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History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
History and Philosophy of ScienceLecture 9
C. K. Raju
AlBukhary International University, Malaysia,[email protected]
web:http://ckraju.net
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Recap
Non-Western philosophy of proof
Fallibility of deduction
The religious bias
What is science?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The nature of math
I On Western philosophy
I math is metaphysical.
I It uses deductive inference.
I It claims: deduction is superior to induction.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The nature of math
I On Western philosophy
I math is metaphysical.
I It uses deductive inference.
I It claims: deduction is superior to induction.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The nature of math
I On Western philosophy
I math is metaphysical.
I It uses deductive inference.
I It claims: deduction is superior to induction.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The nature of math
I On Western philosophy
I math is metaphysical.
I It uses deductive inference.
I It claims: deduction is superior to induction.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Two key questions
I Q1. Is it true that deduction is more certain thaninduction?
I Q1. What is physics, and what is metaphysics?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Two key questions
I Q1. Is it true that deduction is more certain thaninduction?
I Q1. What is physics, and what is metaphysics?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A change of perspective
I Before going into these questions
I let us look at things from a fresh perspective
I of non-Western philosophy
I on the nature of truth.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A change of perspective
I Before going into these questions
I let us look at things from a fresh perspective
I of non-Western philosophy
I on the nature of truth.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A change of perspective
I Before going into these questions
I let us look at things from a fresh perspective
I of non-Western philosophy
I on the nature of truth.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A change of perspective
I Before going into these questions
I let us look at things from a fresh perspective
I of non-Western philosophy
I on the nature of truth.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Knowledge requires proof
I All philosophies agree that truth/knowledge requiresproof.
I They differ in the nature of proof they accept.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Knowledge requires proof
I All philosophies agree that truth/knowledge requiresproof.
I They differ in the nature of proof they accept.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
General intro
I Non-Western philosophical systems usually do notdiscriminate between
I various kinds of truth.
I (That is, they believe there is only one truth.)
I Hence, they have the same means of proof for all casesof math, science, law, religion.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
General intro
I Non-Western philosophical systems usually do notdiscriminate between
I various kinds of truth.
I (That is, they believe there is only one truth.)
I Hence, they have the same means of proof for all casesof math, science, law, religion.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
General intro
I Non-Western philosophical systems usually do notdiscriminate between
I various kinds of truth.
I (That is, they believe there is only one truth.)
I Hence, they have the same means of proof for all casesof math, science, law, religion.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
General intro
I Non-Western philosophical systems usually do notdiscriminate between
I various kinds of truth.
I (That is, they believe there is only one truth.)
I Hence, they have the same means of proof for all casesof math, science, law, religion.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Why Indian systems first?
I I will start with the Indian systems and go on to Islam
I because these are easy to explain, and I am mostfamiliar with them.
I (Feel free to explain other systems in your assignments.)
I Also, Buddhism deeply influenced the Chinese, thusearly Indian philosophical systems relevant to 40% ofthe world population.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Why Indian systems first?
I I will start with the Indian systems and go on to Islam
I because these are easy to explain, and I am mostfamiliar with them.
I (Feel free to explain other systems in your assignments.)
I Also, Buddhism deeply influenced the Chinese, thusearly Indian philosophical systems relevant to 40% ofthe world population.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Why Indian systems first?
I I will start with the Indian systems and go on to Islam
I because these are easy to explain, and I am mostfamiliar with them.
I (Feel free to explain other systems in your assignments.)
I Also, Buddhism deeply influenced the Chinese, thusearly Indian philosophical systems relevant to 40% ofthe world population.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Why Indian systems first?
I I will start with the Indian systems and go on to Islam
I because these are easy to explain, and I am mostfamiliar with them.
I (Feel free to explain other systems in your assignments.)
I Also, Buddhism deeply influenced the Chinese, thusearly Indian philosophical systems relevant to 40% ofthe world population.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Further reasons
I Many systems flourished in India,
I (In contrast, Western system was dominated by church.)
I In India people debated (no church to kill off or banishopponents)
I so the strengths and weakness of each (and of Westernphilosophy) are most readily understood by studyingthese competing system.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Further reasons
I Many systems flourished in India,
I (In contrast, Western system was dominated by church.)
I In India people debated (no church to kill off or banishopponents)
I so the strengths and weakness of each (and of Westernphilosophy) are most readily understood by studyingthese competing system.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Further reasons
I Many systems flourished in India,
I (In contrast, Western system was dominated by church.)
I In India people debated (no church to kill off or banishopponents)
I so the strengths and weakness of each (and of Westernphilosophy) are most readily understood by studyingthese competing system.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Further reasons
I Many systems flourished in India,
I (In contrast, Western system was dominated by church.)
I In India people debated (no church to kill off or banishopponents)
I so the strengths and weakness of each (and of Westernphilosophy) are most readily understood by studyingthese competing system.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
NyayaTraditional Indian system
I Used 4 means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy (understanding unknown through similaritywith known)
I Reliable testimony (witness, scriptures)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
NyayaTraditional Indian system
I Used 4 means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy (understanding unknown through similaritywith known)
I Reliable testimony (witness, scriptures)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
NyayaTraditional Indian system
I Used 4 means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy (understanding unknown through similaritywith known)
I Reliable testimony (witness, scriptures)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
NyayaTraditional Indian system
I Used 4 means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy (understanding unknown through similaritywith known)
I Reliable testimony (witness, scriptures)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
NyayaTraditional Indian system
I Used 4 means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy (understanding unknown through similaritywith known)
I Reliable testimony (witness, scriptures)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Rules of argument
I First state opponent’s position clearly (purva paks.a).
I Misrepresentation (or failure to understand) means youlose the argument.
I Attack the point of view not the person (personalattacks [or abuse] means you lose the argument).
I E.g. Witzel (Harvard), Whiteside (Cambridge).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Rules of argument
I First state opponent’s position clearly (purva paks.a).
I Misrepresentation (or failure to understand) means youlose the argument.
I Attack the point of view not the person (personalattacks [or abuse] means you lose the argument).
I E.g. Witzel (Harvard), Whiteside (Cambridge).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Rules of argument
I First state opponent’s position clearly (purva paks.a).
I Misrepresentation (or failure to understand) means youlose the argument.
