Nicholas Rescher's Inquiry into the Limits of Knowledge

What are the theoretical and practical limits of human knowledge? What are the reasons for our inability to know certain facts about the world? What distinguishes knowable from unknowable facts?

      How can we ever know whether the universe is finite or infinite? How can we ever know whether it had a beginning, and whether it will have an ending? How can we ever know how space, time, matter, and energy originated?

      How can we ever discover historical facts the evidence of which has been permanently lost?

      How can we ever really know what others are thinking and feeling? The thoughts and feelings of others are to some extent unknowable to us, in the sense that we can't think those thoughts exactly as they think them or feel those feelings exactly as they feel them. We can only say, "I know what you're thinking" or "I know what you're feeling" by means of deduction, inference, reasoning, intuition, imagination, or other means. To use a commonly cited example, we can't ever really know whether others experience the color red in the same way that we experience the color red.

      Some facts (for example, the contents of a classified file or document) may be contingently (but not in principle) unknowable, because they're concealed or because public access to them is forbidden. Our personal data, such as our birthdates, computer passwords, social security numbers, etc., may be contingently unknowable to others, because we generally refuse to share such information with everyone. The details of our own bodies may be contingently unknowable to others, because they're hidden by our clothing.

      To say we know about something may not necessarily be to say that we know everything about it. We may have a relatively complete or incomplete knowledge about a certain thing. If we can't ever really know everything about it, then it may to some extent be unknowable to us, at least in its totality (given our limited cognitive resources).

      Many facts may be unknowable yet trivial, and thus we may not really be interested in knowing them. 

      If there are no facts about certain things, i.e. if there is "no fact of the matter" about them, then they may also be unknowable.

      Nicholas Rescher (2009) explains that reasons for our not being able to know certain things include our not being smart enough to figure them out, and the unavailability of further data we would need to know about them. But we may also not be able to know about certain things because they are in principle unknowable, and this in-principle unknowability is what Rescher is concerned with, rather than unknowability due to our contingent cognitive limitations.

      He describes three kinds of necessary or demonstrable unknowability: (1) logical unknowability (which is demonstrable on the basis of the considerations of epistemic logic), (2) conceptual unknowability (which is demonstrable on the basis of the concepts involved), and (3) in-principle unknowability (which is demonstrable on the basis of the basic principles that delineate some field of inquiry or area of concern).¹

      He also explains that some facts are unknowable because they depend on future contingencies. Thus, we can't know, at the present moment, precisely who will be killed in an automobile accident next year or whose life will be saved by the enactment of a certain automobile speed limit.²

      Some facts may also be unknowable because they're unidentifiable. Examples include claims about the existence of such unidentifiable entities as (1) something whose identity will never be known, (2) some idea that has never occurred to anyone, (3) some person whom no one remembers at all, (4) some event that no one has ever mentioned, and (5) some integer that is never individually specified.³

      Clearly, we may know some facts without being consciously aware that we know them. So every known fact may not be immediately identifiable. We may also be able to individuate some unknowable facts without being able to identify them or say precisely what they are. But we can't know facts that can never be specifically instantiated.

      Rescher also notes that if some facts are unknowable, then we can't rightly be held to be culpably ignorant of them.⁴

      What distinguishes answerable from unanswerable questions? Rescher argues that all scientific questions are potentially answerable (if not at present, then in the future). Even such ultimate questions as "Why is there anything rather than nothing?" and "Why are there any natural laws?" are potentially answerable. The presence of scientific questions that haven't yet been answered doesn't necessarily mean those questions can never be answered or will always remain unanswered. 

      Thus, he rejects the existence of insolubilia (inherently unsolvable scientific problems or inherently unanswerable scientific questions), because of the unpredictability of future scientific developments.⁵ He argues that we can't predict with certainty what will be the future limits of scientific knowledge.

      He also describes four main reasons for the unknowability of, or impracticability of cognitive access to, certain facts about the world: (1) developmental unpredictability (the inability to predict with certainty what will happen in the future and what will be discovered by future science), (2) verificational surdity (the inability to explain facts on the basis of general principles or to derive them from the definitions and laws of their natural domain), (3) ontological detail (the inability to know all the facts about certain things, due to their factual limitlessness and inexhaustibility), and (4) predicative vagrancy (the inability to instantiate any predicates about things that are unspecificable).⁶

      He also discusses the formal logic of unknowability, including such topics as the problem of demonstrating the existence of unknowable truths. This problem has been investigated by many philosophers, including Frederic Fitch, W.D. Hart, J.J. MacIntosh, Richard Routley, Timothy Williamson, Rescher, and others.

