• Mr Bee
    193
    Infinite regress arguments are usually used to demonstrate a reductio ad absurdum against a position.

    For instance, the homunculus regress demonstrates the problem with saying that there is a little man in our brains in order to explain our experience. This is because we can similarly ask the same question of how this little man will have their experiences, and we will have to introduce another man inside that little man to explain their experience and so on and so forth.

    Another, probably less known example is Mctaggart's regress against tensed theories of time (though I don't agree with it, I want to focus on it's structure). He tries to introduce a contradiction by saying that all events have the A-properties of being past, present, and future together simultaneously and then argues that this can only be avoided by saying that an event's being either past, present or future also has A-properties themselves. However, given that they have A-properties as well, then they will also be subject to the same contradiction and a regress ensues.

    However, not all regresses are known to be problematic. Take for instance, the regress of truths. Suppose X is true. Then it is true that "X is true". But it will also be true that " 'X is true' is true", and so on and so forth. In this case we clearly have a regress, but we have no problem in accepting it. In other words, what we have here is a benign regress. The other two regresses above are vicious regresses and they are usually what we refer to when we talk about problematic regresses. So not all regresses are problematic, but what is the distinction between the two? What is difference between a vicious regress like the above and a benign regress?

    ________

    My guess: A vicious regress is one which is created to solve a problem whereas a benign regress isn't. In the two examples above, there is a question or problem that needs to be explained which prompts the introduction of a regress. In the homunculus regress it is the need to explain our experience and in Mctaggart's regress, it is the need to avoid his contradiction. The solution offered in both cases suffer from precisely the same problems as the initial setup, and thus requires a similar solution which in turn faces the same problem ad infinitum. The problem with these regresses is that no progress has been made at all with regards to the initial problem and because of that, the regress becomes frivolous. It is like the equivalent of taking one step forward and one step back an infinite number of times; you haven't made any progress at all.

    In contrast the regress of truths was never introduced to explain or solve anything. We never had any problem to solve when beginning with the understanding that X is true so no problem exists. Instead, the regress was merely the logical result of the fact that X is true.
  • jorndoe
    682
    One variety of vicious infinite regress could be when trying to justify some proposition, p, and justifying p is done with (or requires) a different proposition, p1, which, in turn, depends on p2, ..., ad infinitum, where pn diverges.
    Divergence could, for example, mean never approaching anything in particular (which also has a specific technical meaning in mathematics).
    If explaining a claim is deferred to explaining a larger claim, which, in turn, is deferred to explaining an even larger claim, ad infinitum, then you've likely hit a vicious infinite regress, i.e. a non-explanation to begin with.

    On the other hand, if all propositions/claims can be shown to collapse into one (like pn+1 = pn), for example, then it's not a vicious infinite regress.
  • Mr Bee
    193
    One variety of vicious infinite regress could be when trying to justify some proposition, p, and justifying p is done with (or requires) a different proposition, p1, which, in turn, depends on p2, ..., ad infinitum, where pn diverges.jorndoe

    I think this sounds similar to my own theory, just with different wording. Instead of saying that an infinite regress involves "solving a problem", you instead say that it would involve justification. I've also heard it said that a vicious regress is one that is meant to be explanatory as well, but again it all sounds the same to me.

    On the other hand, if all propositions/claims can be shown to collapse into one (like pn+1 = pn), for example, then it's not a vicious infinite regress.jorndoe

    Interesting. So, would statements such as "Every event has a prior cause" and "Every region of space is composed of smaller regions" work here to describe an infinite past or a continuous interval of space? Though I am not sure if they qualify as regresses, I am inclined to think of continuity and causality as being benign if they are so that'd be nice.
  • sime
    401
    Suppose X is true. Then it is true that "X is true". But it will also be true that " 'X is true' is true", and so on and so forth. In this case we clearly have a regress, but we have no problem in accepting it. In other words, what we have here is a benign regress. TMr Bee

    I doubt that most Quinians or Wittgensteinians would say that it is a benign regress and would reject it, given it's similarity to the Modus-Ponen's infinite regress paradox of Lewis Carroll, as used by critics of truth-by-convention to attack the idea that the notion of logical necessity is representable or derivable from a finite supply of community conventions.
  • Mr Bee
    193
    I doubt that most Quinians or Wittgensteinians would say that it is a benign regress and would reject it, given it's similarity to the Modus-Ponen's infinite regress paradox of Lewis Carroll, as used by critics of truth-by-convention to attack the idea that the notion of logical necessity is representable or derivable from a finite supply of community conventions.sime

    Okay, so what exactly in the infinite chain is objectionable?

    Also, what is this "Modus-Ponen's infinite regress" you're referring to? Quick google search doesn't give me anything.
  • sime
    401


    Sorry, about that, I was implicitly referring to Quine's paper "Truth by convention" and Wittgenstein's analogous remarks in Philosophical Investigations that differentiates what is called following a rule in practice, versus what is called giving a supply of justifications for following a rule.

    https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles
    https://plato.stanford.edu/entries/convention/#TruCon
  • Metaphysician Undercover
    6k
    Take for instance, the regress of truths. Suppose X is true. Then it is true that "X is true". But it will also be true that " 'X is true' is true", and so on and so forth. In this case we clearly have a regress, but we have no problem in accepting it.Mr Bee

    The only thing that this demonstrates, is that if you assume that something is true "suppose X is true", you automatically plunge yourself into infinite regress. It is not a benign case of infinite regress, because to suppose that X is true is not a benign supposition, depending on what is signified by X, there are logical implications. It seems like a benign infinite regress to you, because you have no problem accepting it. But this is just a manifestation of you having already thrown the problem undercover by supposing that X is true. By doing this, you accept the problem of infinite regress, but you do not produce an infinite regress without problems.
  • TheMadFool
    3.8k
    Infinite regress arguments are usually used to demonstrate a reductio ad absurdum against a position.Mr Bee

    Is infinite regress preposterous? By whose standards, one may ask? How do we know that the standards of seriousness are correct? On this view, it seems even more absurd to say an infinite regress is absurd. May be it's turtles all the way down.

    That said, I like the distinction vicious regress vs benign regress. To me, the former undermines a position that led to the regress. The latter, on the other hand, seems to be just an uninteresting fact of a position.
  • Cavacava
    2.4k
    Interesting. So, would statements such as "Every event has a prior cause" and "Every region of space is composed of smaller regions" work here to describe an infinite past or a continuous interval of space? Though I am not sure if they qualify as regresses, I am inclined to think of continuity and causality as being benign if they are so that'd be nice.


    There are no real infinities, every event could have been otherwise, logic trumps math in reality.
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