31 ideas
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 22744 | Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus] |
| Full Idea: If the whole is nothing more than the sum of the parts, the parts will not be parts. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.343) | |
| A reaction: Nice. Bricks lying on the ground are not parts of a wall. For them to be parts of a wall there has to be a wall which is not just the bricks. Nihilists like Van Inwagen can deny the wall in ontology, but in thought we need walls. Conceptual dependence. |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 22748 | Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus] |
| Full Idea: Some assert that motion is perceived by sense, but others that it is not perceived at all by sense but by the intellect through sensation. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.062) | |
| A reaction: Descartes' wax argument defends the idea that change is perceived by intellect. The intellect has to distinguish the relative aspect of each motion, such as when someone is walking around on a moving ship. Even sense also need memory. |
| 22746 | If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus] |
| Full Idea: When we have gone so far as to deprive the length of its breadth altogether, we no longer conceive even the length, but along with the removal of the breadth the conception of the length is also removed. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.392) | |
| A reaction: The only explanation of our retaining an understanding of a line even after we have removed its breadth is that we have abandoned experience and conceptualised the line - by idealising it. |
| 22741 | The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus] |
| Full Idea: The incorporeal will never come into existence from body because the nature of the incorporeal does not exist in body. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.225) | |
| A reaction: So nothing high could be made of pebbles because pebbles are not high? His argument depends on incorporeality having an intrinsically incorporeal nature. Pebbles have some height which can be extended. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 22747 | A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus] |
| Full Idea: If a ship moves forward and a man carries a rod backwards on it, then it is possible for an object to move without quitting its place. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.056) | |
| A reaction: [summary of a verbose paragraph] The point is that you cannot define movement as change of place (contrary to Russell's proposal!). The concept of a place seems to be relative. Walking on a treadmill. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 22749 | Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus] |
| Full Idea: It is absurd to say that when the Universe is destroyed time does not exist; for the statement that it was destroyed once and that it is being destroyed are indicative of times. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.188) | |
| A reaction: Intriguing. He takes it that a proposition can be true even though nothing exists. This is not merely an affirmation of the tensed A-series view of time, but he even offers tenses as evidence that the A-series is correct. That time could cease was a view. |
| 22750 | Time is divisible, into past, present and future [Sext.Empiricus] |
| Full Idea: Time cannot be indivisible, since it is divided into past, present and future. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.193) | |
| A reaction: Does the fact that you can name the parts of something prove that it is divisible? Do electrons have left and right-hand sides? |
| 22742 | Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus] |
| Full Idea: Socrates either dies when existing, or when not existing. …He does not die when he exists, for he is alive, and he does not die when he has died, for then he will be dying twice, which is absurd. So then, Socrates does not die. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.269) | |
| A reaction: A nice dramatisation of a major dilemma. The present moment is just the boundary between the past and the future, and so has no magnitude, and hence nothing can occur during the present. Perhaps my favourite philosophical dilemma. |
| 22751 | If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus] |
| Full Idea: If the present is the limit of the past, and the limit of the past has passed away together with that of which it is the limit, the present no longer exists. And if the present begins the future, which doesn't exist, the present does not yet exist. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], II.201) | |
| A reaction: If I mark a line on the ground where the wall will begin, the limit seems prior to the object. The gun starts the race, but is not part of it. That said, I cannot think of any more mysterious entity than the present moment. It isn't a line or a bang. |
| 22730 | All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus] |
| Full Idea: All men have one common preconception about God, according to which he is a blessed creature and imperishable and perfect in happiness and receptive of nothing evil. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.033) | |
| A reaction: He observes this after he has pointed the enormous variety of religious beliefs. He offers this unanimity as a reason to believe that it is true. |
| 22739 | God must suffer to understand suffering [Sext.Empiricus] |
| Full Idea: God cannot have a notion of suffering if he has not experience it. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.163) | |
| A reaction: Christians like to portray God as suffering because of his son's horrible death. We can imagine experiences we have never had, and presumably God is better at that than we are. |
| 22738 | The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus] |
| Full Idea: If the Divine is all-virtuous, it possesses all the virtues. But it does not possess the virtues of continence and fortitude unless there are certain things which are hard for God to abstain from and hard to endure. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.151) | |
| A reaction: Courage would also be unnecessary, we assume. Good people are not tempted to steal, and hence do not need to resist it. It is a mistake to attribute human virtues to the Divine. Humans lack the virtues of a good frog. |
| 22734 | God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus] |
| Full Idea: Arguments for God have four modes: from universal agreement, from the orderly arrangement of the universe, from the absurd consequences of denying God, and from undermining the opposing arguments. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.060) | |
| A reaction: [compressed] The loss of status of the argument from universal agreement has had a huge influence. We now realise that a very wide consensus is no guarantee of truth in anything. |
| 22736 | God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus] |
| Full Idea: If God has sensation he is altered, …so he is receptive of change, including change for the worse. If so, he is also perishable, but that is absurd; therefore it is absurd also to claim that God exists. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.146) | |
| A reaction: [compressed] It is certainly paradoxical to think that God is eternal and unchanging, but also capable of perception and thought, which necessitate change. Some theological ingenuity is needed to explain this. |
| 22740 | God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus] |
| Full Idea: If the Divine exists it either has or has not virtue. If it has not it is base and unhappy, which is absurd. But if it has it, there will exist something which is better than God, just as a virtue of a horse is better than the horse itself. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.176) | |
| A reaction: It is obviously better to think of a virtue as some mode of a thing, rather than as a separate attachment. This is an ontological argument, because it is inferred from the concept of God. |
| 22735 | The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus] |
| Full Idea: They say that the substance of existing things being of itself motionless and shapeless must be put in motion and shape by some cause. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.075) | |
| A reaction: Interestingly, Sextus doesn't seem to think that the existence of the original substance also needs a cause. This substance sounds like a relative of Aristotle's Prime Matter. The source of motion isn't really a 'design' argument. |
| 22732 | The perfections of God were extrapolations from mankind [Sext.Empiricus] |
| Full Idea: It is said that …the idea that God is eternal and imperishable and perfect in happiness was introduced by way of transference from mankind. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.045) | |
| A reaction: This view is found in Hume, and in Feuerbach. I presume 'transference' means extrapolation and idealisation. If God exists, we may have no option but to think of God anthropomorphically. |
| 22728 | Gods were invented as watchers of people's secret actions [Sext.Empiricus] |
| Full Idea: It is asserted that those who first led mankind …invented gods as watchers of all the sinful and righteous acts of men, so that none should dare to do wrong even in secret. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.016) | |
| A reaction: Sextus is a sceptic about everything, so this scepticism about the gods is nothing special. I'm not sure if this is why the gods were invented, but it seems to be the main role assigned to God by the Christian church, as the basis of religious morality. |
| 22737 | An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus] |
| Full Idea: The Divine is not incorporeal, since that is inanimate and insensitive and incapable of any action; nor is it a body, since that is subject to change and perishable; so the Divine does not exist. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.151) | |
| A reaction: I find this quite persuasive. An incorporeal God has to be ascribed magical powers in order to interact with what is corporeal. A corporeal God is subject to entropy and all the depredations of the physical world. |
| 22731 | It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus] |
| Full Idea: To suppose that lakes and rivers, and whatsoever else is of a nature to be useful to us, are gods surpasses the height of lunacy. | |
| From: Sextus Empiricus (Against the Physicists (two books) [c.180], I.040) | |
| A reaction: He also points out the what is useful to us decays and changes. Sextus lived in a time when monotheism was becoming dominant. |