I Attack the point of view not the person (personalattacks [or abuse] means you lose the argument).
I E.g. Witzel (Harvard), Whiteside (Cambridge).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Rules of argument
I First state opponent’s position clearly (purva paks.a).
I Misrepresentation (or failure to understand) means youlose the argument.
I Attack the point of view not the person (personalattacks [or abuse] means you lose the argument).
I E.g. Witzel (Harvard), Whiteside (Cambridge).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A current example of misrepresentation
I On my paper on “Probability in Ancient India”
I Witzel (Harvard Prof.) wrote that “Raju’s mistake isthat he thinks dice in India had 6 faces”
I and “explained” this mistake by asserting that “Rajurelied on bad translation.
I Misrepresentation: no mention of six-faced dice on mypaper (on website), it mentions five-faced dice.
I I do my own translations from Sanskrit.
I Witzel lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A current example of misrepresentation
I On my paper on “Probability in Ancient India”
I Witzel (Harvard Prof.) wrote that “Raju’s mistake isthat he thinks dice in India had 6 faces”
I and “explained” this mistake by asserting that “Rajurelied on bad translation.
I Misrepresentation: no mention of six-faced dice on mypaper (on website), it mentions five-faced dice.
I I do my own translations from Sanskrit.
I Witzel lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A current example of misrepresentation
I On my paper on “Probability in Ancient India”
I Witzel (Harvard Prof.) wrote that “Raju’s mistake isthat he thinks dice in India had 6 faces”
I and “explained” this mistake by asserting that “Rajurelied on bad translation.
I Misrepresentation: no mention of six-faced dice on mypaper (on website), it mentions five-faced dice.
I I do my own translations from Sanskrit.
I Witzel lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A current example of misrepresentation
I On my paper on “Probability in Ancient India”
I Witzel (Harvard Prof.) wrote that “Raju’s mistake isthat he thinks dice in India had 6 faces”
I and “explained” this mistake by asserting that “Rajurelied on bad translation.
I Misrepresentation: no mention of six-faced dice on mypaper (on website), it mentions five-faced dice.
I I do my own translations from Sanskrit.
I Witzel lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A current example of misrepresentation
I On my paper on “Probability in Ancient India”
I Witzel (Harvard Prof.) wrote that “Raju’s mistake isthat he thinks dice in India had 6 faces”
I and “explained” this mistake by asserting that “Rajurelied on bad translation.
I Misrepresentation: no mention of six-faced dice on mypaper (on website), it mentions five-faced dice.
I I do my own translations from Sanskrit.
I Witzel lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A current example of misrepresentation
I On my paper on “Probability in Ancient India”
I Witzel (Harvard Prof.) wrote that “Raju’s mistake isthat he thinks dice in India had 6 faces”
I and “explained” this mistake by asserting that “Rajurelied on bad translation.
I Misrepresentation: no mention of six-faced dice on mypaper (on website), it mentions five-faced dice.
I I do my own translations from Sanskrit.
I Witzel lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
WhitesideNewton’s suppressed work
I Newton thought the Bible was distorted
I and wrote an 8-volume history of the church to explainthis.
I The work was suppressed for over 250 years (shows howCambridge does history of science).
I On a mailing list (Historia Matematica) someone askedif there were any unpublished Newton manuscripts.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
WhitesideNewton’s suppressed work
I Newton thought the Bible was distorted
I and wrote an 8-volume history of the church to explainthis.
I The work was suppressed for over 250 years (shows howCambridge does history of science).
I On a mailing list (Historia Matematica) someone askedif there were any unpublished Newton manuscripts.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
WhitesideNewton’s suppressed work
I Newton thought the Bible was distorted
I and wrote an 8-volume history of the church to explainthis.
I The work was suppressed for over 250 years (shows howCambridge does history of science).
I On a mailing list (Historia Matematica) someone askedif there were any unpublished Newton manuscripts.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
WhitesideNewton’s suppressed work
I Newton thought the Bible was distorted
I and wrote an 8-volume history of the church to explainthis.
I The work was suppressed for over 250 years (shows howCambridge does history of science).
I On a mailing list (Historia Matematica) someone askedif there were any unpublished Newton manuscripts.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Newton’s suppressed workscontd
I Whiteside responded “NONE, repeat NONE of Newtonmathematical manuscripts are unpublished”.
I I said “a cartload” of Newton’s papers are unpublished.(The “cartload” was an allusion to a 19th c. historian’sstatement.)
I Whiteside turned abusive since he could not deny thetruth.
I (Imperial College has started a project to collectNewton manuscripts, from 1998.)
I Newton’s religious beliefs affected his mathematics(“perfect calculus”) and his physics (“flowing time”)(See Eleven Pictures of Time, and “RetardedGravitation Theory”).
I Whiteside lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Newton’s suppressed workscontd
I Whiteside responded “NONE, repeat NONE of Newtonmathematical manuscripts are unpublished”.
I I said “a cartload” of Newton’s papers are unpublished.(The “cartload” was an allusion to a 19th c. historian’sstatement.)
I Whiteside turned abusive since he could not deny thetruth.
I (Imperial College has started a project to collectNewton manuscripts, from 1998.)
I Newton’s religious beliefs affected his mathematics(“perfect calculus”) and his physics (“flowing time”)(See Eleven Pictures of Time, and “RetardedGravitation Theory”).
I Whiteside lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Newton’s suppressed workscontd
I Whiteside responded “NONE, repeat NONE of Newtonmathematical manuscripts are unpublished”.
I I said “a cartload” of Newton’s papers are unpublished.(The “cartload” was an allusion to a 19th c. historian’sstatement.)
I Whiteside turned abusive since he could not deny thetruth.
I (Imperial College has started a project to collectNewton manuscripts, from 1998.)
I Newton’s religious beliefs affected his mathematics(“perfect calculus”) and his physics (“flowing time”)(See Eleven Pictures of Time, and “RetardedGravitation Theory”).
I Whiteside lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Newton’s suppressed workscontd
I Whiteside responded “NONE, repeat NONE of Newtonmathematical manuscripts are unpublished”.
I I said “a cartload” of Newton’s papers are unpublished.(The “cartload” was an allusion to a 19th c. historian’sstatement.)
