24 ideas
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 15797 | All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer] |
| Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world. | |
| From: J.H. Fetzer (A World of Dispositions [1977], Intro) | |
| A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'. |
| 15800 | All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer] |
| Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 5) | |
| A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics. |
| 3756 | Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske] |
| Full Idea: The basic sources of knowledge and justification are perception, introspection, testimony, memory, reason, and inference. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) |
| 3757 | Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske] |
| Full Idea: The causal theory of perceptions says that to perceive an object is to have a sense-datum caused by that object; it is not enough for the world to be the way we perceive it; the world must cause the perception. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) | |
| A reaction: All causal theories seem dubious to me; what causes something is not the same was what it means, or refers to, or what justifies it. The hallmark of successful perception is truth. I would perceive a tree if God planted the perception in me. |
| 3759 | You can acquire new knowledge by exploring memories [Bernecker/Dretske] |
| Full Idea: You can first come to know by remembering, as in learning how many windows there were in your childhood home by imagining a tour. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) |
| 3752 | Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske] |
| Full Idea: There is a distinction between a person being justified in holding a belief, and the belief itself being justified. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.II Int) | |
| A reaction: This is the crucial and elementary distinction which even the most sophisticated of epistemologists keep losing sight of. Epistemology is about persons. All true beliefs are justified - by the facts! |
| 3753 | Foundationalism aims to avoid an infinite regress [Bernecker/Dretske] |
| Full Idea: The driving force behind foundationalism has always been the threat of an infinite regress. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int) | |
| A reaction: You could just live with the regress (Peter Klein), or say that the regress fades away, or that it is cut off by social epistemological convention, or the regress circles round and rejoins. |
| 3754 | Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske] |
| Full Idea: If sense experiences are non-epistemic they may be infallible, but they are unsuitable for providing the foundations for other beliefs. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int) | |
| A reaction: If we experience flashing lights in the retina, or an afterimage, we don't think we are seeing objects, so why is normal perception different? Ans: because it is supported by judgement. |
| 3755 | Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske] |
| Full Idea: The concept of justification is absolutely central to epistemology; but this concept is normative (i.e. it lays down norms), so epistemology can't be reduced to factual cognitive psychology. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int) | |
| A reaction: A simple rejection of the 'epistemology naturalised' idea. Best to start with slugs rather than people. You can confuse a slug, so it has truth or falsehood, but what is slug normativity? This is an interesting discussion point, not an argument. |
| 3761 | Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske] |
| Full Idea: In modern epistemology the three strategies to rebut the sceptic are 1) epistemological externalism, 2) the 'relevant alternative account of knowledge' (that scepticism is too extreme to be relevant), and 3) semantic externalism. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.IV Int) |
| 3760 | Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske] |
| Full Idea: The new riddle of induction ('grue') seems to demonstrate that sound inductive inferences are arbitrary because they depend on the actual language people use to formulate predictions. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) |
| 3758 | Semantic externalism ties content to the world, reducing error [Bernecker/Dretske] |
| Full Idea: Semantic externalism ties our mental content down to our actual environment so there is no possibility of massive error. | |
| From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int) | |
| A reaction: This sounds more prescriptive than descriptive. People do make massive errors in their concepts. Maybe educated people are more externalist (respectful of experts) than uneducated people? |
| 15798 | Kinds are arrangements of dispositions [Fetzer] |
| Full Idea: Kinds of things are specific arrangements of dispositions. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 2) | |
| A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything. |
| 15799 | Lawlike sentences are general attributions of disposition to all members of some class [Fetzer] |
| Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations. | |
| From: J.H. Fetzer (A World of Dispositions [1977], 3) | |
| A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything. |