15 ideas
| 1564 | True and false statements can use exactly the same words [Anon (Diss)] |
| Full Idea: There is no difference between a true statement and a false statement, because they can use exactly the same words. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §4) |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 1560 | Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)] |
| Full Idea: The Lydians find it acceptable for their daughters to work as prostitutes to raise money for getting married, but no one in Greece would be prepared to marry such a girl. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §2) |
| 1559 | Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)] |
| Full Idea: Thracians think that tattooing enhances a girl's beauty, whereas for everyone else tattooing is a punishment for a crime. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §2) |
| 1561 | Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)] |
| Full Idea: Anything can be acceptable under the right circumstances, and unacceptable under the wrong circumstances. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §2) |
| 1567 | How could someone who knows everything fail to act correctly? [Anon (Diss)] |
| Full Idea: If someone knows the nature of everything, how could he fail to be able also to act correctly in every case? | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §8) |
| 1563 | Every apparent crime can be right in certain circumstances [Anon (Diss), by PG] |
| Full Idea: It can be right, in certain circumstances, to steal, to break a solemn promise, to rob temples, and even (as Orestes did) to murder one's nearest and dearest. | |
| From: report of Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §3) by PG - Db (ideas) | |
| A reaction: Not sure about the last one! I suppose you can justify any hideousness if the fate of the universe depends on it. It must be better to die than the perform certain extreme deeds. |
| 1562 | It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)] |
| Full Idea: It is right to lie to your parents, in order to get them to take a good medicine they are reluctant to take. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §3) | |
| A reaction: I dread to think what the medicines were which convinced the writer of this. A rule such as this strikes me as dangerous. Justifiable in extreme cases. House on fire etc. |
| 7350 | The Torah just says: do not do to your neighbour what is hateful to you [Hillel the Elder] |
| Full Idea: What is hateful to you, do not unto your neighbour: this is the entire Torah. All the rest is commentary - go and study it. | |
| From: Hillel the Elder (reports [c.10]), quoted by Paul Johnson - The History of the Jews Pt II | |
| A reaction: Johnson suggests that this idea, of stripping everything from the Torah except its basic morality, was passed on to Jesus by Hillel. Suppose you hate Arsenal, but your neighbour supports them, and they just won the European Cup? What should you do? |
| 1566 | The first priority in elections is to vote for people who support democracy [Anon (Diss)] |
| Full Idea: A lottery is not democratic, because every state contains people who are not democratic, and if the lottery chooses them they will destroy the democracy. People should elect those who are observed to favour democracy. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §7) |
| 1565 | We learn language, and we don't know who teaches us it [Anon (Diss)] |
| Full Idea: We learn language, and we don't know who teaches us it. | |
| From: Anon (Diss) (Dissoi Logoi - on Double Arguments [c.401 BCE], §6) |