Philosophy 5340

Analysis, Analytically Basic Concepts, and Theoretical Terms

Topic 3 - Part 1: Analytically Basic Concepts






1.  The Concept of Analysis

1.1  The Classical Concept of Analysis

( (1) The relation of analysis is transitive and asymmetric:

(a) If concept A can be analyzed in terms of some set of concepts, B, and if all of the concepts in set B can be analyzed in terms of the concepts in some set of concepts, C, then concept A can be analyzed in terms of the set C of concepts.

 (b) If concept A can be analyzed in terms of some set of concepts, B, then none of the concepts in set B have an analysis that involves concept A.

(Another way of saying that the relation of analysis is asymmetric is to say that the relation of analysis has an intrinsic direction.)

    An immediate consequence of (1) is

(2) In analyses, there can be no looping around in circles.

    Another feature of the classical concept of analysis is

(3) No infinite regress involving concepts that are analytically more and more basic is possible.

    A consequence of (2) and (3) is

(4) If there are any concepts, then there are concepts that are analytically basic.

1.2  Alternatives to the Classical Concept?

An alternative view is that classical analysis is impossible.  What one has is just a web of interrelated concepts, none of which is prior to any other.  So analysis is merely relative.  Any concept can be analyzed; it is just a matter of choosing the right conceptual framework.  (Compare Nelson Goodman, discussed below.)

1.3  Goodman’s New Riddle of Induction: The Problem of Gruesome Concepts

1.3.1  Goodman’s Own Formulation

    In his book Fact, Fiction, and Forecast, Nelson Goodman set out a new problem that any attempt to justify induction must deal with.  Here is how Goodman formulated his “new riddle of induction”  in chapter III, section 4:

It is the predicate "grue" and it applies to all things examined before t just in case they are green but to other things just in case they are blue. Then at time t we have, for each evidence statement asserting that a given emerald is green, a parallel evidence statement asserting that that emerald is grue. And the statements that emerald a is grue, that emerald b is grue, and so on, will each confirm the general hypothesis that all emeralds are grue. Thus according to our definition, the prediction that all emeralds subsequently examined will be green and the prediction that all will be grue are alike confirmed by evidence statements describing the same observations. But if an emerald subsequently examined is grue, it is blue and hence not green.

    Goodman also goes on to introduce the term “bleen: “Consider...the predicate `bleen' that applies to emeralds examined before time t just in case they are blue and to other emeralds just in case they are green.”

    It appears, then, that Goodman’s definitions of the terms “grue” and “bleen” can be put as follows:

X is grue at time t = def. Either X is observed at time t and is green at time t, where t is earlier than t0, or X is blue at time t.

X is bleen at time t = def. Either X is observed at time t and is blue at time t, where t is earlier than t0, or X is green at time t.

(Here I have used ‘t0’ where Goodman uses ‘t’, since I want to use ‘t0’ to refer to the fixed time.)

1.3.2  A Slight Reformulation

    I think that bringing in the idea of observation is an unnecessary complication, so I prefer to put things in terms of the following definitions instead:

X is grue at time t = def. Either X is green at time t and t is earlier than t0, or X is blue at time t and t is either t0 or later than t0.

X is bleen at time t = def. Either X is blue at time t and t is earlier than t0, or X is green at time t and t is either t0 or later than t0.

1.3.3 Grue and Bleen as Highly ‘Artificial’ Concepts

        Regardless of whether one uses Goodman’s original definitions, or my revised definitions, the concepts of being grue and of being bleen certainly strike one as artificial concepts that do not correspond to genuine properties, and that do not “carve nature at the joints,” since the above analyses involve, in addition to the concepts of green and blue, the idea of temporal priority, along with a reference to some special time t0, plus the idea of disjunction.  As a result, while two things that are green necessarily resemble one another rather closely, two things that are grue need not do so, since one may be green, and the other blue.

1.3.4 Goodman’s Response

        Goodman’s response to this charge of artificiality is as follows.  First, he points out that the following necessarily true, analytically equivalences follow from his definitions:

X is green at time t  ⇔  Either X is observed at time t and is grue at time t, where t is earlier than t0, or X is bleen at time t.

X is blue at time t  ⇔  Either X is observed at time t and is bleen at time t, where t is earlier than t0, or X is grue at time t.

