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Philosophy, Abstract Structure, Theorem - Coggle Diagram

- - - - Cognition
        
        Encompasses
        
        Thought
        
        Produces
        
        Idea
        
        Imagination
        
        Judgement
      - Experience
      - Feeling
      - Perception
  - - - A polysemic term used for the designation of the property or set of properties that make an entity or substance what it fundamentally is, which it has by necessity, and without which it loses its identity
- - - - Knowledge
        
        Declarative, Propositional Knowledge
        
        Procedural Knowledge
        
        Knowledge by Acquaintance
        
        Tacit, Implicit Knowledge
        
        Explicit Knowledge
        
        A priori Knowledge
        
        A posteriori Knowledge
      - Justification
      - Truth
      - Belief
    - - Branch of philosophy concerned with knowledge
  - - - Causality
        
        Definition
        
        The influence by which one event, process, state, or object(a cause) contributes to another event process, state, or object(a effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause
      - Meaning
        
        A relationship between two sorts of things: signs and the kinds of things they intend, express, or signify
    - - Ontology
        
        Concepts
        
        Becoming
        
        Reality
        
        Existence
        
        Categorical Distinction
        
        Particulars and Universals
        
        Particular
        
        Are often seen as concrete, spatiotemporal entities as opposed to abstract entities, such as properties or numbers
        
        Universal
        
        Categories
        
        Properties
        
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        Relations
        
        Types or Kinds
        
        Relations
        
        Internal
        
        External
        
        Definition
        
        A relationship between two sorts of things: signs and the kinds of things they intend, express, or signify
        
        Abstract and Concrete
        
        Abstract Concrete Distinction
        
        Abstract Objects and Causality
        
        Type-Token Distinction
        
        Ontological Dependence
        
        Identity
        
        Modality
        
        Substances
      - Cosmology
        
        Definition
        
        A branch of physics and metaphysics dealing with the nature of the universe
        
        Concepts
        
        Monad
        
        Used to refer to a most basic or original substance
    - - Studies questions related to what is it for something to exist and what types of existence are there
  - - - Informal Logic
        
        Uses non-formal criteria and standards to analyze and assess the correctedness of arguments
      - Formal Logic
        
        Formal Systems
        
        Constituents :question:
        
        Formal Language
        
        Constituents
        
        Symbols
        
        5 more items...
        
        Definition
        
        consists of words whose letters are taken from an alphabet and are well-formed according to a set of rules
        
        Aspects
        
        Semantics
        
        1 more item...
        
        Syntax
        
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        Interpretation
        
        An assignment of meaning to the symbols of a formal language
        
        Defined by
        
        Formal System
        
        Formal Grammar, Rules of Formation
        
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        Properties
        
        Makes expressions
        
        Deductive System, Apparatus
        
        Definition
        
        Also callled a deductive apparatus or logic, consists of the set of axioms and rules of inference that can be used to derive theorems of the system
        
        Consists of
        
        Rules of Inference
        
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        Set of Axioms
        
        Types
        
        First-Order Logic
        
        Proof System
        
        Formal Semantics
        
        Defined by
        
        Natural Languge
        
        Logical System
        
        Defined by
        
        Deductive System
        
        Natural Language
        
        Examples
        
        Peano Arithmetic
        
        Logic Translation, Formalize
        
        Through this process becomes...
        
        Logical Form, Argument Form
        
        Rule of Inference, Transformation Rule
        
        3 more items...
        
        Definition
        
        1 more item...
        
        Types
        
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        Definition
        
        The process of representing a text in the formal language of a logical system
        
        Subsumes
        
        Axiomatic System
        
        Contains
        
        Theory
        
        2 more items...
        
        Definition
        
        Any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems
        
        Definition
        
        A set of rules for the manipulation of symbols
        
        Examples
        
        Lambda Calculus
        
        Predicate Calculus
        
        Divisions(of Formal Systems), Logical Systems :question:
        
        Aristotelian (Traditional)
        
        Predicable
        
        A term applied to the classifications of the possible relations a predicate can stand to its subject
        
        Classifications
        
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        Propositional Logic, Calculus
        
        Definition
        
        Comprises formal systems in which formulae are built from which atomic propositions are built from using logical connectives
        
        Clause
        
        A propositional formula formed from a fintie collection of literals (atoms or their negations) and logical connectives
        
        Propositional Formula
        
        Definition
        
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        Comprises
        
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        First Order Logic(Predicate Logic)
        
        Branch
        
        Higher-Order
        
        Definition
        
        A collection of formal systems used in mathematics, philosophy, linguistics, and computer science
        
        Predicate
        
        Definition
        
        1 more item...
        