I Whiteside turned abusive since he could not deny thetruth.
I (Imperial College has started a project to collectNewton manuscripts, from 1998.)
I Newton’s religious beliefs affected his mathematics(“perfect calculus”) and his physics (“flowing time”)(See Eleven Pictures of Time, and “RetardedGravitation Theory”).
I Whiteside lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Newton’s suppressed workscontd
I Whiteside responded “NONE, repeat NONE of Newtonmathematical manuscripts are unpublished”.
I I said “a cartload” of Newton’s papers are unpublished.(The “cartload” was an allusion to a 19th c. historian’sstatement.)
I Whiteside turned abusive since he could not deny thetruth.
I (Imperial College has started a project to collectNewton manuscripts, from 1998.)
I Newton’s religious beliefs affected his mathematics(“perfect calculus”) and his physics (“flowing time”)(See Eleven Pictures of Time, and “RetardedGravitation Theory”).
I Whiteside lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Newton’s suppressed workscontd
I Whiteside responded “NONE, repeat NONE of Newtonmathematical manuscripts are unpublished”.
I I said “a cartload” of Newton’s papers are unpublished.(The “cartload” was an allusion to a 19th c. historian’sstatement.)
I Whiteside turned abusive since he could not deny thetruth.
I (Imperial College has started a project to collectNewton manuscripts, from 1998.)
I Newton’s religious beliefs affected his mathematics(“perfect calculus”) and his physics (“flowing time”)(See Eleven Pictures of Time, and “RetardedGravitation Theory”).
I Whiteside lost the argument.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Buddhists
I Only 2 reliable means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy is not reliable (blind men and the elephant).
I Reliability of testimony is either manifest or inference.Not a separate means of proof.
I (Note: these 2 also the only means of proof accepted byscience today.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Buddhists
I Only 2 reliable means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy is not reliable (blind men and the elephant).
I Reliability of testimony is either manifest or inference.Not a separate means of proof.
I (Note: these 2 also the only means of proof accepted byscience today.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Buddhists
I Only 2 reliable means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy is not reliable (blind men and the elephant).
I Reliability of testimony is either manifest or inference.Not a separate means of proof.
I (Note: these 2 also the only means of proof accepted byscience today.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Buddhists
I Only 2 reliable means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy is not reliable (blind men and the elephant).
I Reliability of testimony is either manifest or inference.Not a separate means of proof.
I (Note: these 2 also the only means of proof accepted byscience today.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Buddhists
I Only 2 reliable means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy is not reliable (blind men and the elephant).
I Reliability of testimony is either manifest or inference.Not a separate means of proof.
I (Note: these 2 also the only means of proof accepted byscience today.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Buddhists
I Only 2 reliable means of proof:
I Empirically manifest (evidence of senses)
I Inference (reasoning from observation)
I Analogy is not reliable (blind men and the elephant).
I Reliability of testimony is either manifest or inference.Not a separate means of proof.
I (Note: these 2 also the only means of proof accepted byscience today.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy and the elephant
I Everyone has heard the story of the 4 blind men and theelephant.
I But few have heard the story of 4 learned Western menand the Indian elephant in South America.
I (See extract from ckr-China-papaper.)
I However, analogy can have other uses and misuses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy and the elephant
I Everyone has heard the story of the 4 blind men and theelephant.
I But few have heard the story of 4 learned Western menand the Indian elephant in South America.
I (See extract from ckr-China-papaper.)
I However, analogy can have other uses and misuses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy and the elephant
I Everyone has heard the story of the 4 blind men and theelephant.
I But few have heard the story of 4 learned Western menand the Indian elephant in South America.
I (See extract from ckr-China-papaper.)
I However, analogy can have other uses and misuses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy and the elephant
I Everyone has heard the story of the 4 blind men and theelephant.
I But few have heard the story of 4 learned Western menand the Indian elephant in South America.
I (See extract from ckr-China-papaper.)
I However, analogy can have other uses and misuses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy in History
I Huntington’s Clash of Civilizations military strategybased on
I Toynbee’s theory of history (which coined the phrase“barbarian incursions”)
I Toynbee was responding to Spengler’s Decline of theWest
I which said present condition of the West is similar(analogous) to that of Roman empire in decline
I and that analogy is useful for history (unlike science).
I See Eleven Pictures of Time, chp. 3.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy in History
I Huntington’s Clash of Civilizations military strategybased on
I Toynbee’s theory of history (which coined the phrase“barbarian incursions”)
I Toynbee was responding to Spengler’s Decline of theWest
I which said present condition of the West is similar(analogous) to that of Roman empire in decline
I and that analogy is useful for history (unlike science).
I See Eleven Pictures of Time, chp. 3.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy in History
I Huntington’s Clash of Civilizations military strategybased on
I Toynbee’s theory of history (which coined the phrase“barbarian incursions”)
I Toynbee was responding to Spengler’s Decline of theWest
I which said present condition of the West is similar(analogous) to that of Roman empire in decline
I and that analogy is useful for history (unlike science).
I See Eleven Pictures of Time, chp. 3.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy in History
I Huntington’s Clash of Civilizations military strategybased on
I Toynbee’s theory of history (which coined the phrase“barbarian incursions”)
I Toynbee was responding to Spengler’s Decline of theWest
I which said present condition of the West is similar(analogous) to that of Roman empire in decline
I and that analogy is useful for history (unlike science).
I See Eleven Pictures of Time, chp. 3.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy in History
I Huntington’s Clash of Civilizations military strategybased on
I Toynbee’s theory of history (which coined the phrase“barbarian incursions”)
I Toynbee was responding to Spengler’s Decline of theWest
I which said present condition of the West is similar(analogous) to that of Roman empire in decline
I and that analogy is useful for history (unlike science).
I See Eleven Pictures of Time, chp. 3.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Analogy in History
I Huntington’s Clash of Civilizations military strategybased on
I Toynbee’s theory of history (which coined the phrase“barbarian incursions”)
I Toynbee was responding to Spengler’s Decline of theWest
I which said present condition of the West is similar(analogous) to that of Roman empire in decline
I and that analogy is useful for history (unlike science).
