Moore, Russell & Early Wittgenstein

Answer : Wittgenstein discusses what can and cannot be expected of a logical notation. Here we get a clearer idea of what atomic facts really are, as Wittgenstein is forced to grapple with the issue of how we represent them logically in propositions. As we saw earlier, an atomic fact is a relational structure of “objects”, which individually can only be defined in terms of their potential to combine into such structures. Elementary propositions, since they represent atomic facts, are likewise combinations of “names”, combined into relational structures, where each name refers to an object. But just as an object cannot exist apart from the whole relational structure, a name does not by itself refer. It only refers by virtue of how it is used, so as to form such relational structures.” a” in itself is just a notational device and cannot on its own have meaning. “a=a”, then, cannot possibly be an elementary proposition. There is no relational structure here, nothing with a sense that it could be true or false. We call such a proposition a “tautology”, since it is true for all truth assignments of elementary propositions. If, on the other hand, a proposition were false for all truth assignments of elementary propositions, then it would be a “contradiction”. Neither of these extreme kinds of propositions, according to Wittgenstein, really have sense. Since a tautology is always true, it literally says nothing about the world. A contradiction likewise says nothing about the world, since it cannot possibly be true. Tautologies and contradictions show through their logical form that they say nothing. Yet in between certainty (tautology) and impossibility (contradiction) lies the possible: the propositions with sense (they can possibly be true or false, but which they are cannot be shown logically).

Answer : Moore’s main intention is to refute idealism as it is based on hypothetical notions and makes life more complex than it is, as Moore says. An important aspect of Moore’s rejection of idealism was his affirmation of a ‘common sense’ realist position, according to which our ordinary common-sense view of the world is largely correct. Moore begins by listing a large number of ‘truisms’ such as that ‘the earth had existed also for many years before my body was born’. Concerning these truisms he then asserts, first, that he knows them for certain, second, that other people likewise know for certain the truth of comparable truisms about themselves and, third, that he knows this second general truth (and, by implication, others do too). So the truth and general knowledge of these truisms is a matter of common sense. Having set out these truisms, Moore then acknowledges that some philosophers have denied their truth or, more commonly, denied our knowledge of them (even though, according to Moore, they also know them) and he attempts to show that these denials are incoherent or unwarranted. These claims might seem to leave little space for radical philosophical argument. But Moore argues that his defense of common sense leaves completely undecided the question as to how the true propositions which make up the common sense view of the world are to be analyzed; the analysis may be as radical as one likes as long as it is consistent with the truth of the propositions analyzed. Thus, for example, he is content to allow that philosophical argument may show that a phenomenological analysis of propositions about the physical world is correct. This last point shows that Moore’s defense of common sense is not as much of a constraint on philosophical theory as one might at first have thought; for philosophical analysis can reveal to us facts about the ‘principal or ultimate subject’ of a true proposition which are by no means what common sense supposes. Moore devoted to working out what counts as an ‘external object’, and Moore claims that these are things whose existence is not dependent upon our experience. So, he argues, if he can prove the existence of any such things, then he will have proved the existence of an ‘External World’.

Answer : Definite description is a denoting phrase in the form of “the X” where X is a noun-phrase or a singular common noun. The definite description is proper if X applies to a unique individual or object. For example: “the first person in space” and “the 42nd President of the United States of America”, are proper. The definite descriptions “the person in space” and “the Senator from Ohio” are improper because the noun phrase X applies to more than one thing, and the definite descriptions “the first man on Mars” and “the largest prime number” are improper because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content. France is a republic, and has no king.

Consider the statement “The present King of France is bald.” Is this statement true? Is it false? Is it meaningless? It does not seem to be true, for there is no present King of France. But if it is false, then one would suppose that the negation of the statement, that is, “It is not the case that the present King of France is bald,” or its logical equivalence, “The present King of France is not bald,” is true. But that seems no truer than the original statement. Is it meaningless, then? One might suppose so (and some philosophers have; see below), because it certainly does fail to denote in a sense, but on the other hand it seems to mean something that we can quite clearly understand. Bertrand Russell, extending the work of Gottlob Frege, who had similar thoughts, proposed according to his ‘theory of descriptions’ that when we say “the present King of France is bald”, we are making three separate assertions:

There is an x such that x is the present King of France.

For every x that is the present King of France and every y that is the present King of France, x equals y (i.e. there is at most one present King of France).

For every x that is the present King of France, x is bald.

Since assertion 1 is plainly false, and our statement is the conjunction of all three assertions, our statement is false. Similarly, for “the present King of France is not bald”, we have the identical assertions 1 and 2 plus 3. For every x that is the present King of France, x is not bald so “the present King of France is not bald”, because it consists of a conjunction, one of whose terms is assertion 1, is also false. The law of the excluded middle is not violated because by denying both “the King of France is bald” and “the King of France is not bald,” we are not asserting the existence of some x which is neither bald nor not bald, but denying the existence of some x which is the King of France.

There is a second way of stating “the present King of France is not bald”. Instead of substituting x in the sentence “x is not bald” as we have done above, we may negate (1) yielding “it is not the case that there exists an x and x is bald” (alternatively “it is not the case that there exists an x, therefore x is neither bald nor not bald”.

This sentence is true as opposed to the statement obtained by the previous method. Second, it is easier to see that it does not violate the law of excluded middle. Russell’s analysis has been attacked by P.F. Strawson, Keith Donnellan and others, and it has been defended and refined by Stephen Neale. P. F. Strawson argued that Russell had misrepresented what one means when one says “The present King of France is bald.” According to Strawson, this sentence is not contradicted by “No one is the present King of France,” for the former sentence contains not an existential assertion, but attempts to use “the present King of France” as a referring (or denoting) phrase. Since there is no present King of France, the phrase fails to refer, and so the sentence is neither true nor false.