        Individual Constant
        
        Definition
        
        Uses formal languages to express and analyze arguments
        
        Predicate
        
        A symbol that represents a property or relation
    - - Reasoning
        
        Argument
        
        Constituents
        
        Proposition
        
        Premise
        
        A proposition used in an argument to prove the truth of another proposition called the conclusion
        
        Truth-Bearer
        
        Definition
        
        1 more item...
        
        Definition
        
        Collins Dictionary has a definition for proposition as " a statement or an idea that people can consider or discuss whether it is true"
        
        Conclusion
        
        Also
        
        1 more item...
        
        Consequence
        
        The second half of a hypothetical proposition
        
        Inferences
        
        Steps in reasoning, moving from premises to logical conclusions
        
        Truth, Logical Value
        
        A value indicating the relation of a proposition to truth, which in classical logic has only two possible values, true or false
        
        Values
        
        True
        
        False
        
        Possible Properties
        
        Sound
        
        An argument is sound if it both valid in form and its premises are true
        
        Valid
        
        A form of an argument which makes it impossible for the premsies to be true and the conclusion to be false
        
        Statement
        
        Definition
        
        A proposition, which is the assertion made(its meaning) by a true or false declarative sentence
        
        Axiom, Postulate, Assumption
        
        A statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments
        
        Definition
        
        A series of sentences, statements, or propositions, some of which are called premises and one is the conclusion
        
        Entailment
        
        A fundamental concept in logic which describes the relationships between statements that hold true when one statement logically follows from one or more statements
        
        Types
        
        Fallacy
        
        Informal Fallacy
        
        The source of the error not just due to the form of the argument, but can also be due to their content and context
        
        Definition
        
        The use of invalid or otherwise faulty reasoning in the construction of an argument which may appear to be a well reasoned argument if unnoticed
        
        Formal Fallacy
        
        A pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic
        
        Deductive Reasoning
        
        Inferences
        
        Steps in reasoning, moving from premises to logical conclusions
        
        Process
        
        Definition
        
        Conclusion of a deductive argument is certain, given the premises are correct
        
        Deduction
        
        Constituents
        
        Conclusion
        
        Chain of Intermediates
        
        Premise
        
        Proof
        
        A deduction whose premises are known truths
        
        Definition
        
        A three-part system composed of premises, conclusions, and a chain of intermediates- steps in reasoning showing that its conclusion is a consequence of its premises
        
        Inductive Reasoning
        
        Truth of the conclusion of an inductive argument is probable, based upon the evidence given
        
        Abductive Reasoning
        
        Definition
        
        The capacity of applying logic consciously, by drawing conclusions from new or existing information with the aim of seeking the truth
        
        Formal Proof, Derivation
        
        A finite sequence of sentences(called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference
      - Properties of a Concept
        
        Comprehension
        
        Intension
        
        Any property or quality connoted by a word, phrase, or another symbol
        
        Definition
        
        The totality of intensions that the object possesses or else the totality of intensions that are pertinent to the context of a given discussion
        
        Extension
        
        Definition
        
        Extension of a concept, idea, or sign consists of the things to which it appiles, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question
        
        Denotation
        
        Definition
        
        The literal meaning of an expression
        
        Meaning
      - Predicate
        
        A symbol that represents a property or relation
        
        Noun
        
        The part of a sentence or clause containing a verb and stating something about the subject
        
        Verb
        
        State, affirm, or assert (something ) about the subject of a sentence or the argument of a proposition
      - Truth-Function
        
        A function that accepts truth values as input and produces a unique truth value as output
      - Rewriting
        
        Covers a wide range of methods for replacing subterms of a formula with other terms
        
        Types
        
        Phrase Structure Rule
    - - The study of correct reasoning
  - - - Commensurability
        
        Nomenclature