Rationalism: Empiricism and Knowledge Essay

First published Thu Aug 19, 2004 hearty revision Thu Mar 21, 2013 The struggle between freethinking and empiricism botherations the extent to which we argon dependent upon soul datum give in our effort to gain acquaintance. Rationalists claim that in that location atomic come up 18 signifi contri thatet ship trend in which our concepts and hunch overledge argon gained sever onlyy of adept escort. Empiricists claim that whiz last is the ultimate source of all our concepts and invite. Rationalists in the main develop their view in two focal points.First, they argue that there atomic tally 18 cases where the content of our concepts or whapledge outstrips the in chassisation that intellect bring it a charge stand put forward. Second, they construct reputations of how case in round shape or otherwise yields that supernumerary information rough the world. Empiricists present complementary lines of thought. First, they develop accounts of how experience p rovides the information that positivists cite, insofar as we do it in the first place. (Empiricists go out at times opt for skepticism as an alternative to ratiocination(prenominal)ism if experience mess non provide the concepts or distinguishledge the positivists cite, then we dont have them.)Second, empiricists attack the keen-sightedists accounts of how reason is a source of concepts or acquaintance. 1. innovation The dispute between rationalism and empiricism purports place at heart epistemology, the section of philosophy devoted to studying the temperament, sources and limits of bedledge. The defining questions of epistemology include the pursuit. 1. What is the nature of pro rangeal copeledge, intimacy that a picky proposition close the world is lawful? To tell a char chiper reference a proposition, we mustiness believe it and it must be true, neertheless or sothing much(prenominal)(prenominal) is required, roughthing that distinguishes int imacy from a lucky guess.Lets call this additional element warrant. A good deal of philosophical utilisation has been invested in trying to determine the nature of warrant. 2. How bed we gain bangledge? We bear form true imprints effective by making lucky guesses. How to gain warranted beliefs is less clear. Moreover, to know the world, we must think more than or less it, and it is unreadable how we gain the concepts we determination in thought or what assurance, if any, we have that the ways in which we divide up the world using our concepts correspond to pieces that actually exist. 3.What argon the limits of our friendship? whatever aspects of the world may be within the limits of our thought moreover beyond the limits of our acquaintance faced with competing interpretations of them, we fuelnot know which description is true. nearly aspects of the world may crimson be beyond the limits of our thought, so that we cannot form intelligible descriptions of them, let just know that a circumstance description is true. The disagreement between rationalists and empiricists primarily concerns the game question, regarding the sources of our concepts and companionship.In nearly instances, their disagreement on this topic leads them to give conflicting responses to the other questions as well. They may disagree over the nature of warrant or almost the limits of our thought and acquaintance. Our focus here will be on the competing rationalist and empiricist responses to the second question. 1. 1 Rationalism To be a rationalist is to embellish at least(prenominal) one of three claims. The intelligence/ discount rate dissertation concerns how we become warranted in believing propositions in a exceptional sphere range.The science/ certainty thesis or so(a) propositions in a limited sphere atomic number 18a, S, argon knowable by us by acquaintance alone still others argon knowable by being deduced from intuited propositions. dist rust is a form of rational insight. Intellectually reaching a proposition, we just see it to be true in much(prenominal)(prenominal) a way as to form a true, warranted belief in it. (As discussed in constituent 2 below, the nature of this intellectual seeing needs explanation. ) Deduction is a process in which we derive conclusions from intuited premises finished valid line of businesss, ones in which the conclusion must be true if the premises are true.We intuit, for example, that the number three is prime and that it is massiveer than two. We then deduce from this noesis that there is a prime number greater than two. suspicion and proof and then provide us with friendship a priori, which is to put forward knowledge gained independently of sense experience. We can generate different translations of the Intuition/Deduction dissertation by substituting different written report areas for the variable S. Some rationalists take mathematics to be knowable by information a nd certainty. Some place ethical truths in this category.Some include metaphysical claims, such as that perfection exists, we have free will, and our brainpower and dead body are distinct substances. The more propositions rationalists include within the range of science and price reduction, and the more controversial the truth of those propositions or the claims to know them, the more radical their rationalism. Rationalists excessively vary the strength of their view by adjusting their chthonianstanding of warrant. Some take warranted beliefs to be beyond even