37 ideas
| 5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
| Full Idea: We call a belief true when it is belief in a true proposition, ..but it is to propositions that the primary formal meanings of 'truth' and 'falsehood' apply. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV) | |
| A reaction: I think this is wrong. A proposition such as 'it is raining' would need a date-and-time stamp to be a candidate for truth, and an indexical statement such as 'I am ill' would need to be asserted by a person. Of course, books can contain unread truths. |
| 5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
| Full Idea: I take it as evident that the truth or falsehood of a belief depends upon a fact to which the belief 'refers'. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], p.285) | |
| A reaction: A nice bold commitment to a controversial idea. The traditional objection is to ask how you are going to formulate the 'facts' except in terms of more beliefs, so you ending up comparing beliefs. Facts are a metaphysical commitment, not an acquaintance. |
| 5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
| Full Idea: The correspondence of proposition and fact grows increasingly complicated as we pass to more complicated types of propositions: existence-propositions, general propositions, disjunctive and hypothetical propositions, and so on. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV) | |
| A reaction: An important point. Truth must not just work for 'it is raining', but also for maths, logic, tautologies, laws etc. This is why so many modern philosophers have retreated to deflationary and minimal accounts of truth, which will cover all cases. |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
|
Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
|
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
| A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3) |
| 5780 | The three questions about belief are its contents, its success, and its character [Russell] |
| Full Idea: There are three issues about belief: 1) the content which is believed, 2) the relation of the content to its 'objective' - the fact which makes it true or false, and 3) the element which is belief, as opposed to consideration or doubt or desire. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: The correct answers to the questions (trust me) are that propositions are the contents, the relation aimed at is truth, which is a 'metaphysical ideal' of correspondence to facts, and belief itself is an indefinable feeling. See Hume, Idea 2208. |
| 5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
| Full Idea: If privacy is the main objection to introspective data, we shall have to include among such data all sensations; a toothache, for example, is essentially private; a dentist may see the bad condition of your tooth, but does not feel your ache. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II) | |
| A reaction: Russell was perhaps the first to see why eliminative behaviourism is a non-starter as a theory of mind. Mental states are clearly a cause of behaviour, so they can't be the same thing. We might 'eliminate' mental states by reducing them, though. |
| 5779 | There are distinct sets of psychological and physical causal laws [Russell] |
| Full Idea: There do seem to be psychological and physical causal laws which are distinct from each other. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II) | |
| A reaction: This sounds like the essence of 'property dualism'. Reductive physicalists (like myself) say there is no distinction. Davidson, usually considered a property dualist, claims there are no psycho-physical laws. Russell notes that reduction may be possible. |
| 5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
| Full Idea: The important beliefs, even if they are not the only ones, are those which, if rendered into explicit words, take the form of a proposition. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: This assertion is close to the heart of the twentieth century linking of ontology and epistemology to language. It is open to challenges. Why is non-propositional belief unimportant? Do dogs have important beliefs? Can propositions exist non-verbally? |
| 5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
| Full Idea: I shall distinguish a proposition expressed in words as a 'word-proposition', and one consisting of images as an 'image-proposition'. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: This, I think, is good, though it raises the question of what exactly an 'image' is when it is non-visual, as when a dog believes its owner called. This distinction prevents us from regarding all knowledge and ontology as verbal in form. |
| 5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
| Full Idea: A proposition may be defined as: what we believe when we believe truly or falsely. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], p.285) | |
| A reaction: If we define belief as 'commitment to truth', Russell's last six words become redundant. "Propositions are the contents of beliefs", it being beliefs which are candidates for truth, not propositions. (Russell agrees, on p.308!) |
| 7096 | We may still admire a person's character even if the traits are involuntary [Statman] |
