21 ideas
| 21406 | Because there is only one human reason, there can only be one true philosophy from principles [Kant] |
| Full Idea: Considered objectively, there can only be one human reason, there cannot be many philosophies; in other words, there can only be one true philosophy from principles, in however many conflicting ways men have philosophised about the same proposition. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], Pref) | |
| A reaction: An idea that embodies the Enlightenment ideal. I like the idea that there is one true philosophy, because there is only one world. Kant is talking of philosophy 'from principles', which means his transendental idealism. |
| 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. |
| 21081 | We are equipped with the a priori intuitions needed for the concept of right [Kant] |
| Full Idea: Reason has taken care that the understanding is as fully equipped as possible with a priori intuitions for the construction of the concept of right. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], Intro E) | |
| A reaction: A priori intuitions are not the same as innate knowledge or innate concepts, but they must require some sort of inbuilt inner resources. Further evidence that Kant is a rationalist philosopher (if we were unsure). |
| 6316 | We translate in a way that makes the largest possible number of statements true [Wilson,NL] |
| Full Idea: We select as designatum that individual which will make the largest possible number of statements true. | |
| From: N.L. Wilson (Substances without Substrata [1959]), quoted by Willard Quine - Word and Object II.§13 n | |
| A reaction: From the Quine's reference, it sounds as if Wilson was the originator of the well-known principle of charity, later taken up by Davidson. If so, he should be famous, because it strikes me as a piece of fundamental and important wisdom. |
| 21082 | A power-based state of nature may not be unjust, but there is no justice without competent judges [Kant] |
| Full Idea: The state of nature need not be a state of injustice merely because those who live in it treat one another in terms of power. But it is devoid of justice, for if a dispute over right occurs in it, there is no competent judge to give valid decisions. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §44) | |
| A reaction: Could you not achieve justice by means of personal violence? Might not a revered older person have been accepted as a judge? |
| 21089 | Monarchs have the highest power; autocrats have complete power [Kant] |
| Full Idea: A monarch has the highest power, while an autocrat or absolute ruler is one who has all the power. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §51) | |
| A reaction: If society is strictly hierarchical (like an army) then the monarch also has all the power. At the other extreme the one holding the highest power may have very little power, because so many others have their share of the power. |
| 21086 | Hereditary nobility has not been earned, and probably won't be earned [Kant] |
| Full Idea: A hereditary nobility is a distinction bestowed before it is earned, and since it gives no ground for hoping that it will be earned, it is wholly unreal and fanciful. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §49 Gen D) | |
| A reaction: As the controller of the region of a country, a hereditary noble is the embodiment of a ruling family, which is a well established way of running things. Daft, perhaps, but there are probably worse ways of doing it. Single combat, for example. |
| 21080 | Actions are right if the maxim respects universal mutual freedoms [Kant] |
| Full Idea: Every action which by itself or by its maxim enables the freedom of each individual's will to co-exist with the freedom of everyone else in accordance with a universal law is right. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], Intro C) | |
| A reaction: This idea shows the moral basis for Kant's liberalism in politics. If all individuals acted without contact or reference to other individuals (a race of hermits) then that would appear to be optimum moral right, by this standard. |
| 21083 | Women have no role in politics [Kant] |
| Full Idea: Women in general …have no civil personality. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §46) | |
| A reaction: In case you were wondering. This is five years after Mary Wollstonecraft's book. |
| 21407 | Equality is not being bound in ways you cannot bind others [Kant] |
| Full Idea: Our innate equality is independence from being bound by others to more than one can in turn bind them. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], Div B) | |
| A reaction: This doesn't seem to capture the whole concept. The two of us may be unequally oppressed by a third. We are unequal with the third, but also with one another, though with no binding relationships. |
| 21084 | In the contract people lose their rights, but immediately regain them, in the new commonwealth [Kant] |
| Full Idea: By the original contract all members of the people give up their external freedom in order to receive it back at once as members of a commonweath. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §47) | |
| A reaction: This tries to give the impression that absolutely nothing is lost in the original alienation of rights. It is probably better to say that you give up one set of freedoms, which are replaced by a different (and presumably superior) set. |
| 21090 | If someone has largely made something, then they own it [Kant] |
| Full Idea: Whatever someone has himself substantially made is his own undisputed property. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §55) | |
| A reaction: To this extent Kant offers clear agreement with Locke about a self-evident property right. Ownership of land is the controversial bit. |
| 21087 | Human life is pointless without justice [Kant] |
| Full Idea: If justice perishes, there is no further point in men living on earth. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §49 Gen E) | |
| A reaction: I suspect that human life is also pointless if it only involves justice, and nothing else worthwhile. Are there other things so good that we might sacrifice justice to achieve them? How about maximal utilitarian happiness? |
| 21088 | Justice asserts the death penalty for murder, from a priori laws [Kant] |
| Full Idea: All murderers …must suffer the death penalty. This is what justice, as the idea of judicial power, wills in accordance with universal laws of a priori origin. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §49 Gen E) | |
| A reaction: Illustration of how giving a principle an a priori origin puts it beyond dispute. Kant is adamant that mercy mustn't interfere with the enactment of justice. And Kant obviously rejects any consequentialist approach. Remind me what is wrong with murder? |
| 21085 | The church has a political role, by offering a supreme power over people [Kant] |
| Full Idea: The church [as opposed to religion] fulfils a genuine political necessity, for it enables the people to regard themselves as subjects of an invisible supreme power to which they must pay homage. | |
| From: Immanuel Kant (Metaphysics of Morals I: Doctrine of Right [1797], §49 Gen C) | |
| A reaction: I'm sure I remember Marx putting a different spin on this point… This idea captures the conservative attitude to established religion, at least in the UK. |