        Secondly, he says that given those analytical equivalences, nothing prevents one from treating them as defining the concepts of being green and of being blue, so that one has:

X is green at time t = def. Either X is observed at time t and is grue at time t, where t is earlier than t0, or X is bleen at time t.

X is bleen at time t = def. Either X is observed at time t and is bleen at time t, where t is earlier than t0, or X is grue at time t.

        Precisely the same sort of claim can be advanced given my alternative definitions of “grue” and “bleen”.  Thus, , given those definitions, one has the following analytical equivalences:

X is green at time t  ⇔  Either X is grue at time t and t is earlier than t0, or X is bleen at time t and t is either t0 or later than t0.

X is blue at time t  ⇔  Either X is bleen at time t and t is earlier than t0, or X is grue at time t and t is either t0 or later than t0.

        One can then go on to claim that, given those analytical equivalences, nothing prevents one from treating them as defining the concepts of being green and of being blue, so that one has:

X is green at time t  = def. Either X is grue at time t and t is earlier than t0, or X is bleen at time t and t is either t0 or later than t0.

X is blue at time t  = def. Either X is bleen at time t and t is earlier than t0, or X is grue at time t and t is either t0 or later than t0.

    The upshot is that there is a complete syntactical parallelism there.  The definitions of the concepts of being grue and being bleen in terms of the concepts of being green, being blue, and temporal priority, can be transformed into what purport to be definitions of the concepts of being green and being blue in terms of the concepts of being grue, being bleen, and temporal priority, and vice versa, simply by interchanging the terms “green” and “grue”, and, similarly, the terms “blue” and “bleen”.

1.3.5 Conceptual Priority

        Goodman is right that there is a complete syntactical parallelism here, and that what purport to be definitions of the concepts of being green and being blue can be given that have precisely the same form as the definitions of the concepts of being grue and of being green.  But do the concepts of being green and of being blue really involve reference to some special time?  And do the concepts of being green and of being blue really involve the concept of temporal priority.

        I think the latter question is sharpened if one notices that while, when one is attributing properties to persisting objects, one needs to specify the time at which something has, for example, a certain shape, if there are instantaneous objects, no specification of a time is needed.  Thus, while if one is talking, for example, about apples, one needs to say things like, “The apple was green at noon on June 12”, so that the predicate green is a dyadic predicate whose logical form can be represented as “Green(x, t)”.  By contrast, if one is using “green” as a predicate of instantaneous objects, the logical form of the predicate can be represented as “Green(x)” –   a monadic predicate, with no place for a temporal reference.  So why would think that the concept of being green involved any temporal concepts, including the concept of temporal priority?

        Still, Goodman’s point will be that if there are instantaneous objects, one can introduce monadic predicates of the form “Grue(x)” and  “Bleen(x)”.  The complete syntactical parallelism remains.

1.3.6 Solving the New Riddle of Induction

        The new riddle of induction, if successful, shows that there is no rational justification for induction, since for any inductive inference that one wants to make, and claims to be sound, a completely parallel induction of the same logical form can be described, and one whose conclusion is incompatible with the conclusion of the original induction.

        It seems to me that the only way of answering Goodman’s challenge is by arguing that some concepts are more fundamental, in some sense, than others.  How can this be done?  The only way, I think, is by arguing that there are some concepts that are analytically basic.  But what notions can be appealed to in order to make sense of that notion?

        Rudolf Carnap, the author of many articles on logical probability and inductive logic, and of the book-length treatment of logical probability, The Logical Foundations of Probability, appealed to the idea of absolute simplicity, and claimed, in effect, that greenness of a specific shade is an absolutely simple property, and that a concept that functions just to attribute such a property to something is an analytically basic concept.

        How can one explain this notion of absolute simplicity?  One idea is an approach along the following lines.  First, one needs the notion of exact resemblance, viewed as a relation between property instances.  Secondly, given that notion, one can define the concept of a property as follows:

P is a property = def. It is necessarily the case that if P1 and P2 are instances of P, then P1 exactly resembles P2.

Thirdly, given the concept of a property, one can define the concept of a simple property as follows:

P is a simple property = def. There is no property Q such that (1) x’s having property P entails x’s having property Q, but (2) x’s having property Q does not entail x’s having property P.