I See Eleven Pictures of Time, chp. 3.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lokayata or People’s philosophyRejection of inference as valid proof
I Only 1 means of proof:
I Empirically manifest (evidence of senses)
I Inference rejected as unreliable
I E.g. case of wolf’s paws.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lokayata or People’s philosophyRejection of inference as valid proof
I Only 1 means of proof:
I Empirically manifest (evidence of senses)
I Inference rejected as unreliable
I E.g. case of wolf’s paws.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lokayata or People’s philosophyRejection of inference as valid proof
I Only 1 means of proof:
I Empirically manifest (evidence of senses)
I Inference rejected as unreliable
I E.g. case of wolf’s paws.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lokayata or People’s philosophyRejection of inference as valid proof
I Only 1 means of proof:
I Empirically manifest (evidence of senses)
I Inference rejected as unreliable
I E.g. case of wolf’s paws.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
IslamMeans of knowledge
I Similar to Nyaya (but no analogy!)
I Evidence of senses (tajurba, empirically manifest)
I Inference
I Reliable testimony
I Difference only in what is considered reliable: Koran,not Veda.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
IslamMeans of knowledge
I Similar to Nyaya (but no analogy!)
I Evidence of senses (tajurba, empirically manifest)
I Inference
I Reliable testimony
I Difference only in what is considered reliable: Koran,not Veda.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
IslamMeans of knowledge
I Similar to Nyaya (but no analogy!)
I Evidence of senses (tajurba, empirically manifest)
I Inference
I Reliable testimony
I Difference only in what is considered reliable: Koran,not Veda.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
IslamMeans of knowledge
I Similar to Nyaya (but no analogy!)
I Evidence of senses (tajurba, empirically manifest)
I Inference
I Reliable testimony
I Difference only in what is considered reliable: Koran,not Veda.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
IslamMeans of knowledge
I Similar to Nyaya (but no analogy!)
I Evidence of senses (tajurba, empirically manifest)
I Inference
I Reliable testimony
I Difference only in what is considered reliable: Koran,not Veda.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Western philosophy teaches that empirical proofs areinferior and fallible.
I No doubt empirical proofs are fallible.
I A snake may be mistaken for a rope or a rope for asnake.
I But the doubt can be settled by repeated observation(called induction).
I We prod the rope/snake to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Western philosophy teaches that empirical proofs areinferior and fallible.
I No doubt empirical proofs are fallible.
I A snake may be mistaken for a rope or a rope for asnake.
I But the doubt can be settled by repeated observation(called induction).
I We prod the rope/snake to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Western philosophy teaches that empirical proofs areinferior and fallible.
I No doubt empirical proofs are fallible.
I A snake may be mistaken for a rope or a rope for asnake.
I But the doubt can be settled by repeated observation(called induction).
I We prod the rope/snake to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Western philosophy teaches that empirical proofs areinferior and fallible.
I No doubt empirical proofs are fallible.
I A snake may be mistaken for a rope or a rope for asnake.
I But the doubt can be settled by repeated observation(called induction).
I We prod the rope/snake to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Western philosophy teaches that empirical proofs areinferior and fallible.
I No doubt empirical proofs are fallible.
I A snake may be mistaken for a rope or a rope for asnake.
I But the doubt can be settled by repeated observation(called induction).
I We prod the rope/snake to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Inductive methods or repeated experiments are alsoused in science.
I However, the Western belief has been that deductiveproofs are infallible.
I This is not true.
I Deductive proofs are even more fallible, and there is nosimple way to check them.
I Let us see some examples.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Inductive methods or repeated experiments are alsoused in science.
I However, the Western belief has been that deductiveproofs are infallible.
I This is not true.
I Deductive proofs are even more fallible, and there is nosimple way to check them.
I Let us see some examples.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Inductive methods or repeated experiments are alsoused in science.
I However, the Western belief has been that deductiveproofs are infallible.
I This is not true.
I Deductive proofs are even more fallible, and there is nosimple way to check them.
I Let us see some examples.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Inductive methods or repeated experiments are alsoused in science.
I However, the Western belief has been that deductiveproofs are infallible.
I This is not true.
I Deductive proofs are even more fallible, and there is nosimple way to check them.
I Let us see some examples.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Induction vs deduction
I Inductive methods or repeated experiments are alsoused in science.
I However, the Western belief has been that deductiveproofs are infallible.
I This is not true.
I Deductive proofs are even more fallible, and there is nosimple way to check them.
I Let us see some examples.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wolf’s paws
I To convert his girlfriend to his point of view
I a man goes around at night carrying a wolf’s paws,
I and makes paw prints on the ground.
I He, then, says “wise men will infer from the paw printsthat a wolf was around”
I and they will be wrong!
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wolf’s paws
I To convert his girlfriend to his point of view
I a man goes around at night carrying a wolf’s paws,
I and makes paw prints on the ground.
I He, then, says “wise men will infer from the paw printsthat a wolf was around”
I and they will be wrong!
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wolf’s paws
I To convert his girlfriend to his point of view
I a man goes around at night carrying a wolf’s paws,
I and makes paw prints on the ground.
I He, then, says “wise men will infer from the paw printsthat a wolf was around”
I and they will be wrong!
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wolf’s paws
I To convert his girlfriend to his point of view
I a man goes around at night carrying a wolf’s paws,
I and makes paw prints on the ground.
I He, then, says “wise men will infer from the paw printsthat a wolf was around”
I and they will be wrong!
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wolf’s paws
I To convert his girlfriend to his point of view
I a man goes around at night carrying a wolf’s paws,
I and makes paw prints on the ground.
I He, then, says “wise men will infer from the paw printsthat a wolf was around”
I and they will be wrong!
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceOnly as good as assumption
I Thus deductive proofs are only as strong as theassumptions.
I if the assumptions are wrong, the conclusions too willbe wrong.
I That is wrong axioms can likewise lead to badmathematics.
I (You don’t even know the axioms used for calculus withlimits! How do you know whether they are right orwrong?)
I Key point: even a valid mathematical theorem mayhave nil practical consequences, since the assumptionsmay be invalid.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceOnly as good as assumption
I Thus deductive proofs are only as strong as theassumptions.
I if the assumptions are wrong, the conclusions too willbe wrong.
I That is wrong axioms can likewise lead to badmathematics.