the slightest doubt and claim that recognition and consequence provide beliefs of this high epistemic status.Others interpret warrant more conservatively, produce as belief beyond a reasonable doubt, and claim that wisdom and deduction provide beliefs of that caliber. Still another dimension of rationalism depends on how its proponents understand the connection between science, on the one hand, and truth, on the o ther. Some take scholarship to be infallible, claiming that whatever we intuit must be true. Others allow for the possibility of false intuited propositions. The second dissertation associated with rationalism is the unlettered association thesis.The naive cognition thesis We have knowledge of whatever truths in a especial(a) subject area, S, as part of our rational nature. Like the Intuition/Deduction thesis, the infixed Knowledge thesis asserts the globe of knowledge gained a priori, independently of experience. The difference between them rests in the come with understanding of how this a priori knowledge is gained. The Intuition/Deduction thesis cites intuition and subsequent deductive reasoning. The Innate Knowledge thesis offers our rational nature. Our internal(p) knowledge is not learned through to each one sense experience or intuition and deduction.It is just part of our nature. Experiences may incite a process by which we bring this knowledge to consciousne ss, but the experiences do not provide us with the knowledge itself. It has in around way been with us all along. gibe to few rationalists, we gained the knowledge in an earlier existence. According to others, God provided us with it at creation. Still others produce it is part of our nature through natural selection. We get different recitals of the Innate Knowledge thesis by substituting different subject areas for the variable S. at one time again, the more subjects included within the range of the thesis or the more controversial the claim to have knowledge in them, the more radical the form of rationalism. Stronger and weaker understandings of warrant yield stronger and weaker versions of the thesis as well. The third cardinal thesis of rationalism is the Innate judgment thesis. The Innate Concept Thesis We have some of the concepts we employ in a particular subject area, S, as part of our rational nature. According to the Innate Concept thesis, some of our concepts are not gained from experience.They are part of our rational nature in such a way that, while sense experiences may trigger a process by which they are brought to consciousness, experience does not provide the concepts or determine the information they blockade. Some claim that the Innate Concept thesis is entailed by the Innate Knowledge Thesis a particular instance of knowledge can hardly be innate if the concepts that are contained in the cognize proposition are also innate. This is Lockes position (1690, Book I, Chapter IV, office 1, p. 91). Others, such as Carruthers, argue against this connection (1992, pp. 5354).The content and strength of the Innate Concept thesis varies with the concepts claimed to be innate. The more a concept seems removed from experience and the mental operations we can perform on experience the more plausibly it may be claimed to be innate. Since we do not experience perfect triangles but do experience pains, our concept of the author is a more promisi ng candidate for being innate than our concept of the latter. The Intuition/Deduction thesis, the Innate Knowledge thesis, and the Innate Concept thesis are essential to rationalism to be a rationalist is to adopt at least one of them.deuce other closely related theses are familiarly adopted by rationalists, although one can certainly be a rationalist without adopting either of them. The first is that experience cannot provide what we gain from reason. The Indispensability of Reason Thesis The knowledge we gain in subject area, S, by intuition and deduction, as well as the ideas and instances of knowledge in S that are innate to us, could not have been gained by us through sense experience. The second is that reason is premium to experience as a source of knowledge.The higher-rankingity of Reason Thesis The knowledge we gain in subject area S by intuition and deduction or have innately is superior to any knowledge gained by sense experience. How reason is superior needs explana tion, and rationalists have offered different accounts. virtuoso view, generally associated with Descartes (1628, Rules II and III, pp. 14), is that what we know a priori is certain, beyond even the slightest doubt, while what we believe, or even know, on the basis of sense experience is at least slenderly uncertain. Another view, generally associated with Plato.(Republic 479e-484c), locates the superiority of a priori knowledge in the objects known. What we know by reason alone, a Platonic form, say, is superior in an Copernican metaphysical way, e. g. unchanging, eternal, perfect, a higher degree of being, to what we are aware of through sense experience. Most forms of rationalism involve notable commitments to other philosophical positions. One is a commitment to the denial of scepticism for at least some area of knowledge. If we claim to know some truths by intuition or deduction or to have some innate knowledge, we plain reject scepticism with regard to those truths.Rationali sm in the form of the Intuition/Deduction thesis is also committed to epistemic foundationalism, the view that we know some truths without basing our belief in them on any others and that we then use this foundational knowledge to know more truths. 