     Timothy Williamson (2000) refers to an argument by Frederic Fitch (1963) called the Paradox of Unknowability, which says that if something is an unknown (but perhaps knowable) truth, then its being an unknown truth is itself an unknowable truth.⁷ An unknown truth cannot be known to be unknown.

      Williamson describes strong verificationism as the theory that every truth is actually known (at some point in the past, present, or future), and weak verificationism as the theory that every truth is in principle knowable. The former is called the "omniscience principle," while the latter is called the "knowability thesis." Fitch's paradox is an argument against both kinds of verificationism.

      Williamson explains that

"As Joseph Melia (1991) points out, [Fitch's argument] does not show that if there are unanswered questions, then there are unanswerable questions. More precisely, it does not show that if for some proposition p, it is unknown whether p is true, then...it is unknowable whether p is true. In particular, if p is an unknown truth, then it is unknowable that p is an unknown truth, but it does not follow that it is unknowable whether p is an unknown truth. For that it is an unknowable truth that p is an unknown truth does not imply the... impossibility of a situation in which p is false and even known to be false, and thereby known not to be an unknown truth. Equally, ...it...does not imply the...impossibility of a situation in which p is shown to be true, and even known to be known to be true, and thereby known not to be an unknown truth. In situations of both kinds, it is known whether p is an unknown truth."⁸

       Verificationism is anti-realist in the sense that it holds that every truth (or fact) is in principle knowable and thus accessible to human thought, while a realist position would hold that at least some truths (or facts) are actually unknowable and exist independently of human thought.

      Helge Rückert (2004) explains that Fitch's paradox may be derived as follows:

      (1)   α → ♢Kα   (which may be read as, "if there is a truth α, then it's possible for it to be known")

      (2)   ロ(Kα → α)  (necessarily, if a truth α is known, then it's a truth α) 

      (3)   ロ(K(α ⋀ β) → (Kα ⋀ Kβ))  (necessarily, if a truth α and a truth β are known, then α is known and β is known)

      (4)   ￢♢K(α ⋀ ￢Kα)  (it's impossible for an α and an unknown α to be known)

      (5)   (α ⋀ ￢Kα) → ♢K(α ⋀ ￢Kα)  (if there is an α and an unknown α, then it's possible for an α and an unknown α to be known)

      (6)   ￢(α ⋀ ￢Kα)  (there can't be an α and an unknown α)

      (7)   α → Kα  (if there is a truth α, then it's known)

So weak verificationism entails or "collapses into" strong verificationism. The relatively plausible thesis that every truth is in principle knowable collapses into the wholly implausible thesis that every truth is actually known. This is a significant problem for verificationism.⁹

FOOTNOTES

¹Nicholas Rescher, Unknowability: An Inquiry into the Limits of Knowledge (Lanham, MD: Rowman & Littlefield, 2009), p. 3.

²Ibid., p. 3.

³Ibid., p. 65.

⁴Ibid., p. 6.

⁵Ibid., p. 16.

⁶Ibid., p. ix.

⁷Timothy Williamson, Knowledge and its Limits (Oxford: Oxford University Press, 2000), p. 270.

⁸Ibid., p. 289.

⁹Helge Rückert, "A Solution to Fitch's Paradox of Knowability," in Logic, Epistemology, and the Unity of Science, edited by Shahid Rahman, John Symons. et al. (Dordrecht: Kluwer Academic Publishers, 2004), pp. 352-353.

OTHER REFERENCES

Frederic Fitch, "A Logical Analysis of Some Value Concepts," in Journal of Symbolic Logic, Vol. 28 (1963), pp. 135-142.

Joseph Melia, "Anti-Realism Untouched," in Mind, 100 (1991), pp. 341-342.

Edith Stein, on Finite and Infinite Being

Edith Stein (1891-1942) was a German Jewish philosopher who converted to Catholicism and became a Carmelite nun. She was born in Breslau, Germany (now Wroclaw, Poland), and died at Auschwitz. She studied at the University of Breslau, the University of Göttingen, and the University of Freiburg, where she completed her doctoral thesis on the phenomenology of empathy. She worked as an assistant to the philosopher Edmund Husserl at Freiburg from 1916-1918. After she read the autobiography of St. Teresa of Avila, she converted to Catholicism, and she was baptized into the Catholic Church in 1922. In 1933 she entered the Carmelite convent at Cologne, taking the religious name Teresa Benedicta of the Cross (Teresia Benedicta a Cruce). In 1938, she and her sister Rosa, who had also converted, were transferred for their own safety to the Carmelite monastery in Echt, Netherlands, but after the Dutch bishops condemned Nazism in 1942, all baptized Catholics of Jewish ancestry were arrested. Edith and Rosa were sent to a concentration camp at Amersfoort, then to Westerbork, and then to Auschwitz, where they died in a gas chamber on August 9, 1942.

