History and Philosophy of Science 2 Lecture 2ckraju.net/hps2-aiu/hps2-aiu-lecture-2.pdf · Iraq, Vietnam. (Didn’t do homework.) I No one mentioned fake case of WMD’s in Iraq

History andPhilosophy ofScience 2Lecture 2

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Deductive proofand its supposedsuperiority

What is deductiveproof?

The religious bias

History and Philosophy of Science 2Lecture 2

C. K. Raju

AlBukhary International University, Malaysia,[email protected]

web:http://ckraju.net

[email protected]

http://ckraju.net


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Deductive proof and its supposed superiority

The religious bias


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The syllabus

I The syllabus for the course is uploaded at http://ckraju.net/hps2-aiu/HPS-2-syllabus.pdf

I The HPS-1 course was intended to expose you to a newpoint of view.

I The HPS-2 course is intended to make you effectivecritics.

I That requires a deeper understanding of (a) the subject,and (b) the tricks of arguments.

http://ckraju.net/hps2-aiu/HPS-2-syllabus.pdf



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E.g. AiU debate on Syria

I Topic very good. But what was missing?

I No one mentioned use of chemical weapons by US inIraq, Vietnam. (Didn’t do homework.)

I No one mentioned fake case of WMD’s in Iraq.

I Accepted BBC as a reliable source. (What did you learnabout reliable sources?)

I Serious debate is about solid points, not just drama forentertainment. Solid points have a long-lasting impact.


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What do you have to defend?The counter story

I The counter-story you may have to defend is thefollowing.

I The present-day history of science was concocted by thechurch to claim that all science was done by Christians(after the renaissance) and earlier by their friends (thepre-Christian Greeks).

I This history concocted during the Crusades, glorifiedChristians and friends and belittled everyone else. E.g.Muslims were belittled as mere keepers of Greekknowledge.

I The very term “renaissance” (re-awakening) was a faketerm coined to connect Europe after Crusades topre-Christian Greece (linked to Egypt), and claim thatthis “Greek” knowledge was a Christian inheritance.


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How the concocted history developedInquisition, racism, colonialism

I This false history developed during the Inquisition,Europeans were too frightened to acknowledgenon-Christian sources. They blanked them out.

I (E.g., Copernicus who copied astronomy from IbnShatir and Nasiruddin Tusi)

I (or Newton and Leibniz who copied the calculus fromMadhava of Sangamgrama from India)

I Afterwards, racist historians built on this false history byblanking out Egypt and all non-Whites.

I Colonial historians blanked out the colonised.


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Wikipedia history

I That false history is maintained today by Wikipedia andcontinues to

I glorify the West

I and belittle others.

I Problem is: how to correct it?

I For this you need to understand the tricks that are used.


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Wikipedia history


I glorify the West





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Wikipedia history


I glorify the West





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I glorify the West





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Wikipedia history


I glorify the West





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Wikipedia tricks

I After HPS-1 you have perhaps understood theWikipedia tricks which help preserve false Westernhistory.

I Wikipedia forces you to use only secondary sources

I and declares only Western sources as reliable andtrustworthy.

I This two tricks make it impossible for you to tell adifferent story.


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Wikipedia tricks






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Reminder: What can you do?

I Did you form Wikipedia action groups?

I Did you study the lower-level tricks like calling someonea sock puppet?

I This course involves self-study. How did you use theprevious 7 hours of self-study?


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But there are other tricksPart of colonial education

I But there are other deeper tricks than Wikipedia.

I which go through the education system.

I HPS-2 aims to teach you about these tricks.

I You must understand not only the falsehoods ofWestern history, but also the tricks by which they arepreserved including bad philosophy,

I and how those falsehoods harm you.


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Colonial education is a church legacyWas used to capture the mind

I False history was used to initiate colonial education bydeclaring it as “superior”.

I Colonial education copied the church education system(the only education system Europe knew in 1830’s).

I The church education started during the Crusades (11thc.); it was designed to produce missionaries to convertMuslims.

I The church education captured the missionary mind;colonial education captured the colonised mind.


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Church educationMeta-superstitions

I Typical trick was to teach meta-superstition: relianceon Western authority as truth.

I Any difference was interpreted as a sign of their ownsuperiority.


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Church educationMeta-superstitions

I Typical trick was to teach meta-superstition: relianceon Western authority as truth.

I Any difference was interpreted as a sign of their ownsuperiority.


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Colonial education

I Hence, the colonially educated learn to think the Westis superior, and that

I only Western authorities are reliable.

I (Like the Wikipedia trick.)


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Colonial education





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How to correct false history?How to change the education system?

