Science Without Numbers Quiz

<p>Conservativeness in scientific theories (C)</p> Signup and view all the answers

<p>Nominalism (B)</p> Signup and view all the answers

<p>0.5 Indispensability (C)</p> Signup and view all the answers

<p>2014 (C)</p> Signup and view all the answers

<p>Great Clarendon Street, Oxford, UK (B)</p> Signup and view all the answers

<p>It requires predicates on an additively complex space. (D)</p> Signup and view all the answers

<p>It requires an analog of the algebra of Hermitian operators. (C)</p> Signup and view all the answers

<p>The notion of chance and its philosophical implications. (A)</p> Signup and view all the answers

<p>It requires consideration of non-simultaneous points. (A)</p> Signup and view all the answers

<p>The space of possible configurations and states of motion. (C)</p> Signup and view all the answers

<p>They serve as bookkeeping for wave function statistics. (D)</p> Signup and view all the answers

<p>It simplifies the interpretation of quantum mechanics. (C)</p> Signup and view all the answers

<p>It complicates the understanding of probabilistic interpretations. (B)</p> Signup and view all the answers

<p>The first motivation for the program (C)</p> Signup and view all the answers

<p>Theories in economics or psychology (B)</p> Signup and view all the answers

<p>Their dependence on mathematical entities (D)</p> Signup and view all the answers

<p>It can facilitate logical reasoning using mathematical entities. (B)</p> Signup and view all the answers

<p>Abstract counterparts are clearer than metaphysical possibilities. (C)</p> Signup and view all the answers

<p>An incomplete sketch of mathematical entities (B)</p> Signup and view all the answers

<p>Moderate and very moderate (C)</p> Signup and view all the answers

<p>Through abstract counterparts (A)</p> Signup and view all the answers

<p>Lack of a clear grasp of second-order consequence (A)</p> Signup and view all the answers

<p>They would be neglected in favor of full first-order logic (C)</p> Signup and view all the answers

<p>An understanding of the divergence between semantic and syntactic characterizations (D)</p> Signup and view all the answers

<p>It leads to a misleading interpretation of second-order logic (D)</p> Signup and view all the answers

<p>It cannot fully explain the properties of second-order logic (B)</p> Signup and view all the answers

<p>The logic of cardinality quantifiers such as Qfin (A)</p> Signup and view all the answers

<p>The notions of truth in different logical contexts (A)</p> Signup and view all the answers

<p>Adding a predicate without treating it as logical (A)</p> Signup and view all the answers

<p>It leads to the expansion of the schema to include sets. (C)</p> Signup and view all the answers

<p>It ensures no new provable statements arise from the expanded theory. (B)</p> Signup and view all the answers

<p>S allows for new consequences that weren't previously provable in N alone. (D)</p> Signup and view all the answers

<p>The schema remains unchanged despite the addition of S. (B)</p> Signup and view all the answers

<p>A logic that treats regions as the primary focus of logical statements. (A)</p> Signup and view all the answers

<p>There will be contradictions that impact the whole theory. (C)</p> Signup and view all the answers

<p>It creates added complexity in interpreting the extended schemas. (C)</p> Signup and view all the answers

<p>They may lack empirical justifications for the new content. (A)</p> Signup and view all the answers

<p>There is no reason to regard sets as relevant to the notion of region. (C)</p> Signup and view all the answers

<p>It lacks obvious physical relevance. (A)</p> Signup and view all the answers

<p>It employs a finiteness predicate viewed as logical. (D)</p> Signup and view all the answers

<p>It helps prove more instances of the completeness schema. (B)</p> Signup and view all the answers

<p>It should have empirical support. (A)</p> Signup and view all the answers

<p>The combination of N and S conceptualized differently. (A)</p> Signup and view all the answers

<p>It provides justification for theoretical expansions. (B)</p> Signup and view all the answers

<p>As unnecessarily complicating the schema. (A)</p> Signup and view all the answers

In mathematics, arithmetic is the branch dealing with numbers and operations such as addition, subtraction, multiplication, and division. It is the basis of many other fields of mathematics and has practical applications in daily life.

Cardinality quantifiers are used to express the size of a set, indicating the number of elements within it. For example, "There are five apples in the basket" uses a cardinality quantifier.

Mereology is a theory dealing with the parts and wholes of objects. It explores how different objects can be combined and broken down. For example, a house consists of several rooms, or a bicycle has wheels, pedals, and a frame.

A representation theorem establishes a connection between two seemingly different mathematical structures, demonstrating that one structure can be represented using another. For example, a theorem could show how geometrical shapes can be represented using algebraic equations.

Conservativeness in logic and mathematics refers to the idea that a theory, when extended with new axioms, preserves all the truths of the original theory but may introduce new truths. Essentially, the new axioms do not contradict the original set of axioms.

The indispensability argument for mathematical objects states that mathematics is essential for our understanding of the physical world. It implies that mathematical entities must exist, as they are crucial for our scientific theories.