I (You don’t even know the axioms used for calculus withlimits! How do you know whether they are right orwrong?)
I Key point: even a valid mathematical theorem mayhave nil practical consequences, since the assumptionsmay be invalid.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceOnly as good as assumption
I Thus deductive proofs are only as strong as theassumptions.
I if the assumptions are wrong, the conclusions too willbe wrong.
I That is wrong axioms can likewise lead to badmathematics.
I (You don’t even know the axioms used for calculus withlimits! How do you know whether they are right orwrong?)
I Key point: even a valid mathematical theorem mayhave nil practical consequences, since the assumptionsmay be invalid.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceOnly as good as assumption
I Thus deductive proofs are only as strong as theassumptions.
I if the assumptions are wrong, the conclusions too willbe wrong.
I That is wrong axioms can likewise lead to badmathematics.
I (You don’t even know the axioms used for calculus withlimits! How do you know whether they are right orwrong?)
I Key point: even a valid mathematical theorem mayhave nil practical consequences, since the assumptionsmay be invalid.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferencePost hoc
I However, there are many common errors in deductiveproofs.
I E.g. classical fallacy of post hoc ergo propter hoc.(“After this, therefore because of this.”
I At a lecture in India, last year, a girl said:
I ”You are able to speak against Western education justbecause you were Western educated”. [Many peopleclapped!]
I A slave was in chains, and became free: did he becomefree because of the chains?
I I became free because of my own efforts to overcomeWestern indoctrination.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferencePost hoc
I However, there are many common errors in deductiveproofs.
I E.g. classical fallacy of post hoc ergo propter hoc.(“After this, therefore because of this.”
I At a lecture in India, last year, a girl said:
I ”You are able to speak against Western education justbecause you were Western educated”. [Many peopleclapped!]
I A slave was in chains, and became free: did he becomefree because of the chains?
I I became free because of my own efforts to overcomeWestern indoctrination.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferencePost hoc
I However, there are many common errors in deductiveproofs.
I E.g. classical fallacy of post hoc ergo propter hoc.(“After this, therefore because of this.”
I At a lecture in India, last year, a girl said:
I ”You are able to speak against Western education justbecause you were Western educated”. [Many peopleclapped!]
I A slave was in chains, and became free: did he becomefree because of the chains?
I I became free because of my own efforts to overcomeWestern indoctrination.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferencePost hoc
I However, there are many common errors in deductiveproofs.
I E.g. classical fallacy of post hoc ergo propter hoc.(“After this, therefore because of this.”
I At a lecture in India, last year, a girl said:
I ”You are able to speak against Western education justbecause you were Western educated”. [Many peopleclapped!]
I A slave was in chains, and became free: did he becomefree because of the chains?
I I became free because of my own efforts to overcomeWestern indoctrination.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferencePost hoc
I However, there are many common errors in deductiveproofs.
I E.g. classical fallacy of post hoc ergo propter hoc.(“After this, therefore because of this.”
I At a lecture in India, last year, a girl said:
I ”You are able to speak against Western education justbecause you were Western educated”. [Many peopleclapped!]
I A slave was in chains, and became free: did he becomefree because of the chains?
I I became free because of my own efforts to overcomeWestern indoctrination.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferencePost hoc
I However, there are many common errors in deductiveproofs.
I E.g. classical fallacy of post hoc ergo propter hoc.(“After this, therefore because of this.”
I At a lecture in India, last year, a girl said:
I ”You are able to speak against Western education justbecause you were Western educated”. [Many peopleclapped!]
I A slave was in chains, and became free: did he becomefree because of the chains?
I I became free because of my own efforts to overcomeWestern indoctrination.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceReversing the implication
I There are many other logical fallacies which lead towrong conclusions.
I E.g. fallacy of asserting the consequent.
I ”All whales are mammals, therefore all mammals arewhales!”
I Encountered, in practice, as follows:
I ”All chauvinists are anti-West, therefore anyoneanti-West is a chauvinist”. (This argument used againstme by Harvard prof. Witzel.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceReversing the implication
I There are many other logical fallacies which lead towrong conclusions.
I E.g. fallacy of asserting the consequent.
I ”All whales are mammals, therefore all mammals arewhales!”
I Encountered, in practice, as follows:
I ”All chauvinists are anti-West, therefore anyoneanti-West is a chauvinist”. (This argument used againstme by Harvard prof. Witzel.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceReversing the implication
I There are many other logical fallacies which lead towrong conclusions.
I E.g. fallacy of asserting the consequent.
I ”All whales are mammals, therefore all mammals arewhales!”
I Encountered, in practice, as follows:
I ”All chauvinists are anti-West, therefore anyoneanti-West is a chauvinist”. (This argument used againstme by Harvard prof. Witzel.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceReversing the implication
I There are many other logical fallacies which lead towrong conclusions.
I E.g. fallacy of asserting the consequent.
I ”All whales are mammals, therefore all mammals arewhales!”
I Encountered, in practice, as follows:
I ”All chauvinists are anti-West, therefore anyoneanti-West is a chauvinist”. (This argument used againstme by Harvard prof. Witzel.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceReversing the implication
I There are many other logical fallacies which lead towrong conclusions.
I E.g. fallacy of asserting the consequent.
I ”All whales are mammals, therefore all mammals arewhales!”
I Encountered, in practice, as follows:
I ”All chauvinists are anti-West, therefore anyoneanti-West is a chauvinist”. (This argument used againstme by Harvard prof. Witzel.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wrong proofsThe first theorem of the Elements
I Math today is taught as metaphysical (deductive) proof
I claiming that this was the superior way of doingmathematics invented by Euclid (who did not exist)
I After 700 years Westerners finally noticed that the veryfirst theorem of the Elements uses an empirical orphysical proof, not a deductive one.
I This shows that all Westerners made a silly mistakeabout deductive proof for 700 years.
I Why, then, should we believe their faith that deductiveproofs are infallible?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wrong proofsThe first theorem of the Elements
I Math today is taught as metaphysical (deductive) proof
I claiming that this was the superior way of doingmathematics invented by Euclid (who did not exist)
I After 700 years Westerners finally noticed that the veryfirst theorem of the Elements uses an empirical orphysical proof, not a deductive one.