I To correct false history

I commonsense, and evidence (primary sources) areimportant

I but you also need to learn the basics of philosophy ofscience

I which teaches you about deeper tricks used to “save thestory”.


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Applying the philosophy of science

I The criterion of refutability helps to identify when abelief is not unscientific and metaphysical.

I The criterion of simplicity helps us to identify when therules (standard of proof) are changed to hang onunreasonably to a belief.

I or when hypotheses (or stories) are accumulated.

I The principle of “maximum likelihood” helps us tochoose what is more probably true.


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The present-day philosophy of math

I Claim: Euclid used a philosophy of deductive proof inthe Elements.

I Other people did mathematics differently; they areinferior.

I Westerners say: “We are superior, and our way of doingmath is superior.”

I Therefore, others should imitate us. “We are the norm”which everyone else must imitate. (Normativeuniversality.)

I After colonialism this way of doing math is widespread(global universality).


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Key questions

I Why is the Western way of doing math “superior”?

I Did Euclid exist?

I Was the Elements about deductive proof?

I Why is deductive proof “superior” to empirical proof?

I Is the belief in “superiority” of deductive proofconnected to the Christian theology of reason? (Is therea religious bias?)


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I Did Euclid exist?





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I Did Euclid exist?





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I Did Euclid exist?





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Did Euclid exist?

I You already know the Wikipedia trick

I For every early Greek, the story goes that “he wasextraordinarily great”, “but we know little about him”

I The “little that we know about him” supposedly comesfrom a 5th c. commentator 800 years after the fact

I The actual primary source the comment comes fromanother 800-1000 years later (i.e., from the 13th c. orlater).


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Summary of “Euclid”

I The “archaeological evidence” for “Euclid” (a 3rd c.papyrus) may be evidence only for Egyptian mysterygeometry (it does not agree with the “received” versionof the Elements.)

I The textual “evidence” for “Euclid comes from acomment supposedly made by Proclus (5th c.)

I Our evidence for Proclus’s comment comes from a 15thc. manuscript.

I The “Proclus passage” is a forgery, since it refers to acitation of the Elements by “Archimedes”, and thisisolated citation is known to be a later-dayinterpolation.

I But, if that passage is false, then there is no longer anyhistorical basis for the claim that the Elements is aboutdeductive proof.


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What is deductive proof?

I This was done in HPS-1, but I repeat it here

I since you must clearly understand this foundationalpoint.

I Deductive proof is a purely logical proof, which makesno reference to the empirical world (i.e, to what you cansee, touch, hear, smell or taste) but only to certainaxioms or postulates.


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A clarification

I “Axiom” originally meant uncontested truth

I while postulate originally meant a hypothesis.

I Today both mean the same: a hypothesis.


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What is deductive proofcontd

I What is the number 2? Why is 2 + 2 = 4?

I Most people think the number 2 is an abstraction basedon empirical observation of two dogs, two tables, twochairs,

I just like the abstract noun “dog” is an abstractionbased on observing many dogs.


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How does present-day math define 2?

I But this is not how present-day mathematics defines thenumber 2.

I 2 + 2 = 4 is not proved by lining up 2 objects with 2objects to show 4 objects.

I Everything must be done by referring only to axioms(such as Peano’s axioms)


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Peano’s axiomsfor Natural numbers

I 1 is a natural number

I if n is a natural number so is n′ (called the successor ofn

I (Axioms for addition, i.e., the symbol +) If n and m arenatural numbers, then

n + 1 = n′

n + m′ = (n + m)′

I (Definitions) 1’ = 2, 2’ = 3, 3’ = 4, . . . .

I (Note this definition made no reference to two finger orto two dogs, etc.)


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n + 1 = n′

n + m′ = (n + m)′

I (Definitions) 1’ = 2, 2’ = 3, 3’ = 4, . . . .



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n + 1 = n′

n + m′ = (n + m)′

I (Definitions) 1’ = 2, 2’ = 3, 3’ = 4, . . . .



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n + 1 = n′

n + m′ = (n + m)′

I (Definitions) 1’ = 2, 2’ = 3, 3’ = 4, . . . .



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n + 1 = n′

n + m′ = (n + m)′

I (Definitions) 1’ = 2, 2’ = 3, 3’ = 4, . . . .



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(Semi-) Formal proof of 2 + 2 = 4

I 2 = 1′ (definition of 2)

I 2 + 2 = 2 + 1′ = (2 + 1)′ (by axiom for addition)

I 2 + 1 = 2′ (by axiom for addition)

I 2′ = 3 (by definition of 3)

I Hence, (2 + 1)′ = 3′ = 4 (by definition of 4).

