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Per Se Statements: Getting a Handle on Truth

 

Rev. Sebastian Walshe, O.Praem. (’94)
Professor of Philosophy
St. Michael’s Abbey
St. Vincent de Paul Lecture and Concert Series
Thomas Aquinas College, New England
November 8, 2019

 

Introduction

Aristotle observed that the human race lives by art.  That observation may seem obvious, but it is not less profound for being obvious.

The range and scope of goods possible for the human race so exceeds the physical capacities of our bodies that unlike the other species of animals who are provided with definite organs and tools sufficient to acquire their limited goods, man must fashion for himself other tools as a means to the variety of goods possible to human reason.  Here is what St. Thomas says about that:

There is a difference between the way something is naturally provided for man and for the other animals: both in regard to the body and the soul.  For to the other animals there are provided particular coverings such as a tough hide and feathers, and other things of this kind, as well as special weapons such as horns and claws, and things of this kind.  This is because they have fewer ways of acting to which determinate instruments can be ordained.

But to man these things are provided in a general way, inasmuch as there are given to him hands by nature, by which he might prepare for himself various coverings and weapons.  And this is because the reason of man is so multiform and extends itself to diverse things, so that there cannot be sufficiently prepared determinate instruments for him.   

And it is similar on the part of apprehension because other animals are endowed with special conceptions necessary for them by a certain natural instinct: just as the lamb which knows that the wolf is its enemy, and other things of this kind.  But in place of these things for man the understanding is naturally endowed with universal principles by which he is able to proceed in all those matters necessary for him.  (De Ver. Q.22, a.7, c.)

Art is the knowledge by which reason obtains these goods by fashioning appropriate tools.

In this lecture I want to focus upon one such art, Logic, and a special tool of that art, per se statements: that is statements in which the predicate belongs to the subject through the subject itself.

In order to understand a tool precisely it is important to grasp its purpose within the larger art.  For example to understand a rudder completely, it is important to see its contribution to the art of boat navigation.  So I will first give a brief overview of Logic, and then specifically explain the usefulness of per se statements as tools with the art of Logic.

The Art of Logic

Every art is established to procure some good: either to procure it at all, or at least more easily.  For example agriculture is for the sake of procuring healthy and nutritious food; architecture is for the sake of making shelter and a suitable living environment; the military art is for the sake of procuring victory over an enemy, and so forth.  Logic is no different.  Logic was established for the sake of procuring the good of the speculative intellect, and that good is truth known for its own sake.

This good is certainly unlike the other goods I mentioned: food, shelter, victory, are all bodily goods, and hence better known and even more necessary. Truth known for its own sake is not a bodily good, but a good of the soul.  Because these goods are less known some might even deny that speculative truth is good for man at all: it seems like a waste of time.  It would take a lecture of its own to establish that speculative truth is a good for man, indeed his greatest good.  So I will simply give some signs or indications that speculative truth does contribute to human happiness: first, given the choice to lose your house or to lose your knowledge, which would you rather lose?  Your knowledge seems to be more intimately bound up with your very person and identity.  Again, speculative knowledge seems to be a possession unique to man alone, and whatever is the good perfective of human nature as such, ought to be a good specific to human nature.  For example, we should not expect to find man’s primary good in swimming or eating, since these are common to many species of animal.

So if truth known for its own sake really is a good for man, and if it is not something always readily accessible and easy to acquire and possess, then it is clear that an art is needed for the sake of acquiring and possessing this good, and that art is Logic. (One corollary from this conclusion is that Logic is an utterly different art from so-called “Symbolic Logic”, since Symbolic Logic does not have the attainment of truth as its end.)

At this point someone might object: But truth is something readily accessible and easy to acquire.  It is easy to come to truth, at least the truths necessary for living.  Many people live good productive lives without ever taking a course in Logic.  Aristotle agrees to some extent.  He quotes the proverb “Who will miss a door” in support of the opinion that truth is in a sense easy for everyone to find (Met. II.1).  Yet, while it is easy to grasp some part of the truth, it is difficult if not impossible for someone to grasp the whole truth.  And while it is easy to grasp realities and causes close to sensation, it is difficult to know realities and causes far from sensation.  For example, it is easy to know the cause of this man, his parents, but it is difficult to know the cause of man as such.  The case of truth is much like the case of eyesight.  Eyesight works fine so long as things are big enough and close enough.  But as soon as they get far away or very small, our eyes need some tool to help them see, whether it be a telescope or a microscope.  So Logic is necessary to know difficult truths, and even to know ordinary truths well.

