Combining Texts

All the ideas for 'Universal Prescriptivism', 'Procedural republic and unencumbered self' and 'Higher-Order Logic'

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27 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice is controversial, but it could be replaced [Shapiro]
     Full Idea: The axiom of choice has a troubled history, but is now standard in mathematics. It could be replaced with a principle of comprehension for functions), or one could omit the variables ranging over functions.
     From: Stewart Shapiro (Higher-Order Logic [2001], n 3)
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
     Full Idea: Early study of first-order logic revealed a number of important features. Gödel showed that there is a complete, sound and effective deductive system. It follows that it is Compact, and there are also the downward and upward Löwenheim-Skolem Theorems.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.1)
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Some say that second-order logic is mathematics, not logic [Shapiro]
     Full Idea: Some authors argue that second-order logic (with standard semantics) is not logic at all, but is a rather obscure form of mathematics.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.4)
If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
     Full Idea: If the goal of logical study is to present a canon of inference, a calculus which codifies correct inference patterns, then second-order logic is a non-starter.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.4)
     A reaction: This seems to be because it is not 'complete'. However, moves like plural quantification seem aimed at capturing ordinary language inferences, so the difficulty is only that there isn't a precise 'calculus'.
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence can be defined in terms of the logical terminology [Shapiro]
     Full Idea: Informally, logical consequence is sometimes defined in terms of the meanings of a certain collection of terms, the so-called 'logical terminology'.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.4)
     A reaction: This seems to be a compositional account, where we build a full account from an account of the atomic bits, perhaps presented as truth-tables.
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Second-order variables also range over properties, sets, relations or functions [Shapiro]
     Full Idea: Second-order variables can range over properties, sets, or relations on the items in the domain-of-discourse, or over functions from the domain itself.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.1)
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
     Full Idea: Upward Löwenheim-Skolem: if a set of first-order formulas is satisfied by a domain of at least the natural numbers, then it is satisfied by a model of at least some infinite cardinal.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.1)
The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
     Full Idea: Both of the Löwenheim-Skolem Theorems fail for second-order languages with a standard semantics
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.3.2)
The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
     Full Idea: The Löwenheim-Skolem theorem is usually taken as a sort of defect (often thought to be inevitable) of the first-order logic.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.4)
     A reaction: [He is quoting Wang 1974 p.154]
Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
     Full Idea: Downward Löwenheim-Skolem: a finite or denumerable set of first-order formulas that is satisfied by a model whose domain is infinite is satisfied in a model whose domain is the natural numbers
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.1)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
     Full Idea: Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.1)
     A reaction: [he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point?
8. Modes of Existence / B. Properties / 11. Properties as Sets
Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
     Full Idea: In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably.
     From: Stewart Shapiro (Higher-Order Logic [2001], 2.2.1)
     A reaction: Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
How can intuitionists distinguish universal convictions from local cultural ones? [Hare]
     Full Idea: There are convictions which are common to most societies; but there are others which are not, and no way is given by intuitionists of telling which are the authoritative data.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.454)
     A reaction: It seems unfair on intuitionists to say they haven't given a way to evaluate such things, given that they have offered intuition. The issue is what exactly they mean by 'intuition'.
You can't use intuitions to decide which intuitions you should cultivate [Hare]
     Full Idea: If it comes to deciding what intuitions and dispositions to cultivate, we cannot rely on the intuitions themselves, as intuitionists do.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.461)
     A reaction: Makes intuitionists sound a bit dim. Surely Hume identifies dispositions (such as benevolence) which should be cultivated, because they self-evidently improve social life?
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare]
     Full Idea: Emotivists concluded too hastily that because naturalism and intuitionism are false, you cannot reason about moral questions, because they assumed that the only questions you can reason about are factual ones.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.455)
     A reaction: Personally I have a naturalistic view of ethics (based on successful functioning, as indicated by Aristotle), so not my prob. Why can't we reason about expressive emotions? We reason about art.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare]
     Full Idea: Universal prescriptivists hold that 'ought'-judgements are prescriptive like plain imperatives, but differ from them in being universalisable.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.457)
     A reaction: Sounds a bit tautological. Which comes first, the normativity or the universalisability?
If morality is just a natural or intuitive description, that leads to relativism [Hare]
     Full Idea: Non-descriptivists (e.g. prescriptivists) reject descriptivism in its naturalist or intuitionist form, because they are both destined to collapse into relativism.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.453)
     A reaction: I'm not clear from this why prescriptism would not also turn out to be relativist, if it includes evaluations along with facts.
Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare]
     Full Idea: Ethical descriptivism is the view that ethical sentence-meaning is wholly determined by truth-conditions. …Prescriptivists think there is a further element of meaning, which expresses prescriptions or evaluations or attitudes which we assent to.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.452)
     A reaction: Not sure I understand either of these. If all meaning consists of truth-conditions, that will apply to ethics. If meaning includes evaluations, that will apply to non-ethics.
If there can be contradictory prescriptions, then reasoning must be involved [Hare]
     Full Idea: Prescriptivists claim that there are rules of reasoning which govern non-descriptive as well as descriptive speech acts. The standard example is possible logical inconsistency between contradictory prescriptions.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.455)
     A reaction: The example doesn't seem very good. Inconsistency can appear in any area of thought, but that isn't enough to infer full 'rules of reasoning'. I could desire two incompatible crazy things.
An 'ought' statement implies universal application [Hare]
     Full Idea: In any 'ought' statement there is implicit a principle which says that the statement applies to all precisely similar situations.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.456)
     A reaction: No two situations can ever be 'precisely' similar. Indeed, 'precisely similar' may be an oxymoron (at least for situations). Kantians presumably like this idea.
Prescriptivism implies a commitment, but descriptivism doesn't [Hare]
     Full Idea: Prescriptivists hold that moral judgements commit the speaker to motivations and actions, but non-moral facts by themselves do not do this.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.459)
     A reaction: Surely hunger motivates to action? I suppose the key word is 'commit'. But lazy people are allowed to make moral judgements.
23. Ethics / D. Deontological Ethics / 2. Duty
Kant's moral law has no foundation - because that would undermine its priority [Sandel]
     Full Idea: Given the stringent demands of the Kantian ethic, the moral law would seem almost to require a foundation in nothing, for any empirical precondition would undermine its priority.
     From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Kantian')
     A reaction: The idea of a value with 'a foundation in nothing' is particular anathema to me, because my project is to find a foundation for everything (in nature, which is the Given). Kant's only foundational value seems to be rational consistency.
23. Ethics / D. Deontological Ethics / 3. Universalisability
Moral judgements must invoke some sort of principle [Hare]
     Full Idea: To make moral judgements is implicitly to invoke some principle, however specific.
     From: Richard M. Hare (Universal Prescriptivism [1991], p.458)
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Modern liberal rights in democracies protect individuals against the majority [Sandel]
     Full Idea: Liberty in the modern procedural republic is defined in opposition to democracy, as an individual's guarantee against what the majority might will.
     From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Present')
     A reaction: And so I should hope. Sandel is sort of criticising this view, but it seems obvious that rights of this sort must be basic to any civilised democracy. But how do you decide those rights, if not by a majoritarian decision?
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberals say rights always come first, and justice is neutral on social values [Sandel]
     Full Idea: The liberal claim that the right is prior to the good means that individual rights cannot be sacrificed for the sake of the general good, and that the basic principles of justice cannot be premised on any particular vision of the good life.
     From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'The right')
     A reaction: In Rawls, the first thesis is chosen from a neutral position, and the second is all that is needed to affirm rights as basic. These two are the target of Sandel's communitarian claims. Utilitarians will make the sacrifices. No consensus on the good life!
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Liberal justice means the withdrawal of the self, as transcendental or as unencumbered [Sandel]
     Full Idea: For the liberal concept of justice we must stand to our circumstances always at a certain distance, whether as transcendental subject in the case of Kant, or as unencumbered selves in the case of Rawls.
     From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Transcendental')
     A reaction: Maybe the only way to be unencumbered is to be transcendental. There is an insecure feeling that if the self becomes immanent or encumbered it thereby loses its objective rationality. You wake up one morning and find you are a nazi?
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Liberalism concerns rights, and communitarianism concerns the common good [Sandel, by Avineri/De-Shalit]
     Full Idea: Sandel argues that liberalism is the politics of rights, while communitarianism is the politics of the common good.
     From: report of Michael J. Sandel (Procedural republic and unencumbered self [1984]) by Avineri,S/De-Shalit,A - Intro to 'Communitarianism and Individualism' §4
     A reaction: The first thing on the agenda of the common good should be to assert and protect the rights of individual citizens. How could there be a common good which trampled on individuals? I agree that the common good is prior (e.g. in a pandemic).