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I read in an answer somewhere on this site that Modus Ponens involves an infinite regress.

Upon reading Lewis Carroll's Achilles and the tortoise, I fail to see how.

This is the excerpt from wikipedia where I am confused:

A: "Things that are equal to the same are equal to each other"   
B: "The two sides of this triangle are things that are equal to the same"
Therefore, 
Z: "The two sides of this triangle are equal to each other"

The Tortoise then asks Achilles whether a second kind of reader might exist, who accepts that A and B are true, but who does not yet accept the principle that if A and B are both true, then Z must be true.

If A and B are true, I think it follows logically that Z is true, and there are no more steps in between where one might disagree. Could someone please point out what i'm not able to follow?

Z must be true if A and B both are held true.

  • You feel that our logic rules are absolutely true, but they are not. Like how you can't see new color, you can't think outside of our logic rules. But this does not mean other colors do not exist. – rus9384 Jul 7 '18 at 9:38
  • See What the Tortoise Said to Achilles for overview and references. – Mauro ALLEGRANZA Jul 7 '18 at 10:01
  • The infinite regress sketched by LC's article is based on the indubitable fact that in explaining/presenting/elucidating the concept of "valid inference" we have to use logical connectives and logical arguments. – Mauro ALLEGRANZA Jul 7 '18 at 10:03
  • @mauroallegranza I read the wiki page, but im still not quite getting it. As far as i can see we are using logical arguments – novice Jul 7 '18 at 10:11
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    You say: “If A and B are true, […] Z is true”. The tortoise doesn’t deny this and grants (C). Yet this only gets you another true statement, one that is distinct from (Z). In general, the method only generates an ever-growing list of true statements, but never the conclusion. So, we can go on forever without reaching the conclusion. In that sense, it’s an ‘infinite regress’ – although the term ‘regress’ may not seem entirely appropriate. (I don’t think Lewis uses it.) – MarkOxford Jul 7 '18 at 11:12

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