| Full Idea: If we focus on the evaluation of character traits, voluntariness becomes less important. We would not withdraw our admiration for a person only because we found out that his or her being such a person was not a result of voluntary choice. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §3) | |
| A reaction: The need for voluntariness does not disappear. I would not admire the only generous deed you had ever performed if it was the result of hypnotism. I might admire the hypnotist. Nevertheless, I regard this idea as a crucial truth in moral theory. |
| 7098 | There is a new sort of moral scepticism, about the possibility of moral theories [Statman] |
| Full Idea: Since the 1980s, ethics has witnessed a new sort of moral scepticism, this time about the possibility of moral theories. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §4) | |
| A reaction: He cites McDowell, Williams, Nussbaum and Baier as the culprits. 'Particularism' (every situation is different, so there can't be rules) seems an essential part of virtue theory, but total absence of principles sounds to me like moral drift. |
| 7099 | With a broad concept of flourishing, it might be possible without the virtues [Statman] |
| Full Idea: In a rich conception of human flourishing, both individuals and societies seem to be able to flourish without the virtues. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §5) | |
| A reaction: I can see Aristotle clutching his head in despair at this thought. It might look like flourishing, but it couldn't be the real thing. It is Aristotle's fault, though, for including external goods. Money and pleasure offer a kind of flourishing. |
| 7100 | Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman] |
| Full Idea: It can be claimed that universality is a necessary property of any ethical theory and therefore virtue theory, which fails in this respect, is not a theory, and hence poses no alternative to genuine ethical theories. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §5) | |
| A reaction: Replies: a) totally universal morality is an idle dream (part of the 'Enlightenment Project' to prove everything) and we must settle for something more relative; b) virtues aren't totally universal, but they are truths about humanity. I prefer b). |
| 7102 | Promises create moral duties that have nothing to do with character [Statman] |
| Full Idea: That duties are created irrespective of facts about character is obvious from the case of promises, which bind their makers irrespective of their motives or personality. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §5) | |
| A reaction: Just occasionally a promise can be broken, by a sensitive and wise person. I promise to give your son some money; I then discover he is a drug dealer. Promises arise out of character, and cannot be made by robots. |
| 7095 | Moral education is better by concrete example than abstract principle [Statman] |
| Full Idea: According to virtue theory, education through moral exemplars is more effective than education focused on principles and obligations, because it is far more concrete. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §3) | |
| A reaction: Aristotle's view is that virtues must be developed from childhood, when principles don't mean much. The problem is that young people may witness highly virtuous behaviour in their exemplars, but totally fail to appreciate it without mention of principles. |
| 7094 | Friends express friendship even when no utility is involved [Statman] |
| Full Idea: Being a good friend means acting in ways that express the friendship even when those ways do not promote overall utility. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §3) | |
| A reaction: This implies that friendship is a true virtue of character, rather than having friends just being an 'external' good. Having friends is good; being friends is a virtue. There are duties of friendship. |
| 7093 | Behaviour may be disgusting or inhumane, but violate no duty [Statman] |
| Full Idea: It is surely possible, and indeed often the case, that people who violate no duty nevertheless behave in an inhumane and a disgusting manner. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §1) | |
| A reaction: This seems right, though it is easier to be disgusting than to be inhumane if no duty is to be violated. Social duties may not require a high degree of humanity, pure Kantian duties might. |
| 7104 | The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman] |
| Full Idea: The advantage of modern thinkers over the ancient virtue ethicists is that in addition to imperfect duties (i.e. virtues) they also recognise the existence of perfect duties, or duties of justice, which are essential for the existence of society. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §7) | |
| A reaction: Even the Greeks had laws (e.g. Idea 422), so they understood that a society needs rules, but many laws don't seem to be moral rules (e.g. car parking), and the Greeks thought morality was about human excellence, not avoiding traffic jams. |
| 7103 | Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman] |
| Full Idea: Most of the debate on abortion focuses on two issues, the mother's assumed right over her body, and the status of the foetus. | |
| From: Daniel Statman (Introduction to Virtue Ethics [1997], §6) | |
| A reaction: Personally I think society as a whole might have a say (if, perhaps, we are over- or under-populated, or we have a widely accepted state religion, or we are just very shocked). Mother's have virtues and duties as well as rights. |