Ontology and Meta-Ontology 1. Tolerance in the Logical Syntax In the Logical Syntax, Carnap motivates tolerance by considering the properties of the two mathematical languages he has constructed see the supplement on LSS for the details : Language I can be shown to have the property that for each of its closed formulas without free variables , it is either the case that the formula is derivable from the axioms of the system or its negation is derivable from the axioms. This feature constitutes one reason why Language I seems particularly suitable as a rational reconstruction of constructivist or intuitionistic mathematics. In particular, the only provable existence statements in Language I are finitely restricted ones that allow for the construction of verifying instances, as demanded by intuitionists. On the other hand, Carnap does not claim that Language I satisfies each and every feature that one finds discussed in the finitist-constructivist-intuitionist literature. For instance, intuitionists notoriously refrain from certain applications of the logical rule of reductio ad absurdum that would yield unrestricted existence statements which they nonetheless consider well-formed , whereas Carnap prefers to preserve classical logic and avoids such inferences instead by restricting the syntactic formation rules of Language I.
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Stephan Blatti and Sandra Lapointe eds. Quine p. Otherwise, read on and consider obtaining the book. Four positive neo-Carnapian proposals are on offer here: Thomas Hofweber, Eli Hirsch and Amie Thomasson elaborate on positions which they have been developing for some time, and Robert Kraut presents a new brand of expressivism. And Richard Creath and Greg Lavers offer more historical contributions. Carnap Carnap , pp.
And Sidelle p. For example, Hofweber pp. Similarly, Kraut complains p. These strike me as odd complaints to make, precisely because Carnap would not have regarded either as a complaint. As Creath explains p. All true. But, even if his paper is limited to existence-questions, there is no obvious reason for Carnap to limit his attention in this way. Throughout his entire career, Carnap wanted to dissolve the debate between realism and subjective idealism.
According to Sidelle, though, the historical debate is better characterised as a disagreement about whether objects are mind-independent. Sidelle may well be right here. Button , pp. Carnap and neo-Carnapians I have begun by discussing Carnap himself.
But most of the book focuses less on him than on various neo-Carnapians. Neo-Carnapians tend to focus on more specific disputes, like whether fusions exist pp.
Carnap thinks that informal talk should be explicated using some formal framework, to which questions may be internal. However, this surely points to one of the biggest differences between Carnap and neo-Carnapians: 3. Carnap is an empiricist par excellence. Neo-Carnapians scarcely mention empiricism, let alone endorse it.
Eklund p. As such, though, non-empiricist neo-Carnapians who want to win converts will have to supply some arguments. For Hofweber, only the domain-conditions reading is ontologically committing.
Plainly, this is not very Carnapian. But I was left wondering why he wants to tie inferential role to the only ontologically non-committing reading of the quantifier. Suppose, first, that we have a sound and complete inference system for our quantifiers.
But suppose, instead, that we lack a sound and complete inference system for our quantifiers. But this leaves no space for philosophers like Hellman who think that we should embrace full second-order logic which has no sound and complete inference system when doing arithmetic, whilst denying that numbers exist.
Kraut hopes that the focus on explanatory indispensability will allow him to conserve traditional ontological disputes, unchanged. But he also hopes to be able to clarify what is at stake in these disputes. However, I should voice two quick concerns.
First, focussing on explanatory indispensability is characteristic of post-Quinean metaphysics. The role of indispensability in pre-Quinean metaphysics is less clear, and it is correspondingly unclear whether Kraut can conserve pre-Quinean metaphysical disputes.
But it seems quite reasonable to me. Then I want to say that either Fs exist or Gs exist maybe both , but whichever exists is not explanatorily indispensable. He begins by outlining a three-part condition for when people should regard a debate as shallow. His condition is quite long so, rather than quoting it, let me illustrate it with an example. With this translation in place, their superficial disagreements will vanish. Interestingly, this last point may signify a slight shift for Hirsch.
In previous work, he had contrasted the a priori with the empirical, leading Eklund pp. According to Eklund, there are three ways to understand the claim that some dispute is shallow: a Actual [participants to the dispute] are merely speaking past each other. So it might not be the best interpretation. Still, this is compatible with my d ; we need only say that Ana and Ori are here being unreasonable. But he does talk about what participants to a debate ought to do, so that my option d is compatible with his approach.
The upshot, then, is this. With Hirsch, we can invoke shallowness in the course of showing that there is something wrong with some ontological dispute per se. However, Eklund has drawn attention to the fact that we must do more than merely invoke shallowness.
If translations are to play a big role in metaontology, then we need to know what translations must preserve. Hirsch argues that translations only need to preserve truth-conditions, i. Hirsch replies in this volume, and ultimately offers the following: in different ontological languages there are different truths of the form "Such and such is a hyperintensional structure.
