24 ideas
| 4739 | In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel] |
| Full Idea: Necessary and sufficient conditions are usually expressed by "if and only if" (abbr. "iff"), where "if" is the sufficient condition, and "only if" is the necessary condition. | |
| From: Pascal Engel (Truth [2002], §1.1) | |
| A reaction: 'I take my umbrella if and only if it is raining' (oh, and if I'm still alive). There may be other necessary conditions than the one specified. Oh, and I take it if my wife slips it into my car… |
| 4737 | Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel] |
| Full Idea: The tradition of the Stoics and Frege says that truth-bearers are propositions, Descartes and the classical empiricist say they are ideas or beliefs, and Ockham and Quine say they are sentences or utterances. | |
| From: Pascal Engel (Truth [2002], §1.1) | |
| A reaction: I'm with propositions, which are unambiguous, can be expressed in a variety of ways, embody the 'logical form' of sentences, and could be physically embodied in brains (the language of thought?). |
| 4750 | The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel] |
| Full Idea: The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p'. | |
| From: Pascal Engel (Truth [2002], §2.2) | |
| A reaction: But then when you ask what p means, you have to give the truth-conditions for its assertion, and you find you have to mention the facts after all. |
| 4744 | We can't explain the corresponding structure of the world except by referring to our thoughts [Engel] |
| Full Idea: The correspondence theory implies displaying an identity or similarity of structure between the contents of thoughts and the way the world is structured, but we seem only to be able to say that the world's structure corresponds to our thoughts. | |
| From: Pascal Engel (Truth [2002], §1.2) | |
| A reaction: I don't accept this. The structure of the world gives rise to our thoughts. There is an epistemological problem here (big time!), but that doesn't alter the metaphysical situation of what truth is supposed to be, which is correspondence. |
| 4738 | The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel] |
| Full Idea: The coherence theory of truth says that it is a relationship between truth-bearers themselves, that is between propositions or beliefs or sentences. | |
| From: Pascal Engel (Truth [2002], §1.1) | |
| A reaction: We immediately begin to wonder how many truth-bearers are required. Two lies can be coherent. It is hard to make thousands of lies coherent, but not impossible. What fixes the critical number. 'All possible propositions' is not much help. |
| 4745 | Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel] |
| Full Idea: Any coherent set of beliefs can be made more coherent by adding to it one or more false beliefs. | |
| From: Pascal Engel (Truth [2002], §1.3) | |
| A reaction: A simple but rather devastating point. It is the policeman manufacturing a bogus piece of evidence to clinch the conviction, the scientist faking a single observation to fill in the last corner of a promising theory. |
| 4755 | Deflationism cannot explain why we hold beliefs for reasons [Engel] |
| Full Idea: The deflationist view is silent about the fact that our assertions and beliefs are generally made or held for certain reasons. | |
| From: Pascal Engel (Truth [2002], §2.5) | |
| A reaction: The point here must be that I attribute strength to my beliefs, depending on how much support I have for them - how much support for their real truth. I scream "That's really TRUE!" when I have very good reasons. |
| 4753 | Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel] |
| Full Idea: Deflationism about truth seems to deprive us of any hope of asking genuinely metatheoretical questions, which are the questions that occupy philosophers most of the time. | |
| From: Pascal Engel (Truth [2002], §2.5) | |
| A reaction: This seems like the best reason for moving from deflationism to at least minimalism. Clearly one can talk meaningfully about the success of assertions and theories. You can say a sentence is true, but not assert it. |
| 4751 | Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel] |
| Full Idea: We could compare the status of 'true' with the status of the logical operator 'and' in logic. Once we have explained how it functions to conjoin two propositions, there is not much more to be said about it. | |
| From: Pascal Engel (Truth [2002], §2.4) | |
| A reaction: A good statement of the minimalist view. I don't believe it, because I don't believe that truth is confined to language. An uneasy feeling I can't put into words can turn out to be true. Truth is a relational feature of mental states. |
