Science Without Numbers Quiz

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Questions and Answers

What is the primary focus of 'Science Without Numbers'?

The significance of counting in everyday life

A defense of nominalism (correct)

The use of numerical data in scientific research

Mathematical modeling in science

In which chapter is 'Arithmetic and Cardinality Quantifiers' discussed?

0.2 Mereology and Logic

0.1 Arithmetic and Cardinality Quantifiers (correct)

0.3 Representation Theorems

0.4 Conservativeness

Which topic is NOT listed in the contents of 'Science Without Numbers'?

Representation Theorems

Mereology and Logic

Integration and Calculus (correct)

Indispensability

What aspect does the chapter on 'Conservativeness' likely address?

Conservativeness in scientific theories Signup and view all the answers

What philosophical position does Hartry Field primarily defend in this work?

Nominalism Signup and view all the answers

Which chapter deals directly with the concept of 'Indispensability'?

0.5 Indispensability Signup and view all the answers

What is the publication year of the first edition of 'Science Without Numbers'?

2014 Signup and view all the answers

Where is Oxford University Press located?

Great Clarendon Street, Oxford, UK Signup and view all the answers

What is a challenge associated with describing the wave function in quantum theory?

It requires predicates on an additively complex space. Signup and view all the answers

Why might nominalization be problematic in quantum mechanics?

It requires an analog of the algebra of Hermitian operators. Signup and view all the answers

What aspect of classical and quantum mechanics suggests a partially instrumentalist viewpoint?

The notion of chance and its philosophical implications. Signup and view all the answers

What complicates the comparative phase difference in quantum mechanics?

It requires consideration of non-simultaneous points. Signup and view all the answers

What does the term 'phase space' refer to in this context?

The space of possible configurations and states of motion. Signup and view all the answers

Which perspective challenges the view of operator observables in quantum mechanics?

They serve as bookkeeping for wave function statistics. Signup and view all the answers

What is primarily seen as an advantage of the wave function representation?

It simplifies the interpretation of quantum mechanics. Signup and view all the answers

What philosophical issue does the role of chance in mechanics raise?

It complicates the understanding of probabilistic interpretations. Signup and view all the answers

What was the primary focus of the philosophical justification mentioned in the content?

The first motivation for the program Signup and view all the answers

Which of the following theories does the content suggest might be heavily idealized?

Theories in economics or psychology Signup and view all the answers

What is suggested as a limiting factor in the formulation of fundamental physical theories?

Their dependence on mathematical entities Signup and view all the answers

Which statement best describes the author's view on metalogic?

It can facilitate logical reasoning using mathematical entities. Signup and view all the answers

What is the difference between 'abstract counterparts' and 'metaphysical possibility' according to the content?

Abstract counterparts are clearer than metaphysical possibilities. Signup and view all the answers

What does 'SWN' refer to in the content?

An incomplete sketch of mathematical entities Signup and view all the answers

Which two forms of platonism are mentioned in relation to the first motivation?

Moderate and very moderate Signup and view all the answers

Which of the following methods does the content suggest for formulating physical theories?

Through abstract counterparts Signup and view all the answers

What issue remains in the understanding of second-order logic as mentioned in the content?

Lack of a clear grasp of second-order consequence Signup and view all the answers

What was assumed about the addition of quantifiers without considering them as logical?

They would be neglected in favor of full first-order logic Signup and view all the answers

Which of the following is essential for understanding the notion of consequence in the logic of cardinality quantifiers?

An understanding of the divergence between semantic and syntactic characterizations Signup and view all the answers

What rhetorical issue arises from the author’s stand on semantic conservativeness?

It leads to a misleading interpretation of second-order logic Signup and view all the answers

What is implied about the induction principle in connection to first-order language?

It cannot fully explain the properties of second-order logic Signup and view all the answers

What concept did the author consider more appealing than the idea of a second-order consequence?

The logic of cardinality quantifiers such as Qfin Signup and view all the answers

What distinguishes semantic relationships from syntactic ones according to the content?

The notions of truth in different logical contexts Signup and view all the answers

What assumption did the author not consider regarding predicates?

Adding a predicate without treating it as logical Signup and view all the answers

What happens when N is regarded as a second-order theory?

It leads to the expansion of the schema to include sets. Signup and view all the answers

What does the term 'conservativeness' imply in the context of adding mathematical content?

It ensures no new provable statements arise from the expanded theory. Signup and view all the answers

What is indicated if S is added to N and N is considered a second-order theory?

S allows for new consequences that weren't previously provable in N alone. Signup and view all the answers

What happens when N is taken as a first-order theory?

The schema remains unchanged despite the addition of S. Signup and view all the answers

What is meant by 'second-order mereology' in this context?

A logic that treats regions as the primary focus of logical statements. Signup and view all the answers

What may occur if N + S includes a mathematically bad set theory?

There will be contradictions that impact the whole theory. Signup and view all the answers

How does introducing mathematical apparatus affect the complexity of a theory?

It creates added complexity in interpreting the extended schemas. Signup and view all the answers

Why might extending schemas in non-logical and non-mathematical theories be viewed skeptically?

They may lack empirical justifications for the new content. Signup and view all the answers

What is the main premise regarding sets in relation to regions in the text?

There is no reason to regard sets as relevant to the notion of region. Signup and view all the answers

What does the author imply about the Banach-Tarski decomposition?

It lacks obvious physical relevance. Signup and view all the answers

What characterizes the theory N as discussed in the passage?

It employs a finiteness predicate viewed as logical. Signup and view all the answers

What does the author suggest about the completeness schema when S is added to N?

It helps prove more instances of the completeness schema. Signup and view all the answers

What condition must be met for the expansion of the completeness schema to set-theoretic instances?

It should have empirical support. Signup and view all the answers

What does ‘N + S’ refer to in this context?

The combination of N and S conceptualized differently. Signup and view all the answers

In the context provided, what is the role of empirical support?

It provides justification for theoretical expansions. Signup and view all the answers

How does the author view the addition of claims about sets within the framework discussed?

As unnecessarily complicating the schema. Signup and view all the answers

Study Notes

Book Title and Edition

Science Without Numbers, Second Edition
Hartry Field
Oxford University Press

Preface to Second Edition
Arithmetic and Cardinality Quantifiers
Mereology and Logic
Representation Theorems
Conservativeness
Indispensability
Miscellaneous Technicalia: Integral Calculus, Point Particles, The Quantities, Poisson's Equation, Inner Products, Gradients, Differentiation of Vector Fields
Bibliography for Second Preface
Preface to First Edition
Contents of First Edition
Bibliography for Original Text
Index(to entire volume)

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Description

Test your knowledge of 'Science Without Numbers' by Hartry Field. This quiz covers key concepts, chapters, and the philosophical positions defended in the work. It's perfect for students and enthusiasts wanting to explore the intersections of mathematics and philosophy.