15 ideas
| 20923 | We take part in objective truth, rather than observe it from a distance [Zimmermann,J] |
| Full Idea: Hermeneutic thinkers insist that we need to redefine objective truth as something we take part in rather than something we merely observe from a distance. | |
| From: Jens Zimmermann (Hermeneutics: a very short introduction [2015], 1 'Truth') | |
| A reaction: Don't get it. If I objectively judge that there are some cows in a field, I judge that they will probably still be there if I turn away and forget them, so any passionate involvement I have with cows is irrelevant to the objective facts. Am I wrong? |
| 20926 | Hermeneutic knowledge is not objective, but embraces interpretations [Zimmermann,J] |
| Full Idea: In the hermeneutic ideal of knowledge, not distance but involvement, not impersonal observation but personal interaction, not thinking against prejudice or tradition but accessing knowledge through them, characterizes our perception of the world. | |
| From: Jens Zimmermann (Hermeneutics: a very short introduction [2015], 3 'Beyond') | |
| A reaction: To make this stick it will have to challenge scientific knowledge which results from mathematical summaries of measurements done by instruments. Is a stop watch an interpretation? |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 20924 | In phenomenology, all perception is 'seeing as' [Zimmermann,J] |
| Full Idea: That human perception is always a 'seeing as' was the cardinal insight of what Husserl called 'phenomenology'. | |
| From: Jens Zimmermann (Hermeneutics: a very short introduction [2015], 2 'Husserl's') | |
| A reaction: I presume that 'cardinal insight' means there is no possibility of Husserl being wrong about this. What's happening before you figure out what it is you are looking at? |
| 21687 | It seems obvious to prefer the simpler of two theories, on grounds of beauty and convenience [Quine] |
| Full Idea: It is not to be wondered that theory makers seek simplicity. When two theories are equally defensible on other counts, certainly the simpler of the two is to be preferred on the score of both beauty and convenience. | |
| From: Willard Quine (On Simple Theories of a Complex World [1960], p.255) | |
| A reaction: A simple application of Ockham's Razor. Quine goes on to nicely deconstruct what is involved in simplicity, and identify a certain amount of dubious prejudice in the concept. |
| 21688 | There are four suspicious reasons why we prefer simpler theories [Quine] |
| Full Idea: We prefer simpler theories through wishful thinking, or a bias which slants the data, or a bias where the simpler hypothesis is more open to confirmation, or simpler hypotheses tolerating wider deviations in score-keeping. | |
| From: Willard Quine (On Simple Theories of a Complex World [1960], p.258) | |
| A reaction: [a compression of his summary of the paper] Quine is not dismissing our preference for simpler theories, but just very nicely inviting us to focus of aspects about which we should be cautious. |
| 20927 | The hermeneutic circle is between the reader's self-understanding, and the world of the text [Zimmermann,J] |
| Full Idea: The 'hermeneutic circle' of understanding is not between the author and the reader, but between my understanding myself in my own world, and the world projected by the text, with its possibilities for life. | |
| From: Jens Zimmermann (Hermeneutics: a very short introduction [2015], 4 'How texts') | |
| A reaction: I'm not much of a fan of hermeneutics, but this idea seems quite important. Readings of Dickens in1860, 1930 and 2020 are very different events. For example, which parts catch the reader's interest, or jar with their sensibilities? |
| 20933 | Natural law theorists fear that without morality, law could be based on efficiency [Zimmermann,J] |
| Full Idea: Natural law theorists fear that by denying the intrinsic connection between law and morality, positivists could encourage the validation of law based on efficiency alone. | |
| From: Jens Zimmermann (Hermeneutics: a very short introduction [2015], 6 'Natural') | |
| A reaction: The law's the law. The issue can only be whether one can ever be justified in breaking a law, and that isn't a legal question. I am sympathetic to the positiviists. |
| 20929 | Traditionally, God dictated the Torah to Moses, unlike the later biblical writings [Zimmermann,J] |
| Full Idea: Jewish traditionalists hold that the first five books of the Hebrew Bible (the 'Torah') were dictated word for word by God to Moses, while the remaining sacred writings were more generally inspired. | |
| From: Jens Zimmermann (Hermeneutics: a very short introduction [2015], 5 'Inspiration') | |
| A reaction: This gives the Torah a similar status to the Quran, and presumably also to the actual words which are ascribed to Jesus in the four gospels. |