I This shows that all Westerners made a silly mistakeabout deductive proof for 700 years.
I Why, then, should we believe their faith that deductiveproofs are infallible?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wrong proofsThe first theorem of the Elements
I Math today is taught as metaphysical (deductive) proof
I claiming that this was the superior way of doingmathematics invented by Euclid (who did not exist)
I After 700 years Westerners finally noticed that the veryfirst theorem of the Elements uses an empirical orphysical proof, not a deductive one.
I This shows that all Westerners made a silly mistakeabout deductive proof for 700 years.
I Why, then, should we believe their faith that deductiveproofs are infallible?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wrong proofsThe first theorem of the Elements
I Math today is taught as metaphysical (deductive) proof
I claiming that this was the superior way of doingmathematics invented by Euclid (who did not exist)
I After 700 years Westerners finally noticed that the veryfirst theorem of the Elements uses an empirical orphysical proof, not a deductive one.
I This shows that all Westerners made a silly mistakeabout deductive proof for 700 years.
I Why, then, should we believe their faith that deductiveproofs are infallible?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Wrong proofsThe first theorem of the Elements
I Math today is taught as metaphysical (deductive) proof
I claiming that this was the superior way of doingmathematics invented by Euclid (who did not exist)
I After 700 years Westerners finally noticed that the veryfirst theorem of the Elements uses an empirical orphysical proof, not a deductive one.
I This shows that all Westerners made a silly mistakeabout deductive proof for 700 years.
I Why, then, should we believe their faith that deductiveproofs are infallible?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceWrong mathematical proofs
I Many wrong attempts to prove the parallel postulate inElements down the centuries.
I Many wrong proofs of Fermat’s last theorem, Riemannhypothesis, etc.
I For a complicated proof it may be impossible to decidewhether it is right or wrong.
I Four colour theorem: any map requires only four coloursif no two adjacent countries have the same colour.
I Proof of this theorem (obtained using computers) toocomplicated for the human mind to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceWrong mathematical proofs
I Many wrong attempts to prove the parallel postulate inElements down the centuries.
I Many wrong proofs of Fermat’s last theorem, Riemannhypothesis, etc.
I For a complicated proof it may be impossible to decidewhether it is right or wrong.
I Four colour theorem: any map requires only four coloursif no two adjacent countries have the same colour.
I Proof of this theorem (obtained using computers) toocomplicated for the human mind to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceWrong mathematical proofs
I Many wrong attempts to prove the parallel postulate inElements down the centuries.
I Many wrong proofs of Fermat’s last theorem, Riemannhypothesis, etc.
I For a complicated proof it may be impossible to decidewhether it is right or wrong.
I Four colour theorem: any map requires only four coloursif no two adjacent countries have the same colour.
I Proof of this theorem (obtained using computers) toocomplicated for the human mind to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceWrong mathematical proofs
I Many wrong attempts to prove the parallel postulate inElements down the centuries.
I Many wrong proofs of Fermat’s last theorem, Riemannhypothesis, etc.
I For a complicated proof it may be impossible to decidewhether it is right or wrong.
I Four colour theorem: any map requires only four coloursif no two adjacent countries have the same colour.
I Proof of this theorem (obtained using computers) toocomplicated for the human mind to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceWrong mathematical proofs
I Many wrong attempts to prove the parallel postulate inElements down the centuries.
I Many wrong proofs of Fermat’s last theorem, Riemannhypothesis, etc.
I For a complicated proof it may be impossible to decidewhether it is right or wrong.
I Four colour theorem: any map requires only four coloursif no two adjacent countries have the same colour.
I Proof of this theorem (obtained using computers) toocomplicated for the human mind to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inferenceWrong mathematical proofs
I Many wrong attempts to prove the parallel postulate inElements down the centuries.
I Many wrong proofs of Fermat’s last theorem, Riemannhypothesis, etc.
I For a complicated proof it may be impossible to decidewhether it is right or wrong.
I Four colour theorem: any map requires only four coloursif no two adjacent countries have the same colour.
I Proof of this theorem (obtained using computers) toocomplicated for the human mind to check.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A question
I If deduction too is frequently fallible
I why harp on the fallibility of induction?
I and why excuse the fallibility of deduction?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A question
I If deduction too is frequently fallible
I why harp on the fallibility of induction?
I and why excuse the fallibility of deduction?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
A question
I If deduction too is frequently fallible
I why harp on the fallibility of induction?
I and why excuse the fallibility of deduction?
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Crusading theology
I During the Crusades, Thomas Aquinas put forward theChristian theology of reason
I (borrowed from Islamic rational theology).
I According to this, the Christian God ruled the world butwas ruled by reason:
I That is the God could make any empirical facts of hischoice, but could not make an illogical world.
I Thus, the West assigned to reason a status even higherthan God.
I Hence, the West believes that reason is infallible.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Crusading theology
I During the Crusades, Thomas Aquinas put forward theChristian theology of reason
I (borrowed from Islamic rational theology).
I According to this, the Christian God ruled the world butwas ruled by reason:
I That is the God could make any empirical facts of hischoice, but could not make an illogical world.
I Thus, the West assigned to reason a status even higherthan God.
I Hence, the West believes that reason is infallible.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Crusading theology
I During the Crusades, Thomas Aquinas put forward theChristian theology of reason
I (borrowed from Islamic rational theology).
I According to this, the Christian God ruled the world butwas ruled by reason:
I That is the God could make any empirical facts of hischoice, but could not make an illogical world.
I Thus, the West assigned to reason a status even higherthan God.
I Hence, the West believes that reason is infallible.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Crusading theology
I During the Crusades, Thomas Aquinas put forward theChristian theology of reason
I (borrowed from Islamic rational theology).
I According to this, the Christian God ruled the world butwas ruled by reason:
I That is the God could make any empirical facts of hischoice, but could not make an illogical world.
I Thus, the West assigned to reason a status even higherthan God.
I Hence, the West believes that reason is infallible.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Crusading theology
I During the Crusades, Thomas Aquinas put forward theChristian theology of reason
I (borrowed from Islamic rational theology).
I According to this, the Christian God ruled the world butwas ruled by reason:
I That is the God could make any empirical facts of hischoice, but could not make an illogical world.
