Sunday, December 2, 2012

The Argument from Gradation

As a self-described Aristotelian-Thomist, I admit that the argument from gradation (the "Fourth Way") gives me the most difficulty.  I don't understand the manner in which Thomas derives his conclusion in the Summa Theologica.  However, the Summa Contra Gentiles has made the proof much easier for me to understand, even though I still have questions about it.  Here's how I would roughly summarize it:

1. A flaw can only be known if there is a standard of supremacy. (Premise)

2. There are flaws in one's perception of truth. (Premise)

3. Therefore, there exists a Supreme Truth. (From 1 and 2)

In support of (1), I'm reminded of C.S. Lewis's famous analogy: one cannot know a line is crooked without having some idea of what a straight line looks like.

Premise (2) should be obvious to anyone who doesn't claim omniscience.  Based on these two premises, (3) necessarily follows.  However, what's the significance of stating there exists a Supreme Truth?  As far as I can tell, propositional truth is an abstract object, but no classical theist equates God with a mere abstraction.

One solution to this problem is to postulate that abstract objects, such as truth, exist as mental concepts, as opposed to mind-independent realities (the latter of which Plato held, whereas St. Augustine postulated the former).  If conceptualism is true, then the Supreme Truth, which includes necessary and contingent truths, would have to be the concept of a necessary and omniscient mind, e.g. God.


  1. This is an interesting take on the Fourth Way. Have you read OFloinn's blog post on the subject? I still don't understand the Fourth Way perfectly, but his post helped.

    1. That someone isn't onmiscient is obvious if this person realizes he does not knoperson Xsomeone does not know the square root of 48837194.23558 by no means entails that there is a supreme truth. It only means that person X does not know everything.
      Do you also think that, in order for me to know that you run faster than me, it is necessary that there is a fastest runner?
      A hypothetical fastest runner is a mental construct based on a comparison of runners. Likewise, a perfect straight line is an mental construct based on observations. So, yes, abstractions are mental concepts, but they are mental concepts of contingent minds, like ours.

  2. I don't think the example of a fastest runner is analogous, since that involves concrete objects. You're quite right in saying that we can have mental constructs of speed, and so forth, but I don't see any connection with any of that with the conclusion that abstract objects are the concepts of contingent minds. After all, if there are necessary abstract objects, such as the laws of logic, then they couldn't possibly the concepts of contingent minds.

    1. Abstracts can be derived from concrete objects. A straight line can be derived form e.g. the shortest distance between two concrete points or even positions.

      If you treat the laws of logic as prescriptive, then conceptualism runs into deep trouble, because these necessary 'prescriptions' would then also prescribe how this necessary mind must operate. That way, you get into an infinite regress. The behaviour of this necessary mind is prescribed by the laws of logic, which presuppose a necessary mind, which presupposes the laws of logic, which presupposes a necessary mind...
      The only way out of this is to either adopt Platonism, which would mean the argument from gradation cannot be used as an argument for Theism, or to treat the laws of logic as merely descriptive of reality, which has the same consequences.
      I really do not see how you can save the argument from gradation, though.

  3. I haven't read OFloinn's piece. Thanks for the link. :)

  4. Abstract objects can't be derived from concrete objects. We impose our knowledge of the laws of logic, for instance, onto our observations in order to make those same observations intelligible. If our knowledge of logic didn't precede those observations, then the observations would be unintelligible. We wouldn't be able to know that a crooked line is not also a straight line (law of non-contradiction).

    Now, when you talk about an infinite regress, we have to be very careful. It seems to me that you're committing a category error in placing the laws of logic in some kind of regress of explanation. Abstract objects, including the laws of logic, don't stand in causal relations, so it's unclear what kind of infinite regress you're postulating. Moreover, an explanation doesn't have to be in terms of some external cause. If, as I claim, the laws of logic are necessary, then they don't have an external cause. The claim has never been that God *causes* the laws of logic, but rather that the laws of logic are concepts in the mind of God.

    As always, I appreciate your comments.

    1. Our knowledge of the laws of logic can be treated as axiomatic. Axioms do not have to be true, they can be considered 'game-rules'. In order to play the game of trying to make some sense of our surroundings, we need some basic axioms, which can be comfirmed by observations.

      As to the infinite regress, the very fact that you claim some mind is necessary means that this mind is logically necessary, which means that, according to the laws of logic, this mind must exist, and, moreover, that according to the laws of logic, this mind has to hold the truth of these laws as a concept. Or, to put it differently, this mind cannot hold a false proposition because the laws of logic hold that that proposition is false. So, the laws of logic, although causally effete, nevertheless somehow put limits of this mind. So, the way you put it, necessarily entails that the laws of logic 'exist' as Platonic entities. They cannot be internal to God, because they restrict what the mind of God can hold as concepts.

  5. If the laws of logic are merely conventional axioms, they should be falsifiable. Can you name any law of logic that could possibly be false?

    As for the infinite regress, we're just going to have to agree to disagree. I feel you're equivocating terms like "limit" and "restrict," and that the argument doesn't even get off the ground as a result.