I (Note: this proof made no reference to lining up twoobjects with two objects.)


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Why is deductive proof superior?A general rule for serious debate

I Never be satisfied with refuting a weak opponent.

I Always first give the strongest possible argument youcan think of from your opponent’s side.

I And then refute that.

I This will ensure that you are defending the truth, andnot just a position.


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Why is deductive proof superior?

I Claim: deductive proof is infallible while empirical proofis fallible.

I Empirical proof is fallible, one might mistake a rope fora snake or vice versa, but the mistake can soon becorrected by performing an experiment.

I Prod the rope/snake with a stick and see if it moves onits own.

I But how do we know deductive proof is infallible? Andhow do we know that the Elements was written to showthis kind of proof?


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Fallacies of deduction

I We have seen the common fallacies of purely logicalproof.

I E.g., fallacy of asserting the consequent: from “IfPandu loves Sujata, then Pandu will marry Sujata” todeduce that “Pandu will marry Sujata”. [Never saidthat Pandu actually loves Sujata.]

I E.g. fallacy of shifting the burden of proof: “you havenot proved that “Euclid” did not exist. [Burden ofproving existence of “Euclid” is on those who claim heexisted.]

I However, there are fallacious proofs which have beenbelieved to be valid deductive proofs for centuries.


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Example: Elements proposition 1

I The first proposition of the Elements says (see“primary” source T. Heath: The thirteen books ofEuclid’s Elements”, vol 1. Dover Books, availableonline, p. 241 (book) p. 262 (pdf).).

I On a given finite straight line to construct anequilateral triangle.

I If AB is the finite straight line, the proof requires theconstruction of two circles, one with centre A andradius AB, and the other with centre B and radius AB.

I If the two circles intersect at C, we join C to A and B toobtain the equilateral triangle ABC.


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Why this proof is defective

I There is a postulate for constructing the two circles.

I There is a postulate for drawing the straight lines CA,and CB.

I But there is no postulate to tell us whether the twocircles with intersect.

I We see them intersecting, but that is empirical proof,not deductive proof.


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Why this proof is defectivecontd

I To apply the same argument as earlier

I we may see two straight lines intersect on a computerscreen

I but this may be an illusion,

I for “lines” on a computer screen are just a collection ofpixels,

I and the two collections may “pass through” each otherwithout having any pixel in common.


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Deductive proofs are more fallible

I Hence, the very first proposition of the Elementsprovides a defective deductive proof.

I Western scholars discovered this mistake only in the19th c. with Dedekind (and his theory of cuts or formalreal numbers).

I The Elements came to Europe in the 12th c.

I That means for seven hundred years all the leadingWestern minds wrongly believed this to be a “perfect”and “irrefragable” deductive proof.

I Thus, a fallacy in a most elementary deductive proofmay last for 600 years. What about more complicatedproofs? Is such an error possible for a mistake about arope/snake?

I Thus shows that deductive proofs are fallible, and, infact, more fallible than empirical proofs.


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Example: Elements proposition 4Side Angle Side proposition

I The fourth proposition of the Elements says (Heath, vol1., p. 247 (book), p. 268 (pdf))

I If two triangle have two sides equal to the two sides,respectively, and have the angles contained by the equalstraight lines equal, they will also have the base equalto the base, the triangle will be equal to the triangle,and the remaining angles will be equal to the remainingangles respectively, namely those which the equal sidessubtend.


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Example: Elements proposition 4Side Angle Side proposition

I The fourth proposition of the Elements says (Heath, vol1., p. 247 (book), p. 268 (pdf))

I If two triangle have two sides equal to the two sides,respectively, and have the angles contained by the equalstraight lines equal, they will also have the base equalto the base, the triangle will be equal to the triangle,and the remaining angles will be equal to the remainingangles respectively, namely those which the equal sidessubtend.


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SAS is critical to the Elements

I This 4th proposition (called the Side-angle-sideproposition, or SAS, in short) is critical to the wholebook Elements

I The proof of the 47th (second last) proposition, calledthe Pythagorean theorem, depends upon the proof ofSAS.

I So, if the proof of SAS is faulty, the whole bookElements is faulty (if it is really about deductive proof).


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The proof of SAS is faulty(As a deductive proof)

I But the proof of SAS in the Elements is faulty as adeductive proof. Let us examine it.

I The proof requires “the triangle ABC to be applied tothe triangle DEF”

I What does “applying” mean?

I It means that we pick a triangle (say ABC) and put iton top of the other (DEF) in such a way that onetriangle exactly covers the other.

I Thus, we see that the two triangles are equal.

I But that is an empirical proof.


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The proof of SAS is faulty

I To put it differently, the proof of SAS in the Elementsis a defective deductive proof.

