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Accoding to Michel Potter!4 u Every finite set is countable where infinty is countable but not finite. If the function A onto B. A is countable then B is countable. A set is said to be countably infinite if it is both countable and infinite. The set of natural numbers is countably infinite proposition o X o countably infinite. For proof consider the function which maps any finite string
n,, n..... n
Thus to exclude or overcome the fallacy of Law of excluded middle Moore in his the infinite proves it through a syllogisms.
If some « is true then no « becomes false There exists some infinite Therefore no infinite is false
The recent concept of relative and absolute infinite would assist the Jaina conept of infinity for better comprhenstion. According to Ali Enayat and Roman Kossak' A set is absolutely uncountable when this property is not in the model but in real world can be studied by non-formal mathematics a i.e it is an infinite set that is by contrast of something that is model dependent)*" Non absolute concept by contrast is something that is model dependent'.
The eight kinds of infinte explained in Jaina scriptures are relative. The ninth which goes to absolute is absent.
Conclusion
Thus the study concludes that the concept of minimum and maximum in Jainism are relative as it is Realistic philosophy.
* O does not exist. hence cannot be minimum
* Since infinite is also relative there can be its types which can be proved through diagrams encompassed.
* The existence of absolute infinite must also be admitted at least in the logical world.
* As Ali Enayat and Roman Kossak opines, Non absolure concept of I is model dependent in contrast to the is something absolute I which is not :: = x/ Ina = a set of all sets.
Reference : 1. A.W. Moore, The Infinite, Routledge London, 1990 2. Nathmal Tatia That which is, english translation of Tattvārtha Sūtra p. 266 c.f. Anuyoga
dārāim 596-603 commentary p. 332 Thānam, 3.7 ed by Muni Nathmala, Jain Vishva Bharati, Ladnun, 1976 tivihā neraiya
Pannttā, akati sancita, akati sancita, avaktvy sancita 4. Commentary of Thānam, ed by Muni Nathmala, p.261 5. Anuyogadārāim, 574 vịtti of haribhadra, p. 109 6. Lokaprakāśa, 4. 310-312
Mahavira Raja Gelada, Jain Vidya Aur Vigyan, p. 219.
Arhat Vacana, 24 (1), 2012
