John Vincent Atanasoff 1903-1995

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Thought mechanisms required

1. Zero and place-value system (positional)
2. Development of algebraic thought
3. Development of logical thought
4. From classical logic to algebraic and binary logic

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Thought mechanisms required

1. Development of artificial logical calculation
2. From classical algebra to set theory
3. From philosophical logic to mathematical logic
4. Development of symbolic calculus

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Thought mechanisms required
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Zero and place-value system (positional)
Zero no other human creation has been so
influential in the development of mankinds
intelligence
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Thought mechanisms required

• Development of algebraic thought
• ordinary arithmetic algebra
  2 X 3 6 a X b b X a
• Algebrisation of fundamental concepts of
  mechanical calculation

Babbage
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Thought mechanisms required

• Development of Logical Thought
• Logikê technê (Greek) - the art or science
  of discourse
• Logos concerning words, reason, thought
• Aim to determine which
  intellectual operations leading
  toward truth are valid and which
  are not

Aristotle
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The syllogism

• Sullogismos (Greek) counting, calculation,
  reasoning (from sullegein to bring together)
• A deductive scheme of a formal argument
  consisting of a major and a minor premise and a
  conclusion
• If.., then.

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A syllogism ?
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Thought mechanisms required

• From classical logic to algebraic and binary
  logic
• No formal university degree
• Assistant-master of a school at age 16
• Established his own school at age 20
• Professor of Mathematics Queens College, Cork
  1846

George Boole1815 - 1864
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Thought mechanisms required

• George Boole
• Principal Publications
• Mathematical Analysis of Logic (1847)
• The Laws of Thought (1854)
• Booles life marked a turning point in the
  science of human reasoning. We must thus
  recognize that Boole discovered a true general
  form of logic and gave tothat science the form
  it will keep for ever.
• W. S. Jevon

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Thought mechanisms required

• George Boole
• Mathematician Philosopher
• Boolean Algebra - Placed the procedures of
  propositional logic within the operations of a
  true algebra
• Independent of any notion of number or magnitude
• True proposition 1
• False proposition 0
• x and y arbitrary propositions

Queens College, Cork, Ireland
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Fundamental operations of Boolean algebra

1. Logical addition the disjunction of two given
   propositions
2. Logical multiplication the conjunction of two
   given propositions
3. Logical negation the proposition which is
   opposite to a given true or false proposition

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Thought mechanisms required

• Development of Artificial Logical
  CalculationChronological Landmarks
• 12th century Arab soothsayers / circular tables
  of the universe, zairjat al alam
• 1275 Ramon Lull / a scheme of syllogistic
  mechanics inspired by the zairjat
• 1666 Leibniz / lingua characteristica
  universalis
• 1810 - Stanhope / the Demonstrator
• 1847-1854 Booles major publications

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Thought mechanisms required

• Development of Artificial Logical
  CalculationChronological Landmarks
• 1869 W. S. Jevon / Logical Piano an aid to the
  teaching of the new logic of classes and
  propositions
• 1881 Allan Marquand / bigger and better
  logical machine
• 1886 Charles Peirce / isomorphism between
  Boolean algebra and electrical switching
  circuits
• 1903 Annibale Pastore/ reasoning machine
  based on the rules of the syllogism
  (3 pulleys)

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Thought mechanisms required

• Development of Artificial Logical
  CalculationChronological Landmarks
• 1910 Leonardo Torres y Quevedo / automatic
  chess player
• 1936 Benjamin Burack / electrical logic machine
  able to solve complex syllogisms
• 1943 1st generation Colossus / binary logical
  calculations / deciphering
• 1946 Kalin Burhart / small logical truth
  calculator electric programmable /
  automatic control unit supervising the
  sequences of logical operations

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Thought mechanisms required

• From Classical Algebra to Set Theory

Organisms
Fungi
Plants
dicots
invertebrates
monocots
Animals
Georg Cantor 1845-1918
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Thought mechanisms required

• From Philosophical Logic to Mathematical
  Logic
• Classical logic Bivalent logic
• only two truth values
• 1) true
• 2) false
• Contemporary logicians have developed
  multi-valued logics

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Modal Logicmulti-valued logics

• Logics with n values / introduction of (n -
  2) intermediate values between the true and the
  false
• The criterion of the coherence of a system of
  axioms, expressed as relations between symbols,
  has replaced the criterion of the self-evidence
  of the principles and theorems of a deductive
  theory

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In the 19th and 20th century, logic was drawn
away from philosophy and tied closer to
mathematics

• There are no logical constants
• Symbols must be free of all pre-established
  intuitive meaning
• Signs combined according to rules laid down by
  the primary propositions
• Logic must be arbitrary and as empty as
  mathematics

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Thought mechanisms required
The Development of Symbolic Calculus

• Logic has become more mathematical and
  mathematics more logical
• Bertrand Russell

1872 - 1970
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Logistics the art of organizing a calculation
into successive steps

• From logistikos, Greek, concerning calculations
• From logismos calculations
• And logistikê technê the art of calculation

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Logistics symbolic calculus

• Establishes a system of symbols, modeled on the
  forms of thought
• Combines these, according to the rules of its
  axioms
• While completely abstracting their meaning

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The Theory of Algorithms

1. A technique in the calculus of thought
2. A high-powered generalization of classical
   reasoning
3. Entirely formalized logic, based on a series of
   coherent axioms
4. Operands are executed on symbols that are
   independent of the nature of the reality they
   represent

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The Theory of Algorithms

1. Propositions themselves are formalized
   propositions
2. The relations that exist between the propositions
   are expressed by means of algorithms
3. Algorithms - finite series of symbols and
   computational procedures

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Who invented the computer ?
?