      Stein's many writings included Zum Problem der Einfühlung (1917, On the Problem of Empathy, 1989), Potenz und Akt: Studien zu einer Philosophie des Seins (1931, Potency and Act: Studies on a Philosophy of Being, 2009), Endliches und ewiges Sein (1949, Finite and Eternal Being, 2002), Kreuzeswissenschaft (1942, The Science of the Cross, 2003), and Wege der Gotteserkenntnis (1940, Ways to Know God, 1993). She was beatified by the Catholic Church in 1987, and was canonized Saint Teresa Benedicta of the Cross in 1988.

      In Finite and Eternal Being: An Attempt at an Ascent to the Meaning of Being, Stein takes as her starting point the fact of our own being. She takes our own being as given, rather than as a conclusion (as suggested by Descartes' cogito). She asks, "What is that being of which I am conscious?" and "What is that self which is conscious of itself?"¹

       She explains that Husserl calls the self that is immediately given in conscious experience the pure ego, and that the pure ego knows itself simultaneously as an actually present existent and as an actual existent that emerges from a past and lives into the future.²

        She also explains that our own being is inseparable from temporality, while pure being has no temporality. Our own being is an actually present being, a "now" between a "no longer" and a "not yet." But in pure being, there isn't a "no longer" or "not yet." Pure being is eternal, and not temporal.³

      Our own present actual being contains within itself the possibility of future actual being and is thus both actual and potential. In this sense, our own being is always a becoming. The becoming actual of our future being is a transition from potentiality to actuality, and the transition from potential to actual being is a transition from one mode of being to another.⁴ 

      Stein thus accepts St. Thomas Aquinas's distinction between act and potency as modes of being. She argues that we must distinguish between active and passive potency, and that the potency belonging to God is active potency. In God, there is no unactivated potency. God's potency is completely actualized.⁵

      She also accepts Aquinas's view of the "first existent" as pure being and pure act. In our own being, which is finite being, we encounter a kind of received being that is the support and ground of our being.⁶ This ground and support of our being is a necessary being, of which there can only be one, just as there can only be one first existent. This necessary being is also perfect and eternally immutable being. Indeed, it is being itself. Thus, the distinction between finite and infinite being is also the distinction between the temporal and the eternal, between our own being and God's being. 

      Existents may be divided into various genera according to their quiddity (their natures or essences or whatnesses). Essential being is the being of natures or essences when they are considered apart from their actualization.⁷ Essential being is also a timeless (or non-temporal) being-unfolded or being-unfolding of meaning. Ideal being is a special kind of essential being, and also a special kind of (non-temporal) unfolding of ideal objects. On the other hand, real being is "an unfolding that proceeds from an essential form, from potency toward act, and within time and space."⁸

      Just as a distinction may be made between potential and actual being, a distinction may be made between potential and actual existents. But the first existent (God) is also the first being, and God's existence cannot be separated from God's being. God's being is pure being, in which there is no non-being. In the infinite and eternal, being cannot be separated from existence, but in all finite things, being and existence are different from each other.⁹

      In response to the question of whether any distinction can be made between God's essence and God's existence, Stein explains they are in fact an undivided unity, and thus they cannot be subjected to analytical articulation.¹⁰

      The first being (God) is also pure act, and in this being there is no passing from potentiality to actuality. Temporal being, on the other hand, is not pure act, and it may be a progressive actualization of unfulfilled potentialities.

FOOTNOTES

¹Edith Stein, Finite and Eternal Being: An Attempt at an Ascent to the Meaning of Being, translated by Kurt F. Reinhardt (Washington, D.C.: ICS Publications, 2002), p. 37.      

²Ibid., p. 54

³Ibid., p. 37.

⁴Ibid., p. 34.

⁵Ibid., p. 2.

⁶Ibid., p. 59.

⁷Ibid., p. 91.

⁸Ibid., p. 331.

⁹Ibid., p. 335.

¹⁰Ibid., p. 342.

Problems for the Supposed Maximality of Possible Worlds

Alvin Plantinga (1974) defines a possible world as a possible state of affairs that is maximal or complete. Every possible world is a possible state of affairs, he says, but not every possible state of affairs is a possible world. A state of affairs S is maximal or complete if (and only if) for every state of affairs S', S either includes or precludes S'. The actual world we live in is one of these possible worlds; it's the maximal possible state of affairs that is actual.¹

      The reason for defining possible worlds in terms of maximality or completeness is that not every possible state of affairs is complete enough to be considered a possible world. Plantinga gives as an example the proposition that "Socrates is snubnosed." A possible state of affairs must include or preclude more than that in order to be considered a possible world.

