10 ideas
| 13163 | Circles must be bounded, so cannot be infinite [Leibniz] |
| Full Idea: An infinite circle is impossible, since any circle is bounded by its circumference. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114) | |
| A reaction: This is interesting if one is asking what the essence of a circle must be. If is tempting to say merely that the radii must be equal, but can they have the length of some vast transfinite number? The circumference must be 2π bigger. |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required. | |
| From: Dorothy Edgington (Conditionals [2001], 17.2.1) |
| 13770 | There are many different conditional mental states, and different conditional speech acts [Edgington] |
| Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc. | |
| From: Dorothy Edgington (Conditionals [2001], 17.3.4) |
| 13764 | Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington] |
| Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'? | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional. |
| 13765 | 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington] |
| Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B). | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true. |
| 8406 | Not all explanations are causal, but if a thing can be explained at all, it can be explained causally [Sanford] |
| Full Idea: Although not all explanations are causal, anything which can be explained in any way can be explained causally. | |
| From: David H. Sanford (Causation [1995], p.79) | |
| A reaction: A nice bold claim with which I am in sympathy, but he would have a struggle proving it. Does this imply that causal explanations are basic, or in some way superior? Note that functional explanations would thus have underlying causal explanations. |
| 13162 | Sloth's Syllogism: either it can't happen, or it is inevitable without my effort [Leibniz] |
| Full Idea: The ancient Sloth's Syllogism says that if something is foreseen and infallible, it will happen without my effort, and if it is not foreseen, it will not happen, even though I am able to do it. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.113) | |
| A reaction: Presumable the foreseeing is to be done by the oracle, and not by the slothful person. |
| 8407 | A totality of conditions necessary for an occurrence is usually held to be jointly sufficient for it [Sanford] |
| Full Idea: A totality of conditions necessary for an occurrence is jointly sufficient for it. This is a widely held but controversial view, and it is not a logical truth. | |
| From: David H. Sanford (Causation [1995], p.82) | |
| A reaction: This wouldn't work for an impossible occurrence. What are the necessary conditions to produce a large planet made of uranium? One of them would have to be a naturally impossible necessity. |
| 19339 | Evil is a negation of good, which arises from non-being [Leibniz] |
| Full Idea: The cause of good is positive, but evil is a defect, that is, a privation or negation, and consequently, it arises from nothingness or nonbeing. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.114) | |
| A reaction: He goes on to illustrate his idea from mathematics. He is modifying Augustine's view that evil is an absence of good, by adding nonbeing as the driving force behind it. Doesn't sound very persuasive to me. |
| 13164 | God only made sin possible because a much greater good can be derived from it [Leibniz] |
| Full Idea: We must believe that God would not have allowed sin nor would he have created things he knows will sin, if he could not derive from them a good incomparably greater than the resulting evil. | |
| From: Gottfried Leibniz (Dialogue on human freedom and origin of evil [1695], p.115) | |
| A reaction: Why 'must' we believe this? Do we have to imagine all the genocides shrinking to insignificance once we grasp the wonderful goods that can be derived from them? The end justifies the means. Genocide is actually a good thing. Hm. |