I have been referring to Logic as an art so far, but it is also correct to call it a tool.  For every tool is useful for some good and proportions the agent using it to that good.  For example, a pencil proportions the hand to writing.  The hand is capable of moving itself in the way that forms letters, but it does not have the ability to leave marks on paper.  The pencil has the ability to leave marks on paper, but does not have the ability to move itself to form letters.  The pencil therefore proportions the hand to the good of writing.  So every tool is useful for some good and proportions the agent using it to that good.  But this is precisely what the art of Logic does: it proportions reason to the good of perfect knowledge of the truth.  So Logic is both art and tool, which is why Aristotle called his treatise on Logic the Organon, the tool.

Now just as the human body has many parts and activities proper to those parts (for example the foot for walking, the hand for grasping, the mouth for eating, etc.), so also human reason has distinct parts or powers with activities proper to those parts.  And just as tools are fashioned for different parts of the body based upon their respective activities (for example shoes for the feet, gloves for the hand, a straw for the mouth), so also tools are fashioned for the various powers and activities of reason.  There are three principal activities: 1) understanding what a thing is (corresponding to the tool of definition); 2) understanding the true and the false (corresponding to the tool of statement); and 3) reasoning (corresponding to the tool of argument or syllogism).  By the way, these three acts of reason are the first three human acts ever recorded in the book of Genesis: Adam first names the animals, then he makes a statement “this is bone of my bone, flesh of my flesh”, then he forms an argument “She shall be called woman because she was taken out of her man”.

The good of reason, namely truth known for its own sake, is going to be found in statements, since only statements signify the true.  So why do we need that third act of reasoning and the third tool of argument?  Because not all truths are equal.  Some are more perfective of human reason than others. The statements we know immediately without argument are very certain, but not very perfective of the mind: if knowing that “the whole is greater than the part” were sufficient to perfect man, there would be a lot of happy people out there.  But as it is, truths like “God exists” and “God is good” and the “human soul is immortal” are obviously much more connected to our happiness, but are in no way known without argument.  So if our minds are ever going to get anywhere really important we need this other tool of argument to get to new truths.

This is what Aristotle sets out to do in his Posterior Analytics.  And this is where those tools we called per se statements come in so handy.  Per se statements are the building blocks of demonstrations which get us to those really important truths in such a way that we see that those truths are certain and necessary.  The next part of my lecture will focus upon the tool of demonstration and the role that per se statements play in building a demonstration.

Demonstration

At the beginning of his Posterior Analytics, Aristotle lays out the particular kind of good we are seeking: episteme, perfect reasoned-out knowledge. He says: we are said to possess knowledge simply when “we know the cause of a fact, as the cause of that fact and no other, and the fact cannot be other than it is.”  In other words, knowledge of the proper cause of a necessary conclusion.  Given this is the good we are aiming at, Aristotle reasons backwards to the kind of tools we need to fashion.

He begins by defining the tool of demonstration as the kind of tool that can get us episteme, that is, a tool which can make someone know the proper cause of a necessary conclusion.  So demonstration is a syllogism causing episteme, perfect, reasoned-out knowledge.  This is a definition by final cause.  From the final cause we can reason to the materials from which it must be constructed.  A basilica must be constructed from the best and most noble materials.  A demonstration, likewise, must be constructed from the best and most noble premises.  Aristotle reasons to six qualities which such premises must have, namely the premises must be, in themselves: True, immediate, and first.  Again, in relation to the conclusion, these premises must be: better known than, causes of and prior to conclusion.  It is straightforward to see that these qualities must belong to the premises of a demonstration, once one sees that demonstration must cause episteme.  False premises or premises less known than the conclusion cannot make us know anything, much less know perfectly.  Mediated premises which do not cause the conclusion cannot make us know the proper cause with the certitude and clarity needed for episteme.