1. 2 Empiricism Empiricists endorse the following claim for some subject area. The Empiricism Thesis We have no source of knowledge in S or for the concepts we use in S other than sense experience. Empiricism about a particular subject rejects the jibe version of the Intuition/Deduction thesis and Innate Knowledge thesis.Insofar as we have knowledge in the subject, our knowledge is a posteriori, dependent upon sense experience. Empiricists also deny the implication of the corresponding Innate Concept thesis that we have innate ideas in the subject area. Sense experience is our scarce source of ideas. They reject the corresponding version of the Superiority of Reason thesis. Since reason alone does not give us any knowledge, it certainly does not give us superior knowledge. Empiricists generally reject the Indispensability of Reason thesis, though they need not.The Empiricism thesis does not entail that we have empirical knowledge. It entails that knowledge can only be gained, if at all, by experience. Empiricists may assert, as some do for some subjects, that the rationalists are correct to claim that experience cannot give us knowledge. The conclusion they draw from this rationalist lesson is that we do not know at all. I have stated the basic claims of rationalism and empiricism so that each is relative to a particular subject area. Rationalism and empiricism, so relativized, need not conflict.We can be rationalists in mathematics or a particular area of mathematics and empiricists in all or some of the physical sciences. Rationalism and empiricism only conflict when suppose to cover the resembling subject. Then the argue, Rationalism vs. Empiricism, is joined. The fact that philosophers can be both rationali sts and empiricists has implications for the classification schemes often employed in the history of philosophy, particularly the one traditionally used to describe the Early Modern peak of the seventeenth and eighteenth centuries leading up to Kant.It is standard practice to convocation the major philosophers of this period as either rationalists or empiricists and to suggest that those under one heading share a common agenda in contrary to those under the other. Thus, Descartes, Spinoza and Leibniz are the Continental Rationalists in opposition to Locke, Berkeley and Hume, the British Empiricists. We should adopt such general classification schemes with caution. The views of the individual philosophers are more subtle and complex than the simple-minded classification suggests. (See Loeb (1981) and Kenny (1986) for grand discussions of this point.)Locke rejects rationalism in the form of any version of the Innate Knowledge or Innate Concept theses, but he nonetheless adopts th e Intuition/Deduction thesis with regard to our knowledge of Gods existence. Descartes and Locke have unco similar views on the nature of our ideas, even though Descartes takes many to be innate, while Locke ties them all to experience. The rationalist/empiricist classification also encourages us to live the philosophers on each side of the divide to have common explore programs in areas beyond epistemology.Thus, Descartes, Spinoza and Leibniz are mistakenly seen as applying a reason-centered epistemology to a common metaphysical agenda, with each trying to improve on the efforts of the one to begin with, while Locke, Berkeley and Hume are mistakenly seen as gradually rejecting those metaphysical claims, with each consciously trying to improve on the efforts of his predecessors. It is also important to note that the Rationalist/Empiricist distinction is not exhaustive of the possible sources of knowledge.One cleverness claim, for example, that we can gain knowledge in a particu lar area by a form of Divine revelation or insight that is a product of neither reason nor sense experience. In short, when used carelessly, the labels rationalist and empiricist, as well as the slogan that is the gentle of this essay, Rationalism vs. Empiricism, can retard rather than advance our understanding. no(prenominal)etheless, an important debate properly described as Rationalism vs. Empiricism is joined wheneverthe claims for each view are formulated to cover the same subject. What is perhaps the nearly interesting form of the debate occurs when we take the relevant subject to be truths about the outside world, the world beyond our own minds. A fledged rationalist with regard to our knowledge of the impertinent world holds that some orthogonal world truths can and must be known a priori, that some of the ideas required for that knowledge are and must be innate, and that this knowledge is superior to any that experience could ever provide.The full-fledged empiricist about our knowledge of the external world replies that, when it comes to the nature of the world beyond our own minds, experience is our mend source of information. Reason might inform us of the dealing among our ideas, but those ideas themselves can only be gained, and any truths about the external realness they represent can only be known, on the basis of sense experience. This debate concerning our knowledge of the external world will generally be our main focus in what follows.Historically, the rationalist/empiricist dispute in epistemology has all-encompassing into the area of