        Alternatively – though the two approaches may, in the end, turn out to be closely related, if not identical – one can attempt to explain, as David Armstrong, for example, would, the idea of a universal, and then, given that idea, one could parallel the above definition of a simple property to define the idea of a simple universal.

2. Criteria for Analytically Basic Concepts and Terms

2.1 Analytically Basic Concepts and Terms and the Verbal Indefinability Criterion

        It is natural to divide terms and concepts into logical terms and concepts and non-logical, or descriptive, terms and concepts.  It seems to me that very different accounts have to be offered of the explanation of logical concepts and terms on the one had, and descriptive concepts and terms on the other.  In what follows I shall consider only the case of non-logical terms and concepts.  For the sake of brevity, I shall generally simply say “terms or concepts”, but the discussion that follows should be taken throughout as concerned only with non—logical/descriptive terms and concepts.

        Where should analysis of descriptive terms or concepts start?  Of the descriptive terms or concepts that one has, which of them should form the starting point for the analysis of other terms or concepts?  Which descriptive terms or concepts are analytically/semantically basic?

        The meaning of many descriptive terms can be explained in terms of other terms.  But in the case of some descriptive terms, verbal definition does not seem helpful.  One needs, it certainly seems, to acquire an understanding of some descriptive terms by what is often referred to as "ostensive definition" – by being exposed to situations where the term is actually being used.

        But what counts as an "ostensive definition"?  One view is that one has an ostensive definition of a term where a person is perceptually acquainted with the property or relation in virtue of which the term in question applies to a situation.  As a characterization of ostensive definition, this is probably fine.  However, so understood, many terms that can be ostensively defined can also be defined verbally.  If there is to be a class of analytically/semantically basic terms in a strong sense, it will have to consist of terms that can only be defined ostensively.  Is there such a class?

        The idea behind this question can be brought out if one compares, say, the terms "car", or "table" with the term "red".  Most people will acquire an understanding of the terms “car” and “table” ostensively, but that understanding can also be acquired via a purely verbal definition.  In this respect, such terms seem to differ from a term like "red", since the meaning of the term "red", it might seem, cannot be conveyed via a purely verbal definition.

    This suggests the following thesis:

The Verbal Indefinability y Criterion

A term is semantically basic if and only if the meaning of the term cannot be conveyed to another by a purely verbal definition.

2.2 The Immediate Perceivability Criterion

        The above discussion suggests, however, another criterion.  This other criterion involves a distinction between (a) direct, or immediate, or non-inferential perception, on the one hand, and (b) indirect, or mediate, or inferential perception, on the other.  Exactly how this distinction is best drawn is a somewhat tricky matter, as we shall see in a later seminar, but here we can think in terms of a distinction between (a) perceptual beliefs that involve no inference from other perceptual beliefs and (b) perceptual beliefs that do involve inference from other perceptual beliefs.

Consider a case where you are looking at an orange.  One perceptual belief that you acquire in such a situation is the following:

(a) The belief that there is a certain type of three-dimensional object in front of you – namely, an orange.

Does that perceptual belief involve inference or not?  Initially many people would be tempted to say that it does not involve any inference.  But in thinking about that question, it is important to note that the term “inference” here is used to indicate a certain sort of causal relationship between beliefs, and does not imply the presence of any thoughts, or any conscious process of inference.

    With that in mind, consider the following, closely related belief:

(b) The belief that there is a round, physical expanse that is orange in color in front of one.

When one acquires the belief that there is a certain type of three-dimensional object in front of you – namely, an orange – it will typically be the case both that

(1) One also acquires the belief that there is a round, physical expanse that is orange in color in front of one

and that

(2) One would not have acquired the first of those beliefs if one had not acquired the second.

    The upshot is that while the belief that there is a round, physical expanse that is orange in color in front of one may be a non-inferential perceptual belief, the belief that there is a certain type of three-dimensional object in front of you that is an orange cannot, it would seem, be a non-inferential perceptual belief.

This suggests the following thesis:

The Immediate Perceivability Criterion

A concept is semantically basic if and only if the concept enters into a proposition that can be the content of an immediate perceptual belief.

    But, as we shall now see, this criterion appears to be unsound.