| 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. |
| 4752 | Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel] |
| Full Idea: It is said that deflationism cannot even formulate the principle of bivalence, for 'either p is true or p is false' will amount to the principle of excluded middle, 'either p or not-p'. | |
| From: Pascal Engel (Truth [2002], §2.4) | |
| A reaction: Presumably deflationists don't lost any sleep over this - in fact, it looks like a good concise way to state the deflationist thesis. However, excluded middle refers to a proposition (not-p) that was never mentioned by bivalence. Cf Idea 6163. |
| 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. |
| 4762 | The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel] |
| Full Idea: A problem for the Humean theory of motivation is that it is disputed that beliefs are only representational states, which cannot, unlike desires, move us to act. | |
| From: Pascal Engel (Truth [2002], §4.2) | |
| A reaction: This is a crucial issue for Humeans and empiricists. Rationalists claim that people act for reasons, so that reasons are intrinsically motivational (like the Form of the Good), and reasons may even be considered direct causes of actions. |
| 4754 | Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel] |
| Full Idea: Belief is said to 'aim at truth', in the sense that beliefs are the kind of mental states that have to be true for the mind to 'fit' the world (where our desires have the opposite 'direction of fit'; the world is supposed to fit our desires). | |
| From: Pascal Engel (Truth [2002], §2.5) | |
| A reaction: I don't think it is possible to give a plausible definition of belief without mentioning truth. Hume's account of them as thoughts with a funny feeling attached is ridiculous. Thinking is an activity, not a passive state. |
| 4763 | 'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel] |
| Full Idea: The 'evidentialists' (such as Locke and Hume) deny, and the 'voluntarists' (such as William James) affirm, that we ought to, or at least may, believe for other reasons than evidential epistemic reasons (e.g. for pragmatic reasons). | |
| From: Pascal Engel (Truth [2002], §5.2) | |
| A reaction: No need to be black-or-white here. Blatant evidence compels belief, but we may also come to believe by spotting a coherence, without additional evidence. We can also be in a state of trying to believe something. But see 4764. |
| 4746 | Pragmatism is better understood as a theory of belief than as a theory of truth [Engel] |
| Full Idea: Pragmatism in general is better construed as a certain conception of belief, rather than as a distinctive conception of truth. | |
| From: Pascal Engel (Truth [2002], §1.5) | |
| A reaction: Which is why aspiring relativists drift towards the pragmatic theory - because they want to dispense with truth (and hence knowledge), and put mere belief in its place. |
| 4764 | We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel] |
| Full Idea: Direct psychological voluntarism about beliefs seems to be false, but we can have an indirect voluntary control on many of our beliefs, by manipulating the states in us that are involuntary and which lead to certain beliefs. | |
| From: Pascal Engel (Truth [2002], §5.2) | |
| A reaction: Very nice! This points two ways - to scientific experiments, which can have compelling outcomes (see Fodor), and to brain-washing, and especially auto-brainwashing (only reading articles which support your favourites theories). What magazines do you take? |
| 4759 | Mental states as functions are second-order properties, realised by first-order physical properties [Engel] |
| Full Idea: For functionalism mental states as roles are second-order properties that have to be realised in various ways in first-order physical properties. | |
| From: Pascal Engel (Truth [2002], §3.3) | |
| A reaction: I take that to be properties-of-properties, as in 'bright red' or 'poignantly beautiful'. I am inclined to think (with Edelman) that mind is a process, not a property. |
| 9287 | Bruno said that ancient Egyptian magic was the true religion [Bruno, by Yates] |
| Full Idea: Giordano Bruno maintained that the magical Egyptian religion of the world was not only the most ancient but also the only true religion, which both Judaism and Christianity had obscured and corrupted. | |
| From: report of Giordano Bruno (works [1590]) by Frances A. Yates - Giordano Bruno and Hermetic Tradition Ch.1 | |
| A reaction: His beliefs were based on the Hermetic writings. No wonder he was burned at the stake. Atheists now lay flowers at his memorial in Rome. The sixteenth century was when the hunt for alternatives to established religion began. |