Bertrand Russell found an extremely helpful way to describe an ancient problem in philosophy, sometimes called "the riddle of induction". He noted that, logically speaking, no set of existential statments can entail a universal statement.
Existential statements are those of the form "there is a bat in the pantry", or "there are fifty bats in the pantry". Russell noted, glumly, that no matter how many bats you observe in that pantry, you can never validly conclude that "all bats are in the pantry". ("The Philosophy of Logical Atomism", 1956)
This is a serious problem, because we use universal statements all the time, particularly in the case of scientific laws. To take a simplified, somewhat banal example, physicists do not generally say things like"all 6,454,934 objects I have so far observed on planet Earth have fallen to the ground unless impeded by some other object or force". Rather, they say things like "mass attracts mass", the idea being that a massive object like the Earth will always pull objects towards its center. This is a universal generalization, a law. The problem of induction revolves around the essential difficulty in deriving such laws from a collection of individual instances. It is a pressing problem because our most successful model of epistemic activity, modern science, requires the articulation of universal generalizations or laws.
Yet, as Russell observed, the problem looks even more threatening in its logical form. Insofar as we are empiricists of any kind, existential statements are all we have. We want to give primacy to (or start with) individual observational experiences, and build our larger theories from on that foundation. It seems like a good foundation: I, for one, cannot really doubt that I have observational experiences of a certain character.
Yet, all such experiences are singular events, referring to a limited class of objects. As such, they must be translated into existential and not universal logical sentences. But these are just two different kinds of statements, and as such universal statements do not entail existential ones, and neither do existential statements entail universal ones. Consider:
[1] (Universal) "All bats are in the pantry"
[2] (Existential) "There is a bat in the pantry"
Even if it is a fact that everything that is a bat is in the pantry, there might not actually be any bats, so (1) doesn't entail (2). Conversely, even if a bat (or two bats, or 57 billion bats) are in the pantry, there might be another bat living in a cave far away from our pantry, so (2) doesn't entail (1).
Time and again in the history of philosophy, we see anti-metaphysical thinkers rising up and declaring that metaphysics is nonsense and that we ought to just "attend to the facts". Hume is perhaps the most sophisticated example, but this general position finds echoes both in modern positivism and in certain ancient skeptics. Yet, time and again in their writings, we see these philosophers running headfirst into universal generalizations that they can't justify via their own methods.
I derive a perverse enjoyment from watching thinkers convulse in these crucial moments: witness the otherwise brilliant Hume declaring that we have a natural "propensity" to believe such generalizations (T 1.3.14, 1.4.7), as if that settled anything. It is possible that metaphysics won't go away because, logically, it can't go away. Seen this way, the anti-metaphysician attempts to saw away the logical branch upon which he is sitting.
Existential statements are those of the form "there is a bat in the pantry", or "there are fifty bats in the pantry". Russell noted, glumly, that no matter how many bats you observe in that pantry, you can never validly conclude that "all bats are in the pantry". ("The Philosophy of Logical Atomism", 1956)
This is a serious problem, because we use universal statements all the time, particularly in the case of scientific laws. To take a simplified, somewhat banal example, physicists do not generally say things like"all 6,454,934 objects I have so far observed on planet Earth have fallen to the ground unless impeded by some other object or force". Rather, they say things like "mass attracts mass", the idea being that a massive object like the Earth will always pull objects towards its center. This is a universal generalization, a law. The problem of induction revolves around the essential difficulty in deriving such laws from a collection of individual instances. It is a pressing problem because our most successful model of epistemic activity, modern science, requires the articulation of universal generalizations or laws.
Yet, as Russell observed, the problem looks even more threatening in its logical form. Insofar as we are empiricists of any kind, existential statements are all we have. We want to give primacy to (or start with) individual observational experiences, and build our larger theories from on that foundation. It seems like a good foundation: I, for one, cannot really doubt that I have observational experiences of a certain character.
Yet, all such experiences are singular events, referring to a limited class of objects. As such, they must be translated into existential and not universal logical sentences. But these are just two different kinds of statements, and as such universal statements do not entail existential ones, and neither do existential statements entail universal ones. Consider:
[1] (Universal) "All bats are in the pantry"
[2] (Existential) "There is a bat in the pantry"
Even if it is a fact that everything that is a bat is in the pantry, there might not actually be any bats, so (1) doesn't entail (2). Conversely, even if a bat (or two bats, or 57 billion bats) are in the pantry, there might be another bat living in a cave far away from our pantry, so (2) doesn't entail (1).
Time and again in the history of philosophy, we see anti-metaphysical thinkers rising up and declaring that metaphysics is nonsense and that we ought to just "attend to the facts". Hume is perhaps the most sophisticated example, but this general position finds echoes both in modern positivism and in certain ancient skeptics. Yet, time and again in their writings, we see these philosophers running headfirst into universal generalizations that they can't justify via their own methods.
I derive a perverse enjoyment from watching thinkers convulse in these crucial moments: witness the otherwise brilliant Hume declaring that we have a natural "propensity" to believe such generalizations (T 1.3.14, 1.4.7), as if that settled anything. It is possible that metaphysics won't go away because, logically, it can't go away. Seen this way, the anti-metaphysician attempts to saw away the logical branch upon which he is sitting.
1 comments:
I think this goes back to what Hilary Putnam pointed out: a lot of modern philosophy has a problem reconciling anti-skepticism with fallibilism.
Roderick T. Long has an excellent (if brief) discussion of this on pages 22-27 in "Reason and Value", concluding on p. 25 that there are three ways to bridge these:
1. "maintain extremely high standards for what will count as knowledge, and extremely high standards for what will count as objective reality, and nevertheless heroically attempt to bridge the gulf"
2. "lower the standards for what will count as objective reality" (e.g. by relativising it)
3. "lower the standard for what will count as knowledge" (e.g. by accepting defeasible-but-well-justified beliefs as knowledge)
As I see it, the anti-metaphysical quest has largely been an attempt to do (1) by eliminating the "weakest link" in terms of what we can know or not know. And you get the hilarious results you've pointed out because that is not a realistic task.
(2) was Putnam's response during his "interal realist" period, while (3) is Long's approach and, I think, Donald Davidson's, with Richard Rorty going one step further by doing both (2) and (3), and Feyerabend largely arguing "not (1)." However, I think all of them would agree with Long that:
Still, in the end "ought" implies "can." Since we have no alternative to acting on the beliefs we have, we are justified in doing so, even if we cannot yet demonstrate these beliefs or explain why they are true; and so those beleifs are themselves justified, at least until a case can be made against them.
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