be a rejection of the 'synthesis' in Hegel, in favour of what strikes me as a rather more sensible interpretation of the modern dialectic. Being exists in contrast to nothingness, and truth exists in contrast to its negation? |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 19443 | Truth forges an impersonal unity between people [Feuerbach] |
| Full Idea: The urge to communicate is a fundamental urge - the urge for truth. ...That which is true belongs neither to me nor exclusively to you, but is common to all. The thought in which 'I' and 'You' are united is a true thought. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.65) | |
| A reaction: Sceptics may doubt that there are such truths, but this is certainly how we experience agreement - that there is some truth shared between us which is no longer the possession of either of us. Nice idea. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 19405 | Substances are in harmony, because they each express the one reality in themselves [Leibniz] |
| Full Idea: Every substance expresses the whole sequence of the universe in accordance with its own viewpoint or relationship to the rest, so that all are in perfect correspondence with one another. | |
| From: Gottfried Leibniz (Identity in Substances and True Propositions [1686], p.98) | |
| A reaction: Thus 'expression' (something like mapping what is exterior) is the mechanism through which God achieves harmony in the universe. Instants of time are said to be successive moments of perfect harmony. |
| 19446 | To our consciousness it is language which looks unreal [Feuerbach] |
| Full Idea: To sensuous consciousness it is precisely language that is unreal, nothing. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.77) | |
| A reaction: Offered as a corrective to the view that our ontological commitments entirely concern what we are willing to say. |
| 19447 | The Absolute is the 'and' which unites 'spirit and nature' [Feuerbach] |
| Full Idea: The Absolute is spirit and nature. ...But what then is the Absolute? Nothing other than this 'and', that is, the unity of spirit and nature. | |
| From: Ludwig Feuerbach (Towards a Critique of Hegel's Philosophy [1839], p.82) | |
| A reaction: This is Feuerbach's spin on Hegel. He has been outlining idealist philosophy and the philosophy of nature in Schelling. Is this Spinoza's one substance? |