  6. I have never claimed that the laws of logic are merely conventional axioms. I said that our knowledge of the LoL can be considered axiomatic.

    And I think you are actually special pleading by claiming that logic does not restrict or determine what God can do. Logic most certainly restricts what I can do. I cannot create a square circle, e.g., and I do not think you believe God can do that. With all due respect,I do not see how under your idea of conceptualism anything could be impossible for God.
    Anyway, I have no problem with agreeing to disagree but I would have liked you to present an actual rebuttal of my argument instead of just throwing in an accusation of equivocation without even attempting to show why it would be an equivocation.
    But, never mind, you are free to believe whatever you wish.

  7. "the very fact that you claim some mind is necessary means that this mind is logically necessary"

    First of all, being "necessary" can mean a few things. You should ask about the kind of "necessity" Doug is claiming. And just because something is, say, metaphysically necessary, it does not follow that it is also logically necessary. And the laws of logic, like the law of Non-contradiction, aren't things that "hold God back" or place "restrictions" on God. The Law of Non-contradiction simply tells us that contradictions cannot exist, in any possible world, such as the power to create a rock that cannot be moved by an omnipotent being. It makes no sense to say that God is somehow "limited" if He does not have a power that does not exist and can't ever exist.

    1. Hi, Another Anon.

      Necessary in this context means logically necssary, that's the way Doug is using it.
      And yes, the Law of non-contradiction tells us that contradictions cannot exist. The point is, that they also 'tell' God's mind that it cannot hold false propositions.
      My point is that if some necssary mind did not exist, that would not mean square-circles would be possible. So, this "mind" is in my opinion, completely redundant.

  8. What do you mean by saying that our knowledge of the laws of logic are axiomatic? If my original interpretation is incorrect, how does that contradict my claim that the laws of logic have necessary existence?

    Special pleading only applies to entities that are alike. If I say every human being is mortal, but not Socrates, that's special pleading. God is a concrete object. The laws of logic are abstract objects. Because of this key difference, it's not special pleading to say that one aspect of God does not apply to the laws of logic.

    With this in mind, I think you misunderstood my argument to be a mere dismissal of your claim. That's my fault, though, for not being clear enough. You're quite right that God cannot create a square-circle, but that's entirely different from thinking of logic as some *force* that acts to prevent God from doing so.

    Here's another point. If what you say is true about an infinite regress, then the same would apply to reason itself. Why be rational? Because it's irrational to not be? You can see how treating rationality (the laws of logic of which are a part) the same way we treat other regresses (e.g. John's father was Bill, Bill's father was Steve, etc.) is an equivocation.

    1. It does not contradict your claim that the LoL are necessary, it just shows how deriving abstracts from concrete would be possible. I know you don't believe it is possible, but you cannot prove it.
      Special pleading occurs when you claim that the LoL are necessary but then claim that these laws do not apply to your special concrete object, or when you claim that fast runners are concrete entities, but fail to realise that you describe God as a concrete entity as well.
      And I do not see logic as a "force" that prevents God from doing anything.You are the one claiming that, in order for abtsracts to have 'effects' they must be contained in some necessary mind, which I claim is self-contradictory.
      And as to an infinite regress applying to reason. That is true if you regard reason as a platonic reality, it's even more true if you add to this platonic reality an extra entity (a mind of some kind) but it is not true if, as I do, you regard abstract objects as derivable from the only true reality: concrete reality.
      Now, I am not going into this any further, so agreeing to disagree is the only option here.

  9. How would one go about deriving abstract objects from concrete observations? As I've been arguing, the knowledge of logic must precede the intelligibility of any concrete observations.

    I never claimed the laws of logic don't apply to God. What I said is that it's a category mistake to treat abstract objects like we would concrete objects. So, I'm just going to reiterate what I stated earlier about this not being special pleading. Logic isn't the type of entity that has effects (nowhere did I say they have "effects").

    You don't get out of the infinite regress argument simply by denying realism with respect to abstract objects. There's our knowledge that's to be accounted for, even if one is a solid nominalist. Denying the abstract objects a positive ontological status becomes irrelevant at that point, since you're still talking about a justified theory of knowledge (epistemology), which includes the same "why" questions.

    1. Doug

      I have answered all this. If you want a more detailed theory, I am afraid I won't be able to present this in a few lines or even pages.
      The point is: I have a valid alternative to your theory which does not include unnecessary and unknowable entities.
      That's all I have to say about this. I do not think there is any point in having an endless discussion about this.

  10. Okay, take it down a notch. We're all friends here. I feel I've made my case and you feel you've made yours. If anyone's following along, they can decide for themselves who, if either of us, is correct.

  11. Doug

    I do not think I have said anything "unfriendly", but if you feel I have, then I apologize.
    For the rest, I agree that followers can decide for themselves who is correct.

  12. No need to apologize. I misunderstood. The trouble with the internet is there's no body language or voice inflection to interpret. Be well.