History of Logic by https://padlet.com/lindsayygromo/11khmbwdj70l en-us 2016-12-12 13:53:18 UTC 2024-05-26 13:41:34 UTC hello@padlet.com Ancient Greece lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143125209
  • Used demonstrative proof
  • "dissoi logoi"
    • "contrasting arguments"
  • Thales (500's)
    • 1st Greek philosopher
    • Measured height of pyramids by using their shadows
    • First known to use deductive reasoning
  • Pythagoras (520 BC)
    • Study of proof
    • Believed all was number 
    • ]]>     2016-12-12 14:38:20 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143125209     Early Development lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143127180
  • Heraclitus (500's)
    • Everything changes 
    • There are conflicting opposites 
  • Parmenides
    • Truth
    • Instead of sense perception 
  • Zeno of Elea (400's)
    • Obviously false conclusion from premises 
    • reductio ad absurdum 
    • ]]>     2016-12-12 14:43:45 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143127180     Aristotle lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143128066
  • Syllogism  (300's)
    • Conclusion is based off 2 or more true premises
  • Wrote multiple books about his idea of logic (what is truth?)
  • First to deal with arguments by formal logic to evaluate validity and soundness
    • ]]>     2016-12-12 14:46:06 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143128066     Stoics lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143128767
  • Diodorus Cronus and Philo (200's)
    • Conditional statements
    • Must have all true premises and true conclusion 
      • If p then q 
    • ]]>     2016-12-12 14:48:08 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143128767     Medieval Europe lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143129682
  • "Scholastic logic" (1200-1600)
    • Derived from Artisotle
  • Supposition
    • Predicts range over a domain of individuals
    • All humans are animals
      • Past, present, and future?
    • ]]>     2016-12-12 14:50:18 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143129682     Modern Logic lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143131551
  • Fundamentally calculus
  • "exact" logic would be found through mathematical thought
  • Logic is determined by shape and not meaning
    • ]]>     2016-12-12 14:54:58 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143131551     Embryonic Period lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143132187
  • Leibniz (1847)
    • Notion of calculus developed 
  • Thomas Hobbes
    • All logic can be reduced to mathematical operations (addition and subtraction)
    • ]]>     2016-12-12 14:56:29 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143132187     Algebraic Period lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143132894
  • Truth functions
    • Their expression in disjunctive normal form
  • Boole (1847 
    • Started to use "x" and "y" to replace day to day objects or events and = to see the effect of these objects events 
    • ]]>     2016-12-12 14:58:20 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143132894     Logistic Period lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143133579
  • Gottlob Frege (1879)
    • Arithmetic is logic
  • Relied on two connectives 
    • negational 
    • conditional
  • Relied on two rules of inference 
    • modus ponens
    • substitution
    • ]]>     2016-12-12 14:59:55 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143133579     Metamathematical Period lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143134475
  • Gödel's completeness theorem
    • A first-order sentence is deducible if and only if it is logically valid 
  • Alfred Tarsi (1933)
    • Semantic theory of truth 
    • Separates language's semantics from what actually is


    • ]]>     2016-12-12 15:02:34 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143134475     References lindsayygromo https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143137033
  • Boole, George (1847) The Mathematical Analysis of Logic (Cambridge and London); repr. in Studies in Logic and Probability, ed. R. Rhees (London 1952).
  • Potter, Michael (2004), Set Theory and its Philosophy, Oxford University Press.
  • Boehner, Philotheus, Medieval Logic, Manchester 1950.
  • Jevons, W.S. The Principles of Science, London 1879.
  • Frege, G., Boole's Logical Calculus and the Concept Script, 1882, in Posthumous Writings transl. P. Long and R. White 1969, pp. 9–46.
    • ]]>     2016-12-12 15:09:24 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143137033     Rules https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143266411 2016-12-13 01:16:02 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143266411 Truth Tables https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143266538 2016-12-13 01:18:15 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143266538 Example of Using Rules of Inference https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143266761 2016-12-13 01:22:01 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143266761 https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143267042 2016-12-13 01:26:34 UTC https://padlet.com/lindsayygromo/11khmbwdj70l/wish/143267042