While these six attributes are required for perfect, reasoned-out knowledge, they are not sufficient. Recall that the concluded statement must be necessary and seen as necessary in order for the person who knows it to have perfect, reasoned-out knowledge.  Now one might happen to get a necessary conclusion out of contingent premises as in the following example:

Every circle is wooden
Every wooden thing has the same shape
Therefore, every circle has the same shape

It is perfectly possible that both those premises could be true.  There is nothing impossible about every circle being wooden, or every wooden thing having the same shape.  But such contingent premises could never cause us to see the conclusion as necessary.  So if the conclusion must be seen as necessary, then the premises must be necessary:

[73a21] Since, however, that of which there is scientific knowledge simply speaking cannot be otherwise, what is scientifically knowable according to demonstrative science would be necessary. But the demonstrable is that which we have by having a demonstration. Demonstration, then, is a syllogism from necessary things {premises}. We must grasp, then, from what and what sort demonstrations are.

So the premises of a demonstration have to be necessary.  But necessary in what sense?  St. Thomas brings up various attempts to account for the necessary in his commentary on the Peri Hermeneias: 

Concerning the possible and the necessary certain men have had diverse opinions:

For certain men distinguished them according to what happens, as Diodorus, who said that that is impossible which will never happen, but that is necessary which always will be, and that is possible which sometimes will be and sometimes not be.

But the Stoics distinguished the possible and the necessary based upon external prohibitions.  For they say that the necessary is that which cannot be prevented from being true.  But they say that the impossible is that which is always prevented from being true.  And finally, they say that the possible is what is able to be prevented or not. 

But both of these distinctions seem to be inadequate.  For the first distinction is based upon things which follow upon necessity and possibility.  For something is necessary not because it always will be, but rather it always will be because it is necessary.  And the same is clear regarding [the impossible and the possible].  But the second distinction assigns a reason which is from external somewhat accidental things.  For the reason why something is necessary is not because it does not have an impediment, but rather, since it is necessary it is not able to have an impediment.

And, therefore, others better distinguished the necessary and the possible according to the nature of things, so that they called that necessary which in its nature is determined only to being; while that is impossible which is determined only to non being; and that is possible which is not altogether determined to either, whether it be inclined more towards one than to the other, or hold itself equally to either one, which they called contingent to either one. (In Periherm., I, lect. 14, n.8)

The premises of a demonstration cannot be accidentally necessary.  That is, simply because of something extrinsic to the subject and predicate (for example, if God were to unite the soul and body of an animal for eternity by a miracle), or because the subject and predicate happen to be joined in every case (for example, the statement that every man exists after the year one million BC).  Demonstration must give the exact and necessary cause of the predicate belonging to the subject in the conclusion of a demonstration.  In order to fulfill this condition, Aristotle concludes that the premises of a demonstration must be: Said of all, through itself (kath auto, per se) and universal, or first.  More than anything, the fact that a statement is through itself guarantees the necessary and intrinsic connection between the subject and the predicate.

For [the predicate] cannot not belong [to the subject], either [it belongs] simply or [one of] the opposites belongs…so that if it is necessary to affirm or deny, it is necessary also that what are through themselves {per se} belong.

What does through itself (kath auto, per se) mean?  Does “through itself” mean that the statement is known through itself, and not through another statement (i.e., self-evident)?  Does it mean that the predicate belongs to the subject through no intermediate cause (per se as opposed to per aliud)?  Or does it mean that the predicate belongs to the subject because of what the subject is, rather than because of something outside what the subject is (per se as opposed to per accidens)?  It primarily means the last, though in some way the first two are also at work for premises of a demonstration.

[73b16] The things which are said to be “per se” in the case of things which are simply knowable scientifically, are [per se] thus: as belonging to the things predicated or being inhered in “through themselves” and by necessity.

It is manifest that from principles of this kind, namely per se, a demonstrative syllogism is made, which he proves in this way: Everything which is predicated either is predicated per se or accidentally, and those things which are predicated accidentally are not necessary. (In Post. Ana. Lect. 13).

The Kinds of Per Se Statements

Aristotle lays out four senses of per se in the Book I, chapter 4 of the Posterior Analytics:

[73a34] Whatever belong in the “what it is,” as line in triangle and point in line, is “per se.”  For the substance {essence, ousia} of these is from those, and they belong in the account saying what it is.

[73b36] [Per se], too, are those which belong in the account showing the “what it is” of the things which belong to them, as straight and curved belong to line and odd and even to number, and prime and composite, and equilateral and oblong. In the one case, line, and in the other case, number, belong to all these in the account saying what it is. And I say “per se” similarly in each of the other such cases; but whichever ones do not belong in either way are accidents, as musical or white in animal.