metaphysics, where philosophers are concerned with the basic nature of reality, including the existence of God and such aspects of our nature as freewill and the relation between the mind and body. Major rationalists (e. g. , Descartes 1641) have presented metaphysical theories, which they have claimed to know by reason alone.Major empiricists (e. g. Hume 173940) have rejected the theories as either s peculation, beyond what we can learn from experience, or nonsensical stresss to describe aspects of the world beyond the concepts experience can provide. The debate raises the issue of metaphysics as an area of knowledge. Kant puts the driving self-reliance clearly The very concept of metaphysics ensures that the sources of metaphysics cant be empirical.If something could be known through the senses, that would automatically show that it doesnt belong to metaphysics thats an upshot of the meaning of the word metaphysics. Its basic principles can never be taken from experience, nor can its basic concepts for it is not to be physical but metaphysical knowledge, so it must be beyond experience. 1783, Preamble, I, p. 7 The possibility then of metaphysics so understood, as an area of human knowledge, hinges on how we resolve the rationalist/empiricist debate. The debate also extends into ethics.Some righteous objectivists (e. g. , Ross 1930) take us to know some fundamental objective moral truths by intuition, while some moral skeptics, who reject such knowledge, (e. g. , Mackie 1977) find the appeal to a skill of moral intuition utterly implausible. More recently, the rationalist/empiricist debate has broaden to discussions (e. g. , Bealer 1999, and Alexander & Weinberg 2007) of the very nature of philosophical inquiry to what extent are philosophical questions to be answered by appeals to reason or experience?2. The Intuition/Deduction Thesis The Intuition/Deduction thesis claims that we can know some propositions by intuition and still more by deduction. legion(predicate) empiricists (e. g. , Hume 1748) have been willing to accept the thesis so long as it is restricted to propositions solely about the relations among our own concepts. We can, they agree, know by intuition that our concept of God includes our concept of omniscience. Just by examining the concepts, we can intellectually grasp that the one includes the other.The debate between rationalists a nd empiricists is joined when the former assert, and the latter deny, the Intuition/Deduction Thesis with regard to propositions that contain substantive information about the external world. Rationalists, such as Descartes, have claimed that we can know by intuition and deduction that God exists and created the world, that our mind and body are distinct substances, and that the angles of a triangle equal two respectable angles, where all of these claims are truths about an external reality independent of our thought. such substantive versions of the Intuition/Deduction thesis are our concern in this section. One defense of the Intuition/Deduction thesis assumes that we know some substantive external world truths, adds an analysis of what knowledge requires, and concludes that our knowledge must result from intuition and deduction. Descartes claims that knowledge requires certainty and that certainty about the external world is beyond what empirical evidence can provide. We can nev er be sure our sensory impressions are not part of a dream or a massive, demon orchestrated, deception.Only intuition and deduction can provide the certainty needed for knowledge, and, given that we have some substantive knowledge of the external world, the Intuition/Deduction thesis is true. As Descartes tells us, all knowledge is certain and evident cognition (1628, Rule II, p. 1) and when we check up on all the actions of the intellect by means of which we are able to pull through at a knowledge of things with no fear of being mistaken, we recognize only two intuition and deduction (1628, Rule III, p. 3).This line of aim is one of the least compelling in the rationalist arsenal. First, the assumption that knowledge requires certainty comes at a heavy cost, as it rules out so much of what we commonly take ourselves to know. Second, as many contemporary rationalists accept, intuition is not always a source of certain knowledge. The possibility of a deceiver gives us a reason to doubt our intuitions as well as our empirical beliefs. For all we know, a deceiver might obtain us to intuit false propositions, just as one might cause us to have perceptions of nonexistent objects.Descartess classic way of meeting this challenge in the Meditations is to argue that we can know with certainty that no such deceiver interferes with our intuitions and deductions. They are infallible, as God guarantees their truth. The problem, known as the Cartesian Circle, is that Descartess account of how we gain this knowledge begs the question, by attempting to deduce the conclusion that all our intuitions are true from intuited premises. Moreover, his account does not touch a remaining problem that he himself notes (1628, Rule VII, p.7)Deductions of any appreciable length rely on our fallible memory. A more plausible argument for the Intuition/Deduction thesis again assumes that we know some particular, external world truths, and then appeals to the nature of what we know, rather than to the nature of knowledge itself, to argue that our knowledge must result from intuition