2.3 What Kinds of Terms Are Semantically Basic?

        Consider the term "red".  Does that term really present us with a case where verbal definition is impossible?  There are two closely related lines of thought that suggest that terms such as "red", when applied to physical objects, can, in appropriate circumstances, be verbally defined:

(1) The Blind, or Color-Blind Person;

(2) A World without Red Objects.

2.3.1 The Blind, or Color-Blind Person

        Consider the case of the person who is red/green color-blind.  Couldn't one teach such a person, by appropriately stimulating his or her brain, what it was like to have an experience of the red variety, or an experience of the green variety?  And then, having done that, couldn't one explain what it was for a physical object to be red, and what it was for it to be green?  For in the case of a color-blind person, one could say that redness, understood as a property of physical objects, is a property of the surface of objects – just as blueness is – the difference being that redness gives rise, under normal conditions, to a different sort of experience – namely, an experience of the red variety.

        In the case of a person who, rather than being color-blind, was blind from birth, one couldn't compare redness with other color properties that the person was familiar with.  But even with that possibility removed, couldn't one still explain what it is for a physical object to be red simply by reference to the sort of experience – an experience of the red variety – that a physical object gives rise to under normal conditions, and where one gives the blind person an understanding of what such experiences are like by appropriately stimulating his or her brain?

        In both cases, one would have to explain what normal conditions were.  For without the reference to normal conditions, the resulting account would not be satisfactory: a white object illuminated with red light will give rise to an experience of the red variety, but what one wants to say in such a case is merely that the white object looks red under those circumstances, and not that it is red.

        How can the concept of normal conditions be explained?  Exactly what the right answer is, is a slightly tricky question, but one can certainly see some promising starting points.  Thus, one possibility would be to equate normal conditions in the case of color perception with bright sunlight.  Another idea is to equate normal conditions with those under which one can make maximal color discriminations.  (It is possible – though not, I think, likely in the case of color – that precisely what conditions make for maximal discrimination depends upon the properties that one is perceiving.)

2.3.2 A World without Red Objects.

        Consider a world that contains no red objects.  Once again, one could appeal to the possibility of directly stimulating a person's brain in such a way as to produce experiences of the red variety.  But there is another possibility that would be less invasive.  Stare at a green object, and then look at a white background.  The result is a red after-image.  One could then define the term "red", as applied to physical objects, as picking out that property of objects that, under normal conditions of observation, gives rise to an experience that has the quality that characterizes red after-images.

        The conclusion, in short, seems to be, first, that a person who never saw red physical objects could nevertheless come to understand perfectly well what it is for a physical object to be red, and secondly, that even in a world devoid of red physical objects, it would be possible to come to understand what it would be like for there to be red objects.  Understanding what it is for a physical object to be red does not presuppose, in short, either acquaintance with that property, or even that there is any instantiation of that property, anywhere, at any time.

        Consider, in contrast, redness as a property of sense experiences.  If one had never had that type of experience, it would seem that no verbal definition could supply one with an understanding of what the experience would be like.

2.3.3 The Possibility of Acquiring an Understanding of Semantically Basic Terms without Having any Relevant Experiences

       It is very natural at this point to conclude that one cannot understand what it is to have an experience of the red variety unless one has had such an experience, and that, in general, one cannot understand the meaning of any semantically basic term – or grasp any semantically basic concept – without having an experience of the relevant property or relation.  That claim, however, is exposed to a certain objection – namely, that a person might come to acquire the concept of an experience of the red variety if his or her brain were changed so that it was similar in the relevant respect to the brain of someone who did have the concept of an experience of the red variety.  So isn’t it the case that one could in principle understand semantically basic terms, and grasp semantically basic concepts, even if one had never had any experience of the relevant property or relation?

        In a certain sense, such a person would have the relevant concepts, and would understand the term “red” – both as a term applied to physical objects, and as a term applied to experiences – since, if confronted with a red physical object, or if he or she had the relevant sort of experience, that person would be able to say right off that an apple was red, or that he or she was having an experience of the red variety.  But I am inclined to say that until such a person either (1) has the relevant experience, or (2) imagines having such an experience, he or she does not understand what redness is, though he or she does possess the relevant concept.

2.4 Direct Acquaintance and Semantically Basic Terms and Concepts

        Recall the following criterion:

B. The Immediate Perceivability Criterion

A concept is semantically basic if and only if the concept enters into a proposition that can be the content of an immediate perceptual belief. 