And I would agree that language-independent hyperintensional structures may strike many quantifier variantists as a cumbersome and dispensable complication p. Nonetheless, even if coarse-grained translations are sufficient for dissolving metaphysical disputes, they should not be necessary.
Consider the debate about whether all possible worlds contain at least one entity, or there is an empty possible world. I would hope to dissolve this debate. However, it raises questions about the very possible-world framework which Hirsch assumes in assessing the adequacy of translations. As such, it is unclear how Hirsch can deal with it see Button , pp. In fact, Hirsch agrees that some disputes should be dissolved even though no translation is available. However, his reasons are rather different.
I want to begin, though, by flagging a big difference between her and Hirsch. Hirsch famously advocates quantifier-variantism see his ; he says very little about this in his paper in this volume. To give this thesis more content, we must say what it means for the same quantifier to appear in different languages.
To motivate quantifier-variantism, consider the following. Nihilists treat the same sentence individuated orthographically as contingent. With Putnam, I want to say that universalists and nihilists are both right by their own lights. As such, I must say that the very same sentence individuated orthographically means different things in their mouths. So, if I want to ascribe the difference in sentence-meaning to a difference in subsentential-meanings -- which is contestable -- then I should say that the same quantifiers as individuated by their natural deduction rules mean different things in their languages.
Thomasson rejects this line of thought pp. As such, Thomasson rejects quantifier-variantism, and holds that there is a genuine disagreement between nihilists and universalists. In particular, she thinks that the nihilists are wrong, and that the nihilists cannot even formulate a special nihilistic language in which they would be right.
In passing, Carnap surely would have disagreed with Thomasson here. He considers two principles concerning fusions p. If we take ii as the definition, then we know that all fusions have parts, but not whether any exist. Evnine then claims that there is no good way for Thomasson to combine these two principles into a single definition. I fail to see the problem: if there are enough principles, then they will tell us everything we want them to.
So, if the question is not supposed to be so straightforwardly answerable. But if [traditional metaphysicians] attempt to use the terms while severing them from these rules of use, they make the terms meaningless, and the questions pseudo-questions.
Assessing its Carnapian credentials: 1 the scope is quite broad, since Thomasson applies this dichotomy to all existence questions, and 2 there is no suggestion that the rules need to be given in a formal language. For her part, Thomasson is quite happy to be linked to traditional empiricism in this way although she explicitly disavows verificationism, p.
I shall not attempt to adjudicate their dispute, but both contributions are well worth reading. I should, though, voice a further concern about easy ontology. In the argument just quoted. But I doubt this see my Our ordinary words are governed by indeterminate and conflicting patterns of usage, which may point us in opposite directions simultaneously. For they also aim to turn considerations about linguistic indeterminacy into a partial defence of traditional metaphysics.
They first argue that the indeterminacy of natural kind terms raises problems for Chalmers -- Jackson-style two-dimensional semantics. Biggs and Wilson note that Carnap himself was aware of issues concerning indeterminacy; this, indeed, is why Carnap introduced explication cf. But, having admitted inference to the best explanation in philosophy of language, there will be no way to prevent metaphysicians from using it to their own ends p.
The upshot, then, is an exciting challenge for neo- Carnapians: show us how to avoid inference to the best explanation in the philosophy of language. Many thanks to the Stephen Biggs, Matti Eklund, Thomas Hofweber, Amie Thomasson and Jessica Wilson for discussing a draft of this review with me, and helping to correct my many misunderstandings.
The Limits of Realism. Button, Tim. Deflationary metaphysics and ordinary language. Carnap, Rudolf. Revue Internationale de Philosophie 4 pp. Hawthorne, John.
Stephan Blatti and Sandra Lapointe eds. Quine p. Otherwise, read on and consider obtaining the book. Four positive neo-Carnapian proposals are on offer here: Thomas Hofweber, Eli Hirsch and Amie Thomasson elaborate on positions which they have been developing for some time, and Robert Kraut presents a new brand of expressivism. And Richard Creath and Greg Lavers offer more historical contributions. Carnap Carnap , pp. And Sidelle p.
Empiricism , Semantics , and Ontology
The problem of abstract entities Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc. They usually feel much more in sympathy with nominalists than with realists in the medieval sense. As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i. However, within certain scientific contexts it seems hardly possible to avoid them. In the case of mathematics some empiricists try to find a way out by treating the whole of mathematics as a mere calculus, a formal system for which no interpretation is given, or can be given.
How can I get involved? To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it may obstruct scientific progress. Let us grant to those who work in any special field of investigation the freedom to use any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function. Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms. It lets you quickly and straightforwardly define languages, construct logics for those languages, and stipulate their semantics. Carnap then uses your specifications to figure out how to check proofs in a variety of formal systems using your logic, how to find the meanings of compound expressions, and a whole lot more. Demos Here are some quick examples of what Carnap can do.