and deduction. Leibniz (1704) tells us the following. The senses, although they are necessary for all our actual knowledge, are not equal to give us the whole of it, since the senses never give anything but instances, that is to say particular or individual truths.Now all the instances which confirm a general truth, however numerous they may be, are not able to establish the universal necessity of this same truth, for it does not follow that what happened before will happen in the same way again. From which it appears that necessary truths, such as we find in pure mathematics, and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances, nor hence on the testimony of the senses, although without the senses it would never have occurred to us to think of them (1704, Preface, pp.150151)Leibniz goes on to describe our mathematical knowledge a s innate, and his argument may be directed to support the Innate Knowledge Thesis rather than the Intuition/Deduction Thesis. For our purposes here, we can relate it to the latter, however We have substantive knowledge about the external world in mathematics, and what we know in that area, we know to be necessarily true. Experience cannot warrant beliefs about what is necessarily the case. Hence, experience cannot be the source of our knowledge. The best explanation of our knowledge is that we gain it by intuition and deduction.Leibniz mentions logic, metaphysics and morals as other areas in which our knowledge in addition outstrips what experience can provide. Judgments in logic and metaphysics involve forms of necessity beyond what experience can support. Judgments in morals involve a form of obligation or value that lies beyond experience, which only informs us about what is the case rather than about what ought to be. The strength of this argument varies with its examples of pu rported knowledge. Insofar as we focus on controversial claims in metaphysics, e. g.that God exists, that our mind is a distinct substance from our body, the initial premise that we know the claims is less than compelling. taken with regard to other areas, however, the argument clearly has legs. We know a great deal of mathematics, and what we know, we know to be necessarily true. None of our experiences warrants a belief in such necessity, and we do not seem to base our knowledge on any experiences. The warrant that provides us with knowledge arises from an intellectual grasp of the propositions which is clearly part of our learning.Similarly, we seem to have such moral knowledge as that, all other things being equal, it is wrong to break a promise and that pleasure is intrinsically good. No empirical lesson about how things are can warrant such knowledge of how they ought to be. This argument for the Intuition/Deduction Thesis raises additional questions which rationalists must an swer. Insofar as they maintain that our knowledge of necessary truths in mathematics or elsewhere by intuition and deduction is substantive knowledge of the external world, they owe us an account of this form of necessity.Many empiricists stand ready to argue that necessity resides in the way we talk about things, not in the things we talk about (Quine 1966, p. 174). Similarly, if rationalists claim that our knowledge in morals is knowledge of an objective form of obligation, they owe us an account of how objective values are part of a world of apparently valueless facts. Perhaps most of all, rationalist defenders of the Intuition/Deduction thesis owe us an account of what intuition is and how it provides warranted true beliefs about the external world. What is it to intuit a proposition and how does that act of intuition support a warranted belief?Their argument presents intuition and deduction as an explanation of assumed knowledge that cantthey saybe explained by experience, but such an explanation by intuition and deduction requires that we have a clear understanding of intuition and how it supports warranted beliefs. metaphoric characterizations of intuition as intellectual grasping or seeing are not enough, and if intuition is some form of intellectual grasping, it appears that all that is grasped is relations among our concepts, rather than facts about the external world.Moreover, any intellectual faculty, whether it be sense perception or intuition, provides us with warranted beliefs only if it is generally reliable. The reliability of sense perception stems from the causal connection between how external objects are and how we experience them. What accounts for the reliability of our intuitions regarding the external world? Is our intuition of a particular true proposition the outcome of some causal interaction between ourselves and some aspect of the world? What aspect?What is the nature of this causal interaction? That the number three is prime does not appear to cause anything, let alone our intuition that it is prime. These issues are made all the more pressing by the classic empiricist response to the argument. The reply is generally credited to Hume and begins with a division of all true propositions into two categories. All the objects of human reason or inquiry may naturally be divided into two winnings, to wit, dealings of Ideas, and Matters of Fact. Of the first are the sciences of Geometry, Algebra, and Arithmetic, and, in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypotenuse is equal to the square of the two sides is a proposition which expresses a relation between these figures. That three times fin is equal to half of thirty expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.Though there never were a circle or triangle i n nature, the truths demonstrated by Euclid would evermore retain their certainty and evidence. Matters of fact, which are the second objects of human reason, are not ascertained in the same manner, nor is our evidence of their truth, however great, of a identical nature with the foregoing. The contrary of every matter of fact is still possible, because it can never imply a contradiction and is conceived by the mind with the same facility and distinctness as if ever so conformable to reality.