In the SEP model there is a turtle at the bottom. The fact that there is an order anti-isomorphism between these two structures, so that the distinction amounts to a renaming and order flipping, is irrelevant. Now SEP defines infinite regress as the second case. There's a big honkin' turtle at the bottom, with another turtle on its back and so forth. Which has a first element but no last element. It's turtles all the way down.Ĭontrast that with the structure given by the Peano axioms: The earth sits on a turtle which sits on another turtle which sits on another turtle, without end. An "infinite regress of causes" is said to be impossible by the Kalam cosmological argument, therefore there must be a first cause, which must be God, etc. It has a last member but no first member. My understanding is that infinite regress is a linear order, like this: (Edit) - Perhaps I didn't make my meaning clear. I know of no one who would call that an "infinite regress." SEP is just wrong.Īny insight? Is the SEP article representing a point of view that's prevalent, and in fact directly opposed to the traditional view of infnite regress as going backward without a starting point? How is it that SEP appears to have this matter entirely wrong? Or is my own understanding wrong all these years? are perfectly legal, as exemplified by the finite von Neumann ordinals. But forward chains of membership x1 ∈ x2 ∈ x3 ∈. The axiom of foundation is what prevents an infinite regress of set membership. Set-theoretically, I have always thought that infinite regress is the opposite of well-foundedness. That's what "regress" means: To go backward.
It's the absence of a base case that defines infinite regress.
That is: If there is a base case, it's NOT an infinite regress. It's the negative integers that represent infinite regress and NOT the positive integers. My sense is that SEP is simply entirely wrong on this matter, and that my longtime understanding is correct. The article is confusing induction, which has a base case, with infinite regression, which is essentially a recursion or induction without a base case. "Īs I understand it, this is entirely backwards. "Peano’s axioms for arithmetic, e.g., yield an infinite regress. A base case and endless succession, like the Peano axioms. In other words, this looks like induction.
INFINTE REGRESS SERIES
"An infinite regress is a series of appropriately related elements with a first member but no last member, where each element leads to or generates the next in some sense." Now the SEP article on infinite regress has this exactly backwards: In this model, each event has an immediate cause yet there is no first cause.įor example this is the interpretation of infinite regress in William Lane Craig's Kalam cosmological argument, as I understand it. 1 is "caused" by -2, -2 is caused by -3, -3 is caused by -4, and so forth. A model would be the negative integers, if we viewed them as a model of causation. (Forever as in endlessly, not necessarily temporally). I have always understood infinite regress to mean going backwards forever.
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