Thesaurus / axiom
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Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.
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With an ATP, a programmer can code in all the rules, or axioms, and then ask if a particular conjecture follows those rules.
HOW CLOSE ARE COMPUTERS TO AUTOMATING MATHEMATICAL REASONING?STEPHEN ORNESAUGUST 27, 2020QUANTA MAGAZINEIt would mean that there exists a sequence of formulas built from these axioms that proves the formula that means, metamathematically, “This set of axioms is consistent.”
HOW GÖDEL’S PROOF WORKSNATALIE WOLCHOVERJULY 14, 2020QUANTA MAGAZINEGödel’s main maneuver was to map statements about a system of axioms onto statements within the system — that is, onto statements about numbers.
HOW GÖDEL’S PROOF WORKSNATALIE WOLCHOVERJULY 14, 2020QUANTA MAGAZINEBy the first theorem, this set of axioms would then necessarily be incomplete.
HOW GÖDEL’S PROOF WORKSNATALIE WOLCHOVERJULY 14, 2020QUANTA MAGAZINEHe also showed that no candidate set of axioms can ever prove its own consistency.
HOW GÖDEL’S PROOF WORKSNATALIE WOLCHOVERJULY 14, 2020QUANTA MAGAZINEWe’ve learned that if a set of axioms is consistent, then it is incomplete.
HOW GÖDEL’S PROOF WORKSNATALIE WOLCHOVERJULY 14, 2020QUANTA MAGAZINEIt is a generally accepted axiom that a public man cannot afford to be modest in these go-ahead days of "boom."
THE DOCTOR OF PIMLICOWILLIAM LE QUEUXThis truth is as old as Homer, and its proofs are as capable of demonstration as a mathematical axiom.
THE BOOK OF ANECDOTES AND BUDGET OF FUN;VARIOUSBy this, OLeary understood that he was definitely adopted by virtue of the axiom of what was his was theirs.
THE WOMAN GIVESOWEN JOHNSONThat was an axiom on which was founded a vigorous war against all capillary adornments.
THE BRITISH EXPEDITION TO THE CRIMEAWILLIAM HOWARD RUSSELLWORDS RELATED TO AXIOM
- antecedent
- assumption
- authority
- axiom
- backbone
- background
- backing
- base
- bedrock
- cause
- center
- chief ingredient
- core
- crux
- data
- dictum
- essence
- essential
- evidence
- explanation
- footing
- fundamental
- hard fact
- heart
- infrastructure
- justification
- keynote
- keystone
- law
- nexus
- nucleus
- postulate
- premise
- presumption
- presupposition
- principal element
- principle
- proof
- reason
- root
- rudiment
- sanction
- security
- source
- substratum
- support
- theorem
- theory
- underpinning
- warrant
- acceptance
- admission
- assent
- assumption
- assurance
- avowal
- axiom
- certainty
- conclusion
- confidence
- conjecture
- conviction
- credence
- credit
- deduction
- divination
- expectation
- faith
- fancy
- feeling
- guess
- hope
- hypothesis
- idea
- impression
- intuition
- judgment
- knowledge
- mind
- mindset
- notion
- opinion
- persuasion
- position
- postulation
- presumption
- presupposition
- profession
- reliance
- supposition
- surmise
- suspicion
- theorem
- theory
- thesis
- thinking
- trust
- understanding
- view
Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.