Anti-Platonism is a philosophical perspective that rejects the existence of abstract mathematical objects, such as numbers or sets, independent of our minds. It argues that mathematics can still be meaningful and useful without these abstract entities.

Nominalism is a philosophical view that denies the existence of abstract objects, including numbers, sets, and properties. It argues that only concrete, physical objects exist.

The belief that mathematical entities exist independently of our minds, like abstract objects.

The view that mathematical entities don't exist independently, but are tools or symbols we use to understand the world.

A type of nominalism that aims to formulate scientific theories without referring to mathematical entities.

The idea that a theory in science should be formulated in terms of concepts that are directly understandable and meaningful, without relying on external mathematical structures.

A type of explanation in science that relies on mathematical entities or structures external to the system being explained.

The idea that scientific theories are not meant to be literally believed, but are useful models or approximations of reality.

The study of the methods and principles used in reasoning and logic, particularly focusing on the nature of logical systems and their properties.

A type of theory in physics that attempts to describe the most fundamental laws of nature, often using mathematical tools to model reality at the smallest scales.

A mathematical theory that denies the existence of sets and posits that regions in space-time can be understood without them.

A framework for understanding space-time regions as fundamental

A theory about the relationships between parts and wholes, often involving physical objects.

Empirical evidence that supports the claims made by a theory, often in the form of observations or experiments.

A type of mathematical statement that establishes a connection between different mathematical structures, showing how one can be represented using another.

The addition of new axioms to an existing theory without altering the truths of the original.

In quantum theory, the difficulty arises in describing the wave function using predicates of comparative amplitude and phase-difference. These predicates are defined on configuration space, which represents possible configurations of particles or spatial decorations, and includes an extra time dimension. Attempts to represent this in terms of predicates on ordinary space-time are ad hoc and complex.

Nominalism is a philosophical view that states that only concrete, physical objects exist. In the context of quantum mechanics, nominalism poses a challenge because it rejects the existence of abstract mathematical objects such as the wave function, which is often considered to be a fundamental concept in quantum theory.

The idea of chance plays a significant role in both classical statistical mechanics and quantum mechanics. It can be seen as both a description of reality and a guide for our degrees of belief, leading to philosophical complexities.

The use of configuration space, which describes possible particle arrangements and includes time, introduces complexity in representing the wave function. This complexity arises because we need to navigate a multidimensional space that accounts for both particle positions and the evolution of the system.

The view that

Phase differences in quantum mechanics, unlike amplitude, are not invariant under Galilean transformations. This means that the phase difference between two points in space and time needs to be considered, adding complexity to the description of the wave function.

The program of nominalization in quantum mechanics, attempts to represent the theory using only concrete, physical elements, without relying on abstract mathematical objects. However, it raises the question of representing the algebraic structure of Hermitian operators on Hilbert space, which plays a crucial role in quantum mechanics.

The concept of chance involves both describing the uncertainty of physical systems and influencing our beliefs about their behavior. This dual role presents philosophical difficulties as it blurs the lines between objective reality and subjective interpretation.

In logic, a consequence relation is a way to determine if a conclusion logically follows from a set of premises. It's like a rule that says if certain things are true, then something else must also be true.

Semantic consequence refers to a logical relationship where a conclusion is true in every possible interpretation where the premises are true. It focuses on the meaning of the statements.

Syntactic consequence is a logical relationship where a conclusion can be formally derived from a set of premises using a set of rules. It's a more formal approach.

In logic, a second-order logic allows quantification over properties and relations, while first-order logic only quantifies over individuals. Second-order logic is more expressive but can also be more complex.

Impredicative second-order logic allows defining sets using predicates that refer to themselves, leading to potentially paradoxical situations. This makes it more powerful but harder to grasp.

Conservativeness in logic means that adding new axioms to a theory doesn't change the truth of the original theory's statements. It preserves the original knowledge.

The induction principle is a fundamental concept, especially in mathematics. It states that if something is true for the first element of a sequence and if it's true for any element, then it's true for all elements.

A theory's extension that introduces new mathematical entities, like sets, does not affect the truths already established within the original theory. It simply adds new truths without contradicting the existing framework.

A theory's schema refers to the basic building blocks and language used to express its concepts, such as variables and quantifiers. For instance, a theory about numbers might have variables representing numbers and quantifiers to express properties of those numbers.

A theory's schema is the set of basic building blocks and language used to express its concepts, such as variables and quantifiers.

The Dedekind-completeness schema is a specific set of axioms used in theories of real numbers. It states that every non-empty set of real numbers that is bounded above has a least upper bound.

A theory is called 'conservative' when expanding it with new axioms (statements accepted as true) does not change the truths already established within the original theory. The new axioms might add new truths but won't contradict the original set of axioms.

The comprehension schema is a principle in set theory that allows for the construction of sets based on properties. It states that for every property, there is a set containing all and only those objects that have that property.

A first-order theory is a type of theory in logic that only allows quantifiers to range over individuals, not over properties or sets of individuals. This means it cannot directly express statements about sets or relations between sets.