17 ideas
| 9540 | A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell] |
| Full Idea: A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: In the interpreted version of the logic, 1 and 0 would become T (true) and F (false). The procedure seems to be called nowadays a 'valuation'. |
| 9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
| Full Idea: The Law of Transposition says that (P→Q) → (¬Q→¬P). | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: That is, if the consequent (Q) of a conditional is false, then the antecedent (P) must have been false. |
| 9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
| Full Idea: An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred] |
| 5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
| Full Idea: Quine charges quantified modal systems of logic with giving rise to unintended sense or nonsense, committing us to an incomprehensible ontology, and entailing an implausible or unsustainable Aristotelian essentialism. | |
| From: comment on Willard Quine (Existence and Quantification [1966]) by Joseph Melia - Modality Ch.3 | |
| A reaction: A nice summary. Personally I like essentialism in accounts of science (see Nature|Laws of Nature|Essentialism), so would like to save it in metaphysics. Possible worlds ontology may be very surprising, rather than 'incomprehensible'. |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| Full Idea: Quine said higher-order logic is 'set theory in sheep's clothing', and there is concern about the ontology that is involved. One approach is to deny quantificational ontological commitments, or say that the entities involved are first-order objects. | |
| From: comment on Willard Quine (Existence and Quantification [1966]) by B Hale / C Wright - Logicism in the 21st Century 8 | |
| A reaction: [compressed] The second strategy is from Boolos. This question seems to be right at the heart of the strategy of exploring our ontology through the study of our logic. |
| 9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
| Full Idea: To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [They go on to say that Propositional Logic is strongly complete, but Modal Logic is not] |
| 16966 | Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine] |
| Full Idea: It has been fairly common in philosophy early and late to distinguish between being, as the broadest concept, and existence, as narrower. This is no distinction of mine; I mean 'exist' to cover all there is. | |
| From: Willard Quine (Existence and Quantification [1966], p.100) | |
| A reaction: I sort of agree with Quine, but 'being' has a role in philosophy that is not required in science and daily life, as the name of the central problem of ontology, which probably has to be broken down before any progress can happen. |
| 16965 | All we have of general existence is what existential quantifiers express [Quine] |
| Full Idea: Existence is what existential quantification expresses. …It is unreasonable to ask for an explication of (general) existence in simpler terms. …We may still ask what counts as evidence for existential quantifications. | |
| From: Willard Quine (Existence and Quantification [1966], p.97) | |
| A reaction: This has been orthodoxy for the last 60 years, with philosophers talking of 'quantifying over' instead of 'exists'. But are we allowed second-order logic, and plural quantification, and vague domains? |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| Full Idea: In the quantification '(∃)(x=a)', it is the existential quantifier, not the 'a' itself, which carries the existential import. | |
| From: Willard Quine (Existence and Quantification [1966], p.94) | |
| A reaction: The Fregean idea seems to be that the criterion of existence is participation in an equality, but here the equality seems not more than assigning a name. Why can't I quantify over 'sakes', in 'for the sake of the children'? |
| 16964 | Theories are committed to objects of which some of its predicates must be true [Quine] |
| Full Idea: Another way of saying what objects a theory requires is to say that they are the objects that some of the predicates of the theory have to be true of, in order for the theory to be true. | |
| From: Willard Quine (Existence and Quantification [1966], p.95) | |
| A reaction: The other was for the objects to be needed by the bound variables of the theory. This is the first-order approach, that predication is a commitment to an object. So what of predicates which have no application? |
| 4216 | Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe] |
| Full Idea: According to Quine, we find the ontological commitments of a theory by expressing it in first-order predicate logic, then determining what kind of entities must be admitted as bound variables if the theory is true. | |
| From: report of Willard Quine (Existence and Quantification [1966]) by E.J. Lowe - A Survey of Metaphysics p.216 | |
| A reaction: To me this is horribly wrong. The ontological commitments of our language is not the same as ontology. What are the ontological commitments of a pocket calculator? |
| 18966 | Ontological commitment of theories only arise if they are classically quantified [Quine] |
| Full Idea: I hold that the question of the ontological commitment of a theory does not properly arise except as that theory is expressed in classical quantificational form. | |
| From: Willard Quine (Existence and Quantification [1966], p.106) | |
| A reaction: He is attacking substitutional quantification for its failure to commit. I smell circularity. If it must be quantified in the first-order classical manner, that restricts your ontology to objects before you've even started. Chicken/egg. |
| 14490 | You can be implicitly committed to something without quantifying over it [Thomasson on Quine] |
| Full Idea: Quine's test for ontological commitment ignores the fact that there are often implicit commitments to certain kinds of entities even where we are not yet quantifying over them. | |
| From: comment on Willard Quine (Existence and Quantification [1966]) by Amie L. Thomasson - Ordinary Objects 09.4 | |
| A reaction: Put this with the obvious problem (of which Quine is aware) that we don't quantify over 'sakes' in 'for the sake of the children', and quantification and commitment have been rather clearly pulled apart. |
| 16961 | In formal terms, a category is the range of some style of variables [Quine] |
| Full Idea: In terms of formalized quantification theory, each category comprises the range of some distinctive style of variable. | |
| From: Willard Quine (Existence and Quantification [1966], p.92) | |
| A reaction: I add this for those who dream of formalising everything, but be warned that even Quine thought it of little help in deciding on the categories. Presumably there would be some variable that ranged across tigers. |
| 5517 | Individuals don't exist, but are conventional names for sets of elements [Buddha] |
| Full Idea: There exists no individual, it is only a conventional name given to a set of elements. | |
| From: Buddha (Siddhartha Gautama) (reports [c.540 BCE]), quoted by Derek Parfit - The Unimportance of Identity p.295 | |
| A reaction: I take this to arise from an excessively spiritual concept of a human being, which faces Descartes' problem of how to individuate non-physical minds, when they have no clear boundaries. Combine dualism with a bundle theory, and you have Buddhism. |
| 7600 | The Buddha believed the gods would eventually disappear, and Nirvana was much higher [Buddha, by Armstrong,K] |
| Full Idea: The Buddha believed implicitly in the gods because they were part of his cultural baggage, but they were involved in the cycle of rebirth, and would eventually disappear; the ultimate reality of Nirvana was higher than the gods. | |
| From: report of Buddha (Siddhartha Gautama) (reports [c.540 BCE]) by Karen Armstrong - A History of God Ch.1 | |
| A reaction: We might connect this with Plato's Euthyphro question (Ideas 336 and 337), and the relationship between piety and morality on the one hand, and the gods on the other. |
| 7601 | Life is suffering, from which only compassion, gentleness, truth and sobriety can save us [Buddha] |
| Full Idea: Buddha taught that the only release from 'dukkha' (the meaningless flux of suffering which is human life) is a life of compassion for all living beings, speaking and behaving gently, kindly and accurately, and refraining from all intoxicants. | |
| From: Buddha (Siddhartha Gautama) (reports [c.540 BCE], Ch.1), quoted by Karen Armstrong - A History of God Ch.1 | |
| A reaction: Christians are inclined to give the impression that Jesus invented the idea of being nice, but it ain't so. The obvious thought is that the Buddha seems to be focusing on the individual, but this is actually a formula for a better community. |