24 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. |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| Full Idea: The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1) | |
| A reaction: This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything. |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
| Full Idea: Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008. |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| Full Idea: There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four'). | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1) | |
| A reaction: Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers. |
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| Full Idea: There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related? | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1) | |
| A reaction: A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first? |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| Full Idea: Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2) | |
| A reaction: His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects. |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| Full Idea: I argue for an internalist conception of arithmetic. Arithmetic is not about a domain of entities, not even quantified entities. Quantifiers over natural numbers occur in their inferential-role reading in which they merely generalize over the instances. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: Hofweber offers the hope that modern semantics can disentangle the confusions in platonist arithmetic. Very interesting. The fear is that after digging into the semantics for twenty years, you find the same old problems re-emerging at a lower level. |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| Full Idea: That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2) | |
| A reaction: This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them. |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| Full Idea: Determiner uses of number words may disappear on analysis. This is inspired by Russell's elimination of the word 'the'. The number becomes blocks of first-order quantifiers at the level of semantic representation. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2) | |
| A reaction: [compressed] The proposal comes from platonists, who argue that numbers cannot be analysed away if they are objects. Hofweber says the analogy with Russell is wrong, as 'the' can't occur in different syntactic positions, the way number words can. |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| Full Idea: Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting. |
| 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). |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| Full Idea: Our minds mainly reason about objects. Most cognitive problems we are faced with deal with particular objects, whether they are people or material things. Reasoning about them is what our minds are good at. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.3) | |
| A reaction: Hofweber is suggesting this as an explanation of why we continually reify various concepts, especially numbers. Very plausible. It works for qualities of character, and explains our tendency to talk about universals as objects ('redness'). |
| 19423 | By an 'idea' I mean not an actual thought, but the resources we can draw on to think [Leibniz] |
| Full Idea: What I mean by an idea is not a certain act of thinking, but a power or faculty such that we have an idea of a thing even if we are not thinking about it but know that we can think it when the occasion arises. | |
| From: Gottfried Leibniz (What is an Idea? [1676], p.281) | |
| A reaction: 'Idea' tends to be used in the seventeenth century to mean an actual mental event. It is because Leibniz believes in the unconscious mind that he can offer this rather different, and probably superior, notion of an 'idea'. |
| 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. |