Parmenides Zeno and the Birth of Logic

7/24/2019 Parmenides Zeno and the Birth of Logic

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Stephen Hoffman 12/22/2014

Parmenides, Zeno and the Birth of Logic

In his Stanford Encyclopedia of Philosophyarticle on Zeno the Eleatic p!pil of Parmenides" #ohnPalmer states that according to Diogenes Laertius $Aristotle, in one of his lostdialogues, entitled Sophist, spoke of Zeno as the inventor of dialectic. However,in theMetaphysics, he attributes its invention to both Socrates (.4%10&'(2)!"#$and %lato (A.&.')("*!"$. He attributes to hi+self the invention of theor- ofdialectic, i.e. *+-. 3+., $logic5 for short Sophistici Elenchi".*"b"!*b,%al+er$.

/irst of all, what is dialectic0 1an we trace its origin back to Zeno2s +entor,

%ar+enides, who+ Scott Austin calls the father of logic0 (Parmenides: Being,Bounds and Logic, 3ale 4niversit- %ress, *'&$.

5he science of logic atte+pts to ensure correct confor+it- between the logos(language$ and what language is about. 1orrect confor+it- or correspondencebetween language and realit- ca+e to de6ne truth for all successors toAristotle in the western philosophical tradition. 7ust as gra++ar atte+pts tode6ne allowable restrictions on co+binations of words, so logic atte+pts tode6ne allowable restrictions on the wa- language interacts with realit-. 7ust ass-ntactic rules dictate that a 6nite verb +ust have a sub8ect (e9plicit or i+plicit$so logical rules dictate that an ob8ect of discourse mustnot be the sa+e as its

contrar- (Law of :on;1ontradiction$. if one of the above state+ents is true, so is the other.


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e can alread- see that logic trades heavil- in spatial +etaphors (if the- areindeed +etaphorsB$Csteps, inferences (i.e. carr-ings$ derivationCco+ponent +ove+ents froen or cr-stallied into a static logical structure inwhich the arrow of ti+e is reversible and all +ove+ent is essentiall- annulled.5his structure serves as a fra+e of reference with which the +ove+ent of

persuasion acco+plished b- an- given argu+ent can be tracked as genuine (notillusor-, as when a train +oves out of the station ne9t to -ours$ and as +ove+enttoward, not awa- fro+, truth. 5his +ove+ent of persuasion, genuine andforward;directional, is what %ar+enides calls the wa- of truth (otherwiseknown si+pl- as ti+e$. 5he static, changeless, self;consistent and indivisiblestructure through which the +ove+ent of thought is tracked is nothing otherthan Eeing which, according to %ar+enides, is the sa+e as thought. -< 3= = -< ?@ ? -A? -@ =+< -< C3@+? -@?@ ? -D .@+8 -


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as other sources like Diogenes Laertius and the si9th;centur- 1.K. Aristotleco++entator Si+plicius. Since his proofs are alleged refutations of co++on;sense notions like +otion and pluralit-, so+e have tended to lu+p hi+ in with so;called contentious, eristic Sophists and the like, while %lato, and to a certaine9tent Aristotle, ascribed a +ore serious intention and purport to theseargu+ents of the pupil of %ar+enides. %lato2s and Aristotle2s acknowledg+ent of

serious purport is shared b- +odern philosophers of science and +athe+atics, astesti6ed b- esle- Sal+on>

Zeno2s parado9es have interested philosophers of all periods, but until the +iddleof the nineteenth centur- the parado9es were regarded as +ere sophis+s whichcould be re+oved with little trouble.


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philosophical attac (: a profo!nd and interconnected set of red!cti9e arg!mentations% ]an: men hadmoced ParmenidesT Zeno moced the mocers% His logoi ;ere designed to re9eal the inanities andineptit!des inherent in the ordinar: (elief in a pl!ral ;orld^ he ;anted to startle, to ama_e, to disconcert%He did not ha9e the serio!s metaph:sical p!rpose of s!pporting an Eleatic monism5 Barnes, #%,The

Presocratic Philosophers, 2nd edition, LondonT `o!tledge began Pa!l, 1'2, hapters 12 and 1J, 2J,cited (: Palmer"%

B!t ;h:X ]ost decisi9el:, (eca!se there is no s!ch thing as $Eleatic monism%5 $Eleatic monism5represents a historical mis!nderstanding of ParmenidesD eVtant ;ritings% Palmer contin!esT

Sho!ld ;e%%%thin of Zeno as a sophistX ertainl: Isocrates, the rhetorician and contemporar: of Plato, didnot hesitate to l!mp Uorgias, Zeno, and ]eliss!s together as among the other $sophists5 flo!rishing in theera of Protagoras and all prod!cing tedio!s according to Isocrates treatises ad9ocating the mosto!trageo!s claims Isoc%Hel% Orat% 10 2J"%

PalmerDs treatment of ristotle and Zeno is interestingT

or ristotle, then, Zeno ;as a contro9ersialist and paradoVKmonger, ;hose arg!ments ;ere ne9ertheless(oth sophisticated eno!gh to \!alif: him as the in9entor of dialectic and ;ere important for forcingclarification of concepts f!ndamental to nat!ral science%

ristotle ;as a great in9entor of clarificator: scientific concepts, (!t consistentl: do;npla:ed the rolehis predecessors pla:ed in la:ing the fo!ndations of logic and science on ;hich his o;n terms rest,e9en ;hen he is conscio!sl: a;are of his de(t to them% ]ore to the point, no one is more ac!tel: a;arethan ristotle that the meaning of all scientific terms rests on ;hat later came to (e called$metaph:sical5 fo!ndations (eca!se ristotleDs reflections on these fo!ndations are contained in acollection of treatises ;hich come $after thePhysics5T -=< @-=< -=< 6+"% B!t ristotleDs reflectionson these fo!ndations, ;hich together comprise ;hat he called $first philosoph:5 *>j-.+A="are riddled ;ith gaps and open \!estions ;hich render his o;n $sol!tions5 to Zenonian pro(lems ofmotion pro(lematic at (est, and at ;orst ill!sor:%Whis prompted no less a thiner than the t;entiethcent!r: ngloKmerican philosopher Bertrand `!ssell to proclaim, alleging proofs (: the nineteenth

cent!r: mathematician barl eierstrass H!sserlDs teacher" that Zeno ;as right, and ristotle ;as;rong% $fter (eing ref!ted (: ristotle and (: e9er: s!(se\!ent philosopher from that da: to o!ro;n, these arg!ments ;ere reinstated and made the (asis of a mathematical renaissance (: a Uermanprofessor ;ho pro(a(l: ne9er dreamed of an: connection (et;een himself and Zeno,5 Bertrand`!ssell,Mysticism and Logic, hapter FT $]athematicians and ]etaph:sicians,5 %% korton andompan: Inc%, 12, '0%" Whis sho!ld p!t !s at o!r g!ard against !nderestimating the might of theoriginal Uree thiners% HesiodDs Chaosi%e% the $gaping5 or :a;ning" sprang open and deli9eredParmenides%

BIBLIU`PH

$Zeno of Elea,5 first p!(lished ed #an , 200'^ s!(stanti9e re9ision ed #an 11, 2012,httpT//plato%stanford%ed!/entries/_enoKelea/,Stanford Encyclopedia of Philosophy,(: #ohn Palmer,[palmerphil%!fl%ed!

Parmenides: Being, Bounds and Logic, Scott Austin, 3ale 4niversit- %ress, *'&.

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Zeno's Paradoxes, esle- Sal+on, Eobbs;errill 1o+pan-,

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Parmenides Zeno and the Birth of Logic