[73b5]   Moreover, what is not said according to some other underlying [I call “per se”], e.g., what is walking is something other than the [act of] walking, and the white thing than the [color] white; but the substance, and whatever signifies a “this something”, not being something else, is only the thing it is. Things which are not according to an underlying, then, I call “per se,” but things which are according to an underlying, “accidents.”

[73b10] Moreover, in another way, “per se” is what belongs to each thing “through itself” , while what is not “through itself” is accidental, e.g., if it thunders when one is walking, it is an accident. For it did not thunder through the walking, but this, we say, just happened.  But if something happens “through itself,” then also per se, e.g., if some animal should die when being slaughtered, then it is also according to being slaughtered, because it was through being slaughtered, but it does not just happen that the thing being slaughtered dies.

Let’s say something about each of these.  The first sense of per se belongs to statements in which the predicate is in the definition of the subject.  By way of additional examples: Man is an animal; a crow is a bird; double is a relation; five is a quantity, etc.  This is the easiest sense to see, for if the predicate signifies part of what the subject is, it obviously belongs to the subject through the subject itself.  What could be more the subject itself than the “what it is” of the subject?  So it is easy to see why statements like these are necessary.  St. Thomas observes in his commentary that in this case, the per signifies the mode of formal cause: for the parts of the definition are reduced to formal cause.

The second sense of per se belongs to statements in which the subject is in the definition of the predicate.  Here are some examples: a number is odd; a line is straight; a body is in motion; a surface is colored.  Number is in the definition of odd, body is in the definition of motion; surface is in the definition of color.  Not, of course, as signifying what odd or motion or color are, but as indicating their proper subject.  Odd exists in number and only in number; straight exists in line, and only in line, etc.  Once again, the necessity of these statements is easy to see: how could something which is part of the definition not belong necessarily to the thing defined?  Notice, however, that the necessity here is not always that one predicate or the other belong to the subject, but that either of the two.  For example, it is not necessary for a number to be odd, but it is necessary that it be either odd or even; and it is not necessary that a body be in motion, but it is necessary that it either be in motion or at rest.  Are there any cases where the subject is in the definition of the predicate and there is only one predicate which necessarily belongs to the subject?  I think so.  Let’s consider some examples: a triangle has interior angles equal to two right angles; a natural substance has accidents; dimensive quantity has shape; a living body is ensouled.  In each of these examples the single predicate must belong to that subject and only that subject.  St. Thomas notes that in this case the per signifies the mode of material cause, since a subject stands as matter to the attribute which is in the subject.

The third sense of per se belongs to things which exist through themselves, namely substances.  Is this a kind of statement?  For example the statement that “substance exists”?  Aristotle’s language seems to lead away from this interpretation, since he is talking about per se things, rather than per se statements: “what is not said according to some underlying”.  But this part of the Posterior Analytics is about statements, and in particular the kinds of statements which are necessary.  So what is this sense of per se doing in the list if it is not a kind of per se statement?  And besides, where would we include statements like “substance exists”?  Isn’t that an example of a per se statement?  We will have to return to this question later.

The fourth sense of per se belongs to statements in which the subject is the proper cause of the predicate.  The slaughtered animal died is the example Aristotle gives.  Dying is the proper effect of being slaughtered.  Here are some other examples: a swimming man is wet; a body is together with its shape; a sphere casts a circular shadow.  Notice that unlike the first two kinds of per se statements, the relationship between the subject and the predicate is not a whole/part relationship.  Dying is not in the definition of slaughter, or vice versa; swimming is not in the definition of wet or vice versa.  For this reason, it is harder to see why there is a necessary connection between the subject and predicate in such statements.  St. Thomas says that the per here signifies the mode of extrinsic cause, especially agent cause, as Aristotle’s example makes clear.

Questions about Per Se Statements

At this point I want to answer some questions which students often ask about per se statements. 

First, are per se statements premises of a demonstration or conclusions of a demonstration or both?  Per se 1 statements are always premises in a demonstration (since they are just part of the definition, like man is animal, so always immediate and self-evident), but per se 2 and 4 statements might be used as both.