I Thus, the West assigned to reason a status even higherthan God.
I Hence, the West believes that reason is infallible.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Crusading theology
I During the Crusades, Thomas Aquinas put forward theChristian theology of reason
I (borrowed from Islamic rational theology).
I According to this, the Christian God ruled the world butwas ruled by reason:
I That is the God could make any empirical facts of hischoice, but could not make an illogical world.
I Thus, the West assigned to reason a status even higherthan God.
I Hence, the West believes that reason is infallible.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The religious bias in mathematical proof
I This Western belief that empirical proofs are inferior
I rejects all other systems of philosophy.
I One can with stronger reason reject the Western beliefin the infallibility of its metaphysics
I and, like science, accept empirical proofs as solidevidence (even though fallible).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The religious bias in mathematical proof
I This Western belief that empirical proofs are inferior
I rejects all other systems of philosophy.
I One can with stronger reason reject the Western beliefin the infallibility of its metaphysics
I and, like science, accept empirical proofs as solidevidence (even though fallible).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The religious bias in mathematical proof
I This Western belief that empirical proofs are inferior
I rejects all other systems of philosophy.
I One can with stronger reason reject the Western beliefin the infallibility of its metaphysics
I and, like science, accept empirical proofs as solidevidence (even though fallible).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The religious bias in mathematical proof
I This Western belief that empirical proofs are inferior
I rejects all other systems of philosophy.
I One can with stronger reason reject the Western beliefin the infallibility of its metaphysics
I and, like science, accept empirical proofs as solidevidence (even though fallible).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Which logic?
I Western philosophy supposes that inference ordeduction is infallible. We have seen that it is fallible.
I Further, inference is based on logic. Which is the rightlogic? Changing logic changes the inference.
I Different logical systems flourished in India
I such as Buddhist catus.kot. i (logic of 4 alternatives)
I or Jain syadavada (logic of perhapsism)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Which logic?
I Western philosophy supposes that inference ordeduction is infallible. We have seen that it is fallible.
I Further, inference is based on logic. Which is the rightlogic? Changing logic changes the inference.
I Different logical systems flourished in India
I such as Buddhist catus.kot. i (logic of 4 alternatives)
I or Jain syadavada (logic of perhapsism)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Which logic?
I Western philosophy supposes that inference ordeduction is infallible. We have seen that it is fallible.
I Further, inference is based on logic. Which is the rightlogic? Changing logic changes the inference.
I Different logical systems flourished in India
I such as Buddhist catus.kot. i (logic of 4 alternatives)
I or Jain syadavada (logic of perhapsism)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Which logic?
I Western philosophy supposes that inference ordeduction is infallible. We have seen that it is fallible.
I Further, inference is based on logic. Which is the rightlogic? Changing logic changes the inference.
I Different logical systems flourished in India
I such as Buddhist catus.kot. i (logic of 4 alternatives)
I or Jain syadavada (logic of perhapsism)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Which logic?
I Western philosophy supposes that inference ordeduction is infallible. We have seen that it is fallible.
I Further, inference is based on logic. Which is the rightlogic? Changing logic changes the inference.
I Different logical systems flourished in India
I such as Buddhist catus.kot. i (logic of 4 alternatives)
I or Jain syadavada (logic of perhapsism)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inference
I If logic is not universal then
I e.g., proofs by contradiction fail.
I This changes the mathematical theorems which can beproved.
I Example of Brahmajala sutta and Schrodinger’s cat.(Eleven Pictures of Time).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inference
I If logic is not universal then
I e.g., proofs by contradiction fail.
I This changes the mathematical theorems which can beproved.
I Example of Brahmajala sutta and Schrodinger’s cat.(Eleven Pictures of Time).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inference
I If logic is not universal then
I e.g., proofs by contradiction fail.
I This changes the mathematical theorems which can beproved.
I Example of Brahmajala sutta and Schrodinger’s cat.(Eleven Pictures of Time).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Fallibility of inference
I If logic is not universal then
I e.g., proofs by contradiction fail.
I This changes the mathematical theorems which can beproved.
I Example of Brahmajala sutta and Schrodinger’s cat.(Eleven Pictures of Time).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Cannot establish logic on empirical grounds
I If someone were to say that 2-valued logic
I is what we observe to be the case.
I This would invalidate the supremacy of deduction
I for, if logic is decided empirically, why not allowempirical proofs in math?
I Also, quantum logic (at microphysical level) differs from2-valued logic.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Cannot establish logic on empirical grounds
I If someone were to say that 2-valued logic
I is what we observe to be the case.
I This would invalidate the supremacy of deduction
I for, if logic is decided empirically, why not allowempirical proofs in math?
I Also, quantum logic (at microphysical level) differs from2-valued logic.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Cannot establish logic on empirical grounds
I If someone were to say that 2-valued logic
I is what we observe to be the case.
I This would invalidate the supremacy of deduction
I for, if logic is decided empirically, why not allowempirical proofs in math?
I Also, quantum logic (at microphysical level) differs from2-valued logic.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Cannot establish logic on empirical grounds
I If someone were to say that 2-valued logic
I is what we observe to be the case.
I This would invalidate the supremacy of deduction
I for, if logic is decided empirically, why not allowempirical proofs in math?
I Also, quantum logic (at microphysical level) differs from2-valued logic.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Cannot establish logic on empirical grounds
I If someone were to say that 2-valued logic
I is what we observe to be the case.
I This would invalidate the supremacy of deduction
I for, if logic is decided empirically, why not allowempirical proofs in math?
I Also, quantum logic (at microphysical level) differs from2-valued logic.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experimental method
I Western philosophy distinguishes different kinds oftruth:
I religious truth (proof from scriptural quotes)
I metaphysical truth (e.g. in mathematics or theology)
I scientific truth (proof from experiments)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experimental method
I Western philosophy distinguishes different kinds oftruth:
I religious truth (proof from scriptural quotes)
I metaphysical truth (e.g. in mathematics or theology)
I scientific truth (proof from experiments)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experimental method
I Western philosophy distinguishes different kinds oftruth:
I religious truth (proof from scriptural quotes)
I metaphysical truth (e.g. in mathematics or theology)
I scientific truth (proof from experiments)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experimental method
I Western philosophy distinguishes different kinds oftruth:
I religious truth (proof from scriptural quotes)
I metaphysical truth (e.g. in mathematics or theology)
I scientific truth (proof from experiments)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experiments of Payasi
I The experimental method is attributed to Francis Bacon
I However, Payasi, long ago performed many experimentswith dying persons to test the existence of the soul.