(Hume 1748, Section IV, Part 1, p. 40) Intuition and deduction can provide us with knowledge of necessary truths such as those found in mathematics and logic, but such knowledge is not substantive knowledge of the external world. It is only knowledge of the relations of our own ideas. If the rationalist shifts the argument so it appeals to knowledge in morals, Humes reply is to offer an analysis of our moral concepts by which such knowledge is empirically gained knowledge of matters of fact.Mo rals and criticism are not so properly objects of the understanding as of taste and sentiment. Beauty, whether moral or natural, is felt more properly than perceived. Or if we reason concerning it and tendency to fix the standard, we regard a new fact, to wit, the general taste of mankind, or some other fact which may be the object of reasoning and inquiry. (Hume 1748, Section XII, Part 3, p. 173) If the rationalist appeals to our knowledge in metaphysics to support the argument, Hume denies that we have such knowledge.If we take in our hand any volumeof divinity fudge or school metaphysics, for instancelet us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames, for it can contain nothing but edification and illusion. (Hume 1748, Section XII, Part 3, p. 173) An updated version of this general empiricist reply, with an increased emphasis o n language and the nature of meaning, is given in the twentieth-century by A.J. Ayers version of logical positivism. Adopting positivisms verification theory of meaning, Ayer assigns every cognitively meaningful sentence to one of two categories either it is a tautology, and so true solely by virtue of the meaning of its terms and provides no substantive information about the world, or it is open to empirical verification. on that point is, then, no room for knowledge about the external world by intuition or deduction. There can be no a priori knowledge of reality.For the truths of pure reason, the propositions which we know to be valid independently of all experience, are so only in virtue of their lack of existent content By contrast empirical propositions are one and all hypotheses which may be confirmed or discredited in actual sense experience. Ayer 1952, pp. 86 9394 The rationalists argument for the Intuition/Deduction Thesis goes wrong at the start, according to empiricis ts, by assuming that we can have substantive knowledge of the external world that outstrips what experience can warrant. We cannot. This empiricist reply faces challenges of its own.Our knowledge of mathematics seems to be about something more than our own concepts. Our knowledge of moral judgments seems to concern not just how we feel or act but how we ought to behave. The general principles that provide a basis for the empiricist view, e. g. Humes overall account of our ideas, the hindrance Principle of Meaning, are problematic in their own right. In confused formulations, the Verification Principle fails its own test for having cognitive meaning. A overcareful analysis of Humes Inquiry, relative to its own principles, may require us to consign large sections of it to the flames.In all, rationalists have a strong argument for the Intuition/Deduction thesis relative to our substantive knowledge of the external world, but its success rests on how well they can answer questions ab out the nature and epistemic force of intuition made all the more pressing by the classic empiricist reply. 3. The Innate Knowledge Thesis The Innate Knowledge thesis joins the Intuition/Deduction thesis in take a firm stand that we have a priori knowledge, but it does not offer intuition and deduction as the source of that knowledge.It takes our a priori knowledge to be part of our rational nature. Experience may trigger our awareness of this knowledge, but it does not provide us with it. The knowledge is already there. Plato presents an early version of the Innate Knowledge thesis in the Meno as the dogma of knowledge by recollection. The article of faith is motivated in part by a paradox that arises when we attempt to explain the nature of inquiry. How do we gain knowledge of a theorem in geometry? We inquire into the matter. Yet, knowledge by inquiry seems impossible (Meno, 80d-e).We either already know the theorem at the start of our investigation or we do not. If we already have the knowledge, there is no place for inquiry. If we lack the knowledge, we dont know what we are seeking and cannot recognize it when we find it. Either way we cannot gain knowledge of the theorem by inquiry. Yet, we do know some theorems. The doctrine of knowledge by recollection offers a solution. When we inquire into the truth of a theorem, we both do and do not already know it. We have knowledge in the form of a memory gained from.