       In his book Perception, Frank Jackson defended the view that the immediate objects of perception are sense data.  If Jackson were right about that, then the Immediate Perceivability Criterion would, I think, be correct.  But while I think that Jackson is right that the immediate objects of awareness are mental objects, I am inclined to think that it is wrong to apply the term “perception” to awareness of one’s own mental states, or parts thereof.  My reason for disagreeing with Jackson on this matter is that I am inclined to accept some form of the causal theory of perception, as defended by H. P. Grice, according to which one does not perceive an object unless that object causally gives rise to an experience.

        Because of this, I think that the immediate perceivability criterion needs to be replaced by one that is formulated either in terms of direct awareness, or in terms of direct acquaintance.

        Formulated in terms of direct awareness, the criterion can be stated as follows:

C.  The Direct Awareness Criterion

A concept is semantically basic if and only if the concept applies to something by virtue of that thing’s having some property such that one can be directly aware of instances of that property (and similarly for relations).

What is direct awareness?  The answer is roughly as follows:

(1) S is aware of x = def.

(a) S has the thought or the belief that x exists.

(b) That thought or belief is caused by x.

(2) S is indirectly aware of x = def.

(a) S is aware of x

(b) There is some y such that S is aware of y, and where x caused S to be aware of x by causing S to be aware of y.

(3) S is directly aware of x = def.

(a) S is aware of x

(b) There is some causal process running from x to S’s awareness of x, and that does not involve any thought or belief that y exists, where y is anything that is distinct from x

        Note that these definitions allow it to be the case that there is something that, at a given time, one is aware of both directly and indirectly.

        Alternatively, formulated in terms of direct acquaintance, the criterion can be stated as follows:

D.  The Direct Acquaintance Criterion

A concept is semantically basic if and only if the concept applies to something by virtue of that thing’s having some property such that one can be directly acquainted with instances of that property (and similarly for relations).

        But what is direct acquaintance?   The notion of direct acquaintance presupposes the idea of phenomenal, sensuous, non-dispositional, intrinsic, qualitative properties, including color properties.  In the case of color properties, it is natural to think of them as located on the surfaces of objects, since that is where they appear to be.  Physics, however, provides very good reason for believing that phenomenal, sensuous, non-dispositional, intrinsic, qualitative color properties are not in fact located on the surfaces of physical objects.  If they exist, then, it seems that they must instead be properties that are located within experiences.

        If that is where phenomenal, sensuous, non-dispositional, intrinsic, qualitative properties are located, then they are spoken of as qualia.  That there are qualia is a controversial question in contemporary philosophy of mind.  If qualia do not exist, then there may be nothing to be directly acquainted with, though some philosophers would say that one can be directly acquainted not just with property instances, but also with properties.  By contrast, the notion of direct awareness is such that the existence of phenomenal, sensuous, non-dispositional, intrinsic, qualitative properties is not required in order for there to be something of which one is directly aware.

        In any case, given the idea of phenomenal, sensuous, non-dispositional, intrinsic, qualitative properties – ‘qualitative properties’, for short – one can give the following definition of direct acquaintance:

S is directly acquainted with x = def.

(a) S has an indexical thought or belief about x,

(b) That indexical thought or belief is caused by x,

and

(c) x is a phenomenal, sensuous, non-dispositional, intrinsic, qualitative property, either simple or complex.

        Why “either simple or complex”?  The reason is that one’s visual experiences, for example, typically involve instances of color properties that stand in spatial relations to one another.  So among the properties, instances of which one can be directly acquainted  with, is, for example, the property of consisting of an instance of qualitative greenness between two instances of qualitative redness

2.5 Strong Ostension Versus Weak Ostension

2.5.1 Ostensive Definition Based upon Erroneous Perception

           In addition to the arguments set out in sections 2.3.1 and 2.3.2, there is a third consideration that throws light upon ostensive definition, and which is as follows.

          Regardless of whether there are any red objects in the world, there may be objects that look red under various circumstances, and if the term "red", as a predicate of physical objects, were applied to such objects, and if there were, in addition, a mistaken belief that the conditions were normal, then a person would presumably acquire the concept of what it is for an object to be red, even though he or she had never been exposed, not to any object that really was red, but only to objects that looked red.  This could never happen, in contrast, in the case of "red" where one is dealing with a predicate of sensory experiences.  So there is a distinction between terms that can be ostensively defined in circumstances where the term does not truly apply to the object in question, and terms that can only be ostensively defined in circumstances where they truly apply to the objects in question.