Are per se statements always “said of all”?  That is, is the predicate always said of all the subject?  In a way yes and in a way no.  For instance, odd is not said of all numbers.  So if we take a statement like “a number is odd” to qualify as per se 2, then not every per se 2 statement is “said of all”.  However, one could make such statements to be “said of all” by giving them in an either or form: every surface is either colored or not; every number is either even or odd.

Are per se statements always immediate, that is, self-evident?  Per se 1 statements are always immediate, since it is self-evident that what is in the definition is predicated of the subject having that definition.  But per se 2 and 4 statements need not be immediate. What is essential to the notion of a per se statement is that it the predicate belongs to the subject on account of what the subject is and what the predicate is.

Some Problems with the Third and Fourth Senses of Per Se

So far what I have said is fairly uncontroversial, and easily verified by reading the text of Aristotle.  But some problems remain which I want to address, and the answers to these problems are not clearly found in Aristotle or, to my knowledge, in St. Thomas.

I mentioned before when treating the third sense of per se, that it seems out of place if it’s not a sense in which a statement is said to be per se.  I want to argue dialectically on both sides of this question to see more clearly why Aristotle sets down this third sense of per se.

Could this third sense of per se implicitly be the sense of per se belonging to statements asserting the existence of things, like “substance exists” or “nature exists”?  Based upon our experience we tend to think statements like these are necessary statements, so in principle they should be classifiable in one of the senses of per se statements. 

Are the statements “nature exists” and “substance exists” per se 1 statements?  Existence stands to substance in a way similar to the way substance stands to animal, and since an animal is a substance is per se 1, it seems that substance is a being would also be per se 1.  However, we should distinguish between two possible meanings of the statement “substance exists.”  On the one hand, it could mean “the notion of existence is included in the notion of substance,” (something like a nominal definition) in which case, this would be reduced to a per se 1 statement.  But that is not what we normally mean when we say that substance exists.  Rather, we are asserting real existence outside the mind and apart from our concepts.  But if this kind of existence were in the definition of anything, it would follow that it would be impossible for such a thing not to be.  And this is true only of the first being, God.  Only God has existence in his essence.  Therefore, the statement “substance exists” (taken in its natural sense) cannot be a per se 1 statement.

Could statements like “substance exists” be per se 2 statements?  It is easy to see that that can’t be the case since no particular kind of existing thing can be in the very definition of existence. 

Could statements like “substance exist” be per se 4 statements?  This would seem to require that existence belongs to a subject as an effect to its proper or immediate cause.  But no particular substance could be the cause of being itself, so it seems that statements like “substance exists” cannot be per se 4 statements either.

So if statements like “substance exists” are per se, and yet cannot be per se in any of the other senses enumerated by Aristotle, it seems to follow that there should be another sense of per se statement, and this is what Aristotle is giving us implicitly in the third sense of per se.

On the other hand, the language of Aristotle is unequivocal: this sense is a sense about what is not said.  And in the statement “substance exists”, existence is said of substance.  Aristotle is not talking about the relationship of a subject to a predicate at all, but the existence of a thing in itself.

So how do we untie this knot?  I think what Aristotle is doing is using manuductio to lead us from the second sense of per se to the fourth sense of per se through a sense of per se which is not a kind of statement but rather a kind of being, namely, through the fact that substances are the kind of being which exist per se.  In the fourth sense of per se it is difficult to see that the predicate belongs to the subject through the subject itself.  Does dying really belong to slaughtered animal through slaughtered animal itself?  Death is not in the definition of slaughter nor is slaughter in the definition of death.  So how can anyone expect us to see that dying goes together with slaughtered per se.  Well, in steps this other meaning of per se: substance is per se.  Like the first two senses of per se where the predicate belongs to the subject not through something other than the subject, this third sense of per se has nothing other than a subject, it is an ultimate subject.  But like the fourth sense of per se, the third sense of per se does not involve a part to whole relationship, where the predicate and subject are in one another the way a part is in a whole.  So now the mind can see that not every sense of per se involves a part to whole relationship.  And now we can better understand how a predicate which is not related to its subject as a part to its whole can still belong to the subject per se. 