I He told dying people to come back and tell him if theylived on after death.
I He weighed condemned felons before and after death tocheck the weight of the soul.
I He asked that condemned felons be killed inside asealed pot and made a small hole in the pot to observewhether anything escaped from the body after death.
I (He concluded the soul does not exist. See ElevenPictures of Time, chp. 1.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experiments of Payasi
I The experimental method is attributed to Francis Bacon
I However, Payasi, long ago performed many experimentswith dying persons to test the existence of the soul.
I He told dying people to come back and tell him if theylived on after death.
I He weighed condemned felons before and after death tocheck the weight of the soul.
I He asked that condemned felons be killed inside asealed pot and made a small hole in the pot to observewhether anything escaped from the body after death.
I (He concluded the soul does not exist. See ElevenPictures of Time, chp. 1.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experiments of Payasi
I The experimental method is attributed to Francis Bacon
I However, Payasi, long ago performed many experimentswith dying persons to test the existence of the soul.
I He told dying people to come back and tell him if theylived on after death.
I He weighed condemned felons before and after death tocheck the weight of the soul.
I He asked that condemned felons be killed inside asealed pot and made a small hole in the pot to observewhether anything escaped from the body after death.
I (He concluded the soul does not exist. See ElevenPictures of Time, chp. 1.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experiments of Payasi
I The experimental method is attributed to Francis Bacon
I However, Payasi, long ago performed many experimentswith dying persons to test the existence of the soul.
I He told dying people to come back and tell him if theylived on after death.
I He weighed condemned felons before and after death tocheck the weight of the soul.
I He asked that condemned felons be killed inside asealed pot and made a small hole in the pot to observewhether anything escaped from the body after death.
I (He concluded the soul does not exist. See ElevenPictures of Time, chp. 1.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experiments of Payasi
I The experimental method is attributed to Francis Bacon
I However, Payasi, long ago performed many experimentswith dying persons to test the existence of the soul.
I He told dying people to come back and tell him if theylived on after death.
I He weighed condemned felons before and after death tocheck the weight of the soul.
I He asked that condemned felons be killed inside asealed pot and made a small hole in the pot to observewhether anything escaped from the body after death.
I (He concluded the soul does not exist. See ElevenPictures of Time, chp. 1.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The experiments of Payasi
I The experimental method is attributed to Francis Bacon
I However, Payasi, long ago performed many experimentswith dying persons to test the existence of the soul.
I He told dying people to come back and tell him if theylived on after death.
I He weighed condemned felons before and after death tocheck the weight of the soul.
I He asked that condemned felons be killed inside asealed pot and made a small hole in the pot to observewhether anything escaped from the body after death.
I (He concluded the soul does not exist. See ElevenPictures of Time, chp. 1.)
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lalla on False Notions
I We saw earlier how Lalla (in his chapter on FalseNotions)
I refuted the flatness of the earth by pointing to
I the inability to see far off objects, and
I the observation of eclipses (earth’s round shadow onmoon) etc.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lalla on False Notions
I We saw earlier how Lalla (in his chapter on FalseNotions)
I refuted the flatness of the earth by pointing to
I the inability to see far off objects, and
I the observation of eclipses (earth’s round shadow onmoon) etc.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lalla on False Notions
I We saw earlier how Lalla (in his chapter on FalseNotions)
I refuted the flatness of the earth by pointing to
I the inability to see far off objects, and
I the observation of eclipses (earth’s round shadow onmoon) etc.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
Lalla on False Notions
I We saw earlier how Lalla (in his chapter on FalseNotions)
I refuted the flatness of the earth by pointing to
I the inability to see far off objects, and
I the observation of eclipses (earth’s round shadow onmoon) etc.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The trick of avoiding refutationCriterion of simplicity
I However, there are tricks to avoid refutation of a theoryby experiment.
I Payasi’s opponent argued that the soul was tied to thebody
I like a baby in the womb to the mother, etc.
I The general trick is to accumulate hypotheses (footballmatch).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The trick of avoiding refutationCriterion of simplicity
I However, there are tricks to avoid refutation of a theoryby experiment.
I Payasi’s opponent argued that the soul was tied to thebody
I like a baby in the womb to the mother, etc.
I The general trick is to accumulate hypotheses (footballmatch).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The trick of avoiding refutationCriterion of simplicity
I However, there are tricks to avoid refutation of a theoryby experiment.
I Payasi’s opponent argued that the soul was tied to thebody
I like a baby in the womb to the mother, etc.
I The general trick is to accumulate hypotheses (footballmatch).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The trick of avoiding refutationCriterion of simplicity
I However, there are tricks to avoid refutation of a theoryby experiment.
I Payasi’s opponent argued that the soul was tied to thebody
I like a baby in the womb to the mother, etc.
I The general trick is to accumulate hypotheses (footballmatch).
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The criterion of simplicity(also called Occam’s razor)
I Accumulation of hypotheses is avoided by
I the criterion of simplicity:
I if two theories both explain the same facts,
I accept the theory which needs fewer hypotheses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The criterion of simplicity(also called Occam’s razor)
I Accumulation of hypotheses is avoided by
I the criterion of simplicity:
I if two theories both explain the same facts,
I accept the theory which needs fewer hypotheses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The criterion of simplicity(also called Occam’s razor)
I Accumulation of hypotheses is avoided by
I the criterion of simplicity:
I if two theories both explain the same facts,
I accept the theory which needs fewer hypotheses.
History andPhilosophy of
ScienceLecture 9
C. K. Raju
Outline
Recap
Non-Westernphilosophy of proof
Indian systems
Islam
Fallibility ofdeduction
Logical fallacies
The religious bias
What is science?
The criterion ofsimplicity
The criterion of simplicity(also called Occam’s razor)
I Accumulation of hypotheses is avoided by
I the criterion of simplicity:
I if two theories both explain the same facts,
I accept the theory which needs fewer hypotheses.