        It may be a good idea, accordingly, to introduce the following distinction between weak ostensive definition and strong ostensive definition:

A term, T, is defined via weak ostension if and only if a person acquires an understanding of the meaning of the term by seeing it used in situations to which it does not truly apply.  (The situations may very well be ones where its use is reasonable, or appropriate, given what the user knows or justifiably believes.)

(2) A term, T, is defined via strong ostension if and only if a person acquires an understanding of the meaning of the term by seeing it used in situations to which it does truly apply.

2.5.2 Some Possible Theses Concerning Definition Via Ostension

        Given this distinction, consider whether any of the following theses are true:

1.  If a term is definable only via ostension, it is definable only by strong ostension, and not via weak ostension.

2.  If a term is definable by strong ostension, but not via weak ostension, then it is definable only via ostension.

3.  A term is definable only via ostension if and only if it is definable by strong ostension, but not via weak ostension.

4.  Some terms can be defined only via strong ostension.

        Since thesis 3 is the conjunction of theses 1 and 2, thesis 3 can only be true if both 1 and 2 are true.  I shall argue that 1 is true, but that 2, and so 3, are false.  I shall also argue that thesis 4 is true.

An Argument for Thesis 1

        To think about whether this first thesis is true, consider a term, T, which can be defined via weak ostension, so that a person can come to understand the term T by seeing it used in certain situations, even though the term T does not truly apply to anything in that situation.  If this is the case, then, in the first place, there must surely be something that is true about the situations in question that makes the use of the term T appropriate, or reasonable.  If so, then it would seem that one should be able to describe what it is about the situations in question that makes it appropriate to use the term T, even though it does not actually apply to anything in those situations.  So let us use the term S to refer to whatever that relevant feature is.

        Consider a concrete case.  Earlier, we saw that one can acquire an understanding of the term “red” as applied to physical objects in situations in which no red physical object was present.  But what was present in all such cases was an experience of the red variety.  So what S would be in this case would be a term – call it “red*” – that picks out qualitative redness, where the latter, it turns out, is a property of parts of one’s visual field.

        But if the presence of qualitative redness is to make it appropriate, or reasonable, to believe that there is a red physical object that one is perceiving, must there not be some relation between the term “red*” that picks out the relevant feature and the term “red”, in virtue of which the presence of qualitative redness – the property picked out by the predicate “red*” – raises the likelihood (at least to a sufficient degree) that some red physical object is present?  But how can this be the case unless there is an analytical connection between the property of being red* and the property of being red?  The term “red*”, however, is analytically basic, and cannot be analyzed, and so there can be an analytical connection between the terms “red*” and “red” only if the term “red” is analyzable, and analyzable in a way that involves the term “red*”.  So the term “red’ must be verbally definable.

        It seems to me that this argument is a perfectly general one, so that whenever a term T is definable via weak ostension there must be a term S that, first of all, picks out the property or relation in situations that makes it appropriate or reasonable to apply the term T even thought the situations in question do not involve anything to which the term T truly applies, and, secondly, is such that it is possible to analyze the term T in such a way that the analysis involves the term S.  We have, therefore, the following conclusion:

5.  If a term is definable via weak ostension, then it is verbally definable.

Or, equivalently:

6.  If a term is not verbally definable, then it is not definable via weak ostension.

        But the following thesis is certainly true:

7.  If a term is definable only via ostension, it is not verbally definable.

        Theses 6 and 7 then entail:

8. If a term is definable only via ostension, it is not definable via weak ostension.

        But the following thesis is also true:

9.  If a term is definable only via ostension, it is definable either by strong ostension or via weak ostension.

     Theses 8 and 9 then entail:

1.  If a term is definable only via ostension, it is definable by strong ostension, but not via weak ostension.

So the first thesis is true.