I But Westerners (Bertrand Russell, and David Hilbert)corrected it only in the 20th c.

I So, a wrong elementary proof was believed to be a validdeductive proof by the greatest Western minds foralmost 800 years.

I This shows that deductive proofs are seriously fallible

I (People studied the Elements exactly as you studylimits in calculus today: blindly, and without properunderstanding!)


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Was the Elements about deductive proof?

I Since the fake story of Euclid cannot be the reason tobelieve in the motive for writing the Elements,

I we must examine the book itself.

I Alas! The very first proposition of the book uses anempirical proof.

I The 4th proposition (side-angle-side theorem) also usesan empirical proof.

I That 4th proposition is essential to the whole book(including the “Pythagorean theorem”).


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What we now know

I Did Euclid exist? No!

I Was the Elements about deductive proofs? No!

I Are deductive proofs infallible? No! They are morefallible than empirical proofs.


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Who needed deductive proofs?

I Books are written in response to social circumstances.

I At the supposed time of “Euclid” there was no reasonto provide “irrefragable” proofs.

I At the time of the church’s first religious war (with“pagans”), “pagans” needed a way to demonstrate thevalidity of their concept of the soul.

I Hence, late “Greeks” from Africa, like Theon, Hypatiaand Proclus did so, through the Elements.


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The church need for persuasion

I During the Crusades the church wanted to persuadeMuslims (since force failed)

I That was also the time (early 12th c.) when theElements first came to Europe.

I The book was just reinterpreted to suit the purposes ofthe church.


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Christian rational theologyand Islamic rational theology

I During the Crusades, the church started a new theology

I This is called Christian rational theology (attributed toThomas Aquinas and his schoolmen).

I It reinterpreted Islamic rational theology (aql-i-kalam).


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Reinterpreting aql

I Applying aql does not mean distrusting the senses ascompletely faulty. Islam accepts tajurba.

I However, aql was wrongly reinterpreted as reason, andthe church now glorified reason.

I Deduction actually connects to this church metaphysicsof reason,

I but I will not go into more details on that here, exceptto point out that this involves a metaphysical biasagainst other religions.


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The religious bias

Reinterpreting aql






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Reinterpreting aql






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The religious bias

Bias against other systemsRejection of the empirical

I This denigration of empirical proofs teaches a biasagainst other beliefs

I such as Islam (which accepts tajurba)

I or Nyaya, Buddhism or Jainism (all of which accept thepratyaksa or empirically manifest as the first means ofproof)

I as does science.


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I as does science.


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I as does science.


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I as does science.


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Bias against other systemsLogic is not universal

I Metaphysics (and deduction is metaphysics) is notuniversal.

I Deduction (on present-day math) assumes a two-valuedlogic.

I However, 2-valued logic is not culturally universal.


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Buddhist and Jain logic

I Buddhist logic of catuskoti (4-alternatives)

I and Jain logic of syadavada (perhaps-ism)

I are not 2-valued

I like quantum logic, and the logic of natural language.


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I are not 2-valued



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I are not 2-valued



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I are not 2-valued



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The logic of 4 cases

I E.g. in Brahmajala sutta, Buddha says there are fourcases.

I The world is finite.

I The world is not finite (infinite).

I The world is both finite and infinite.

I The world is neither finite nor infinite.

I Example of the third case: the world is finite in onedirection, and infinite in another.


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Failure of proofs by contradiction

I The third case means that proofs by contradictionwould fail.

I A proof by contradiction goes as follows. “If B thenboth A and not-A”. Therefore, “not-B”.

I Or “If both A and not-A, then C”.

I Rejecting proofs by contradiction itself would change allmathematics.


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Also quantum logic and logic of natural language

I I pointed to Buddhist and Jain logic to show thereligious bias.

I Quantum logic is not 2-valued (but this is too technicalfor you, see my book Time: Towards a ConsistentTheory, chp. 6b, “Quantum mechanical time” availableonline.

I and quantum computers may not use 2-valued logic.

I The logic of natural language is also not 2-valued.

I From the common statement “This person is both goodand bad” we cannot conclude that “Elephants arepink”.


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Summary

I To summarise what we just learnt

I Present-day math teaching is based on beliefs that are

I historically false (e.g. Euclid and deduction)

I philosophically bad (e.g. that deduction is “superior”)

I and involve a religiously biased metaphysics.


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Documents

History and Philosophy of Science 2 Lecture 2ckraju.net/hps2-aiu/hps2-aiu-lecture-2.pdf · Iraq, Vietnam. (Didn’t do homework.) I No one mentioned fake case of WMD’s in Iraq