But this still leaves us with the problem of statements like “substance exists”.  While the third sense of per se is not a kind of per se statement, nevertheless, a statement can be made about the existence of substance, and I think that statement is an instance of the fourth sense of per se.  If that is the case, this further bolsters the claim that the third sense of per se is a kind of bridge between the second and fourth senses.  So how can we see that the statement “substance exists” is per se in the fourth sense?  When we make the assertion that substance exists, we don’t mean “this particular substance exists as a matter of sense experience” (for that would not be a universal statement) but rather, we mean something like “such a thing as substance exists”.  This is a universal statement known in the understanding.  And while existence taken universally as “existence itself” is not a proper effect of substance, nevertheless, the proper kind of existence belonging to substance is a proper effect of the principles of substance being present (namely when the matter and form pertaining to the essence are present).  Thus, St. Thomas will define essence as “that in which and through which a thing exists” (De Ente, Ch.1).  So it is true to say that the kind of existence proper to substance is a proper effect of substance in the mode of an efficient cause.  And the same can be said of more limited subjects such as when we assert that “animal exists” or “man exists.”

Let’s return now to examine the necessity of per se 4 statements.  Can we really see the necessity of per se 4 statements?  Many very intelligent thinkers have denied that the kinds of statement Aristotle describes in this fourth sense of per se are truly necessary statements.  Hume, for example, argued that when one moving object strikes another, there is only a constant conjunction by which we associate the motion of the body which is struck as caused by the motion of the body which strikes it.  He argues that we can’t know with necessity that the first mover moves the thing it contacts.  Hume chooses that example because it is hard to see the necessity there, but what if we could find examples of per se 4 statements for which the necessity is obvious.  Take the following statements: “a thing cannot be and not be” (the famous principle of non-contradiction) and “the whole is greater than its part”.  Neither of those are examples of per se 1 or per se 2 statements.  In neither case is the predicate contained in the definition of the subject or vice-versa.  Rather, they are statements in which the predicate follows from the subject as an immediate consequence of what the subject is.  So if you had to put them in one of these senses of per se, you would put them in the fourth sense of per se.  And yet their necessity is absolutely evident.  For the most part, the difficulty with seeing the necessity of per se 4 statements is not seeing that they are necessary, but how or why they are necessary.  But again, that is not surprising since this is the last sense of per se statement, and it is related to the last sense of in: the way an effect is in its extrinsic cause.  What is extrinsic seems to be that last thing you would call “in”.  What is not a part of the “what it is” of a thing is the last thing you would expect belongs to that thing through itself.

Per Se Statements as Handles with which to Grasp Truth and Knowledge

I want to return to an aspect of a tool which I did not yet point out: every tool needs to have a part which our natural abilities can immediately touch.  The handle on a knife, or the trigger on a gun need to be immediately in contact with the ability of the hand to grasp.  Otherwise we could never use it.  Logic is no different.  It needs to have tools which can be immediately grasped by some natural ability of reason.  And per se statements have exactly that quality: they are the handles which reason uses to grasp truth and knowledge.  The necessity of per se 1 and 2 statements can be immediately grasped by the mind’s ability to see the necessary relationship of whole and part.  The necessity of per se 4 statements can be immediately grasped by the mind’s natural ability to discern a necessary relation between a cause and its proper effect, especially the immediate cause of a thing.  So there is a different ability by which we see the necessity of per se 4 statements.  It is related to the natural ability to perceive the order between cause and effect.  Is a thing good because we want it or do we want it because it is good?  Is reason the cause of risibility, or is risibility the cause of reason?  Just as we see the order of cause and effect with necessity, so too we see with necessity that one thing is the cause and the other its effect.  So without per se statements, we will never be able to grasp truth firmly, in such a way to possess certain knowledge.  We will never have a handle on truth.

Conclusion

Socrates once said in the Meno that “true opinions, for as long a time as they should stay put, are a fine thing and accomplish all kinds of good things.  Yet much of the time they are not willing to stay put, but run away out of the human soul, so that they are not worth much until someone should tether them with causes by reasoning.” (Meno 97e).  Aristotle has fashioned tools by which we can tether these truths permanently to our soul.  And just as an artisan must look not only at the end or purpose of a tool, but also the ability which it proportions to that end, so Aristotle, the master craftsman, has fashioned tools perfectly suitable to our natural abilities and to the end at which they aim: these tools are per se statements.  These statements together with our natural abilities are the roots which keep our knowledge firmly tethered to experience and make our knowledge really to be knowledge.

 

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