An Argument against Theses 2 and 3

    The objection to thesis 2, and so also to thesis 3, which entails thesis 2, is that there can be terms that correspond to conjunctive concepts.  One might, for example, use the term “green-and-round*” as a term that applies to a part of one’s visual field if and only if that part is both qualitatively green and also round.  The meaning of that term can be learned via strong ostension, but not via weak ostension.  But if one has learned the meanings of the terms “green*” and “round*” via strong ostension, then one can acquire an understanding of the meaning of the term “green-and-round*” verbally by the following definition:

“X is green-and-round*” = def. “X is green* and X is round*”

So thesis 2 is not true: terms that can be learned via strong ostension but not via weak ostension can in some cases be verbally defined.

An Argument for Thesis 4

        The argument for the fourth and final thesis requires the following thesis, which I shall not argue for, but which I believe is true:

10.  Every term is in principle definable, either verbally or via ostension.

        Some terms, however, are not verbally definable.  Consider, for example, the term “red*” – the predicate whose meaning is connected with the property of qualitative redness.  So we have:

11.  Some terms are not verbally definable.

        Theses 10 and 11 then entail:

12.  Some terms are only definable via ostension.

        Recall, however, thesis 1:

1.  If a term is definable only via ostension, it is definable by strong ostension, but not via weak ostension.

Theses 12 and 1 then entail:

4.  Some terms can be defined only via strong ostension.  

2.6 The Main Conclusions

        The above lines of thought have suggested certain conclusions concerning what sorts of terms should be taken as the semantical basis for the definition of all other terms.

1.  The first conclusion is that the terms that should be taken as semantically basic are those terms that a person cannot come to understand via any verbal definition.  

2.  A second conclusion is that the following very natural proposal is unsound:

The Immediate Perceivability Criterion

A concept is semantically basic if and only if the concept enters into a proposition that can be the content of an immediate perceptual belief.

3. A third conclusion is that the Immediate Perceivability Criterion needs to be replaced by one of the following  two alternatives:

C.  The Direct Awareness Criterion

A concept is semantically basic if and only if the concept applies to something by virtue of that thing’s having some property such that one can be directly aware of instances of that property (and similarly for relations).

D.  The Direct Acquaintance Criterion

A concept is semantically basic if and only if the concept applies to something by virtue of that thing’s having some property such that one can be directly acquainted with instances of that property (and similarly for relations).

The Direct Acquaintance Criterion

A concept is semantically basic if and only if the concept applies to something by virtue of that thing’s having some property that is such that one can be directly acquainted with instances of that property (and similarly for relations).

4. A fourth conclusion is that terms that are semantically basic can only be defined via strong ostension.

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3.  Some Examples of the Importance of the Idea of Analytically Basic Concepts
       
        A first example of the importance of the idea of analytically basic concepts is from metaphysics – specifically, the philosophy of time.

        Consider the concept of the future.  Whatever may be possible, you and I have not perceived any future events, and so have not perceived an instance of the property of lying in the future.  A fortiori, we have not immediately perceived any instances of that property.  Nor are we either directly aware of, or directly acquainted with, any instances of that property.  Consequently, the concept of the future must be verbally definable.

        Doing so is relatively simple.  Thus, though I favor a somewhat deeper account, it is natural to say that the concept of the future is the concept of what is later than the present.  But many positions in philosophy of time cannot offer such an answer.  One that cannot is presentism, where this is the view that only presently existing states of affairs exist.   Other approaches that also cannot do so are tensed views that attempt to analyze the later than relation in terms of the concepts of pastness, presentness, and futurity, for then defining the future as what is later than the present would land one in a circle.
 
        A second example is from ethics.  G. E. Moore maintained that there were “non-natural” properties of goodness and badness of which one is directly aware, and he also held that the terms “good” and “bad” could not be defined.  But if that were right, then   how could J. L. Mackie’s error theory be true, for it asserts that there are no objective values.  So it is only possible for Mackie’s error theory to be true if normative terms are not analytically basic.
 
        But if normative terms are not analytically basic, how can then be defined?  If one defines them in terms of non-normative, descriptive terms, won’t that imply that normative states of affairs analytically supervene upon non-normative ones – a view that many ethical theorists certainly want to reject?

        The answer is that in the 20th century a method was discovered for defining theoretical terms, and one that does not entail that theoretical states of affairs analytically supervene upon non-theoretical states of affairs.  Consequently, one can use that method to define normative concepts in such a way that the truth of normative propositions does not logically supervene upon non-normative facts.