      Similarly, Robert C. Koons and Timothy K. Pickavance (2017) define a possible world as a possibility that's maximal insofar as every proposition is either true or false according to it.² They also describe concretism and abstractionism as two contrasting views about the nature of possible worlds. While concretism is the view that possible worlds are maximal possible concrete objects, abstractionism is the view that possible worlds are maximal possible abstract objects.³

      Dale Jacquette (2006) explains that if a logically possible world is taken to be a maximal consistent set of propositions, then it could (theoretically) be constructed by randomly choosing one logically possible proposition and then considering an exhaustive ordering of all other logically possible propositions, and adding each one to the given set if and only if it is logically consistent with the propositions already collected, until there are none left. The propositions in a maximally consistent set of propositions would therefore collectively represent every state of affairs associated with a corresponding logically possible world.⁴

     Another conclusion, however, might be that the actual world is the only maximally consistent set of propositions, and that all other logically possible but nonactual worlds are submaximally consistent.

     But what about propositions whose truth or falsehood is indeterminate or undecidable? In the actual world we live in, there are such undecidable propositions. Is the actual world then not a possible world? How then can maximality or completeness be considered a valid criterion for some possible state of affairs to be considered a possible world? Must a possible world be maximal in the sense that every proposition is decidably true or false according to it, and therefore also in the sense that for every proposition there is some rational procedure that can determine in a finite number of steps the truth or falsehood of that proposition according to it?

      These questions are motivated by Gödel's first incompleteness theorem, which says, roughly, that for any consistent system S of formal arithmetic in which (1) the set of axioms and the rules of inference are recursively definable, and (2) every recursive relation is definable, there are undecidable arithmetical propositions of the form xF(x), where F is a recursively defined property of natural numbers.⁵

      Thus, it seems that possible worlds can't be both complete and consistent, because the actual world isn't that way. For every possible proposition expressible within a nontrivial formal system of arithmetic to be provable or disprovable, that system has to be in some way inconsistent. All consistent nontrivial formal systems of arithmetic are deductively incomplete.

     Of what use then is the concept of maximality or completeness as a means of better understanding the metaphysics of modality?

      Patrick Grim (1991) presents an argument similar to the Liar Paradox as a refutation of the maximality of possible worlds. He explains that if possible worlds are taken to be or to correspond to maximal consistent sets or propositions, and if the actual world, on such an account, is taken to be or to correspond to the maximal set of all truths, then we can examine the proposition A: The proposition A is not a member of the maximal set M of all truths. Is A a member of set M or not? If it's a member, then it must not be, and if it's not a member, then it must be.⁶

      Tony Roy (2012) also presents an argument against the maximality of possible worlds, by employing Cantor's Theorem (that the set of all subsets of a given set has a greater cardinality than the set itself):

      "Suppose that for any proposition a, some sentence expresses a and some sentence expresses not-a...Then the supposition that worlds are maximal and so include one of a or not-a for every sentence is incoherent. Consider a world w, and the set P(w) which has as members all the subsets of w. By Cantor's Theorem, there are more sets of sentences in P(w) than sentences in w. Trouble.

      ...And this generates a problem about the maximality of w. Suppose w is maximal; then given our assumption that there are sentences to express any proposition and its negation, for any A in P(w), w includes one or the other of,

      a₁ Some member of A is true; and

      a₂ No member of A is true.

So w includes at least one sentence for each member of P(w); so there are not more members in P(w) than w. This is impossible; reject the assumption; w is not maximal.

     So given a language with adequate expressive power, the very attempt to say everything about a world is self-defeating."⁷

FOOTNOTES

¹Alvin Plantinga, The Nature of Necessity (Oxford: Clarendon Press, 1974), pp. 44-45.

²Robert C. Koons and Timothy K. Pickavance, The Atlas of Reality: A Comprehensive Guide to Metaphysics (Chichester: John Wiley & Sons, 2017), p. 318.

³Ibid., p. 321.

⁴Dale Jacquette, "Propositions, Sets, and Worlds," in Studia Logica, Vol. 82, No. 3, April 2006, pp. 338-340.

⁵Kurt Gödel, "On formally undecidable propositions of Principia Mathematica and related systems," [Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme," 1931] in Kurt Gödel Collected Works, Volume I, edited by Solomon Feferman, et al. (Oxford: Oxford University Press, 2004) p. 181.

⁶Patrick Grim, The Incomplete Universe: Totality, Knowledge, and Truth (Cambridge: MIT Press, 1991), pp. 6-8.

⁷Tony Roy, "Modality," in The Continuum Companion to Metaphysics, edited by Neil A. Manson and Robert W. Barnard (London: Continuum, 2012), pp. 51-52.