Answer : In the picture theory of Wittgenstein, aboutness is not the only semantic property defined in terms of resemblance—truth is also cashed out in pictorial terms. This is a correspondence theory of truth in which correspondence is a species of resemblance. A picturing fact has aboutness in virtue of resembling some possible states of affairs. A picturing fact is true if and only if the possible state of affairs also happens to be actual.What a picturing fact most resembles is that with which it has the most properties in common.

Thus, that which it is most accurately about is that with which it has the most properties in common.What a fact most resembles is itself—what a fact has the most properties in common with is itself.Thus, that which it is most accurately about is itself.In being about itself, a fact cannot fail to be true about it.The possible state of affairs that a fact most resembles is a possible state of affairs that has all of its properties in common with the fact.Since the fact is actual, the possible state of affairs that it most resembles is an also actual state of affairs.

Since the state of affairs that the fact is most about is actual, in being about itself a fact is necessarily true.It could only be false if the possible state of affairs it most resembles was non-actual i.e., a nonexistent state of affairs.But if the state of affairs it is about is nonexistent, and it is about itself, then it is non-existent, i.e., it is not a fact. A fact about itself is necessarily true, it is a tautology.A tautology conveys no information because it does not get beyond itself. There are two ways that a fact instantiates aboutness.The first way is in being about itself.The second way is in being about something else.In other words, the first is self-directed, the second other-directed. One way in which the other-directed mode of aboutness differs from self-directed aboutness is that facts exhibiting other-directed aboutness are not necessarily true.

The things that a fact resembles that are not itself differ from it in varying ways and varying degrees.One of the ways that it may differ from that which it represents is in being real.Some of the possible states of affairs that the fact resembles will be real and some will not.Thus, some of the things that fact is about will be truths and others falsehoods.The truth values of a picturing fact considered under the other-directed mode of aboutness is not intrinsic to the picturing fact itself.They are not given a priori.They are true or false not of necessity but of contingency.Indeed, it is only in virtue of being other-directed that picturing facts can fail to be false at all: The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.

I take the distinction between two modes of aboutness to map directly onto Wittgensteinís distinction between showing and saying.I take showing to be the same as self-directed aboutness and saying to be the same as other-directed aboutness. Wittgenstein often talks about that which cannot be said (described, mentioned, represented) but can only be shown. When Wittgenstein talks about that which is shown, the shown shows it.For instance, he writes that the world is my world, shows itself.

Wittgenstein holds that what can be shown cannot be said.This necessary exclusiveness is explained by construing the distinction in terms of self- and other-directedness.What is shown is shown by itself.What is said is said by something else.Thus, what is shown is necessarily, can’t be said, since what something is necessarily not something other than what it is.

Answer : The proposition which Moore disputed is: esse is percipi. This is a very ambiguous proposition, but, in some sense or other, it has been very widely held. That wherever you can truly predicate esse you can truly predicate percipi, in some sense or other, is, a necessary step in all arguments, properly to be called Idealistic, and, what is more, in all arguments hitherto offered for the idealistic conclusion. If esse is percipi, this is at once equivalent to saying that whatever is, is experienced; and this, again, is equivalent, in a sense, to saving that whatever is, is something mental. But this is not the sense in which the Idealist conclusion must maintain that Reality is mental.

The Idealist conclusion is that esse is percipere; and hence, whether esse be percipi or not, a further and different discussion is needed to show whether or not it is also percipere. And again, even if esse be percipere, we need a vast quantity of further argument to show that what has esse has also those higher mental qualities which are denoted by spiritual. There are three very ambiguous terms in this proposition, and he began by distinguishing the different things that may be meant by some of them. And first with regard to percipi: it was, perhaps, originally used to mean ‘sensation’ only; but the only Idealists to whom the term should now be applied without qualification — as to hold that, if they say esse is percipi, they mean by percipi sensation only. On the contrary he quite agrees with them that, if esse be percipi at all, percipi must be understood to include not sensation only, but that other type of mental fact, which is called ‘thought ‘; and, whether esse be percipi or not, he considers it to be the main service of the philosophic school, to which modern Idealists belong, that they have insisted on distinguishing ‘thought’ and on emphasising the importance of the latter. Against Sensationalism and Empiricism they have maintained the true view. For, in whatever respects they differ, they have at least this in common, that they are both forms of consciousness or, to use a term that seems to be more in fashion just now, they are both ways of experiencing Accordingly, whatever esse is percipi may mean, it does at least assert that whatever is, is experienced. And since what he maintains is, that even if this is untrue, the question whether it be experienced by way of sensation or thought or both is for my purpose quite irrelevant. If it be not experienced at all, it cannot be either an object of thought or an object of sense. It is only if being involves ‘experience’ that the question, whether it involves sensation or thought or both, becomes important.

Thus percipi may be understood, in what follows, to refer merely to what is common to sensation and thought. The next thing to be considered is the next ambiguity in the statement: Esse is percipi. What does the copula mean? What can be meant by saying that Esse is percipi? There are just three meanings, one or other of which such a statement must have, if it is to be true; and of these there is only one which it can have, if it is to be important. (1) The statement may be meant to assert that the word ‘esse’ is used to signify nothing either more or less than the word ‘percipi’: that the two words are precise synonyms: that they are merely different names for one and the same thing: that what is meant by esse is absolutely identical with what is meant by percipi. Here the principle esse is percipi is not thus intended merely to define a word; nor yet that, if it were, it would be an extremely bad definition. But if it does not mean this, only two alternatives remain. The second is (2) that what is meant by esse, though not absolutely identical with what is meant by percipi; yet includes the latter as a part of its meaning. If this were the meaning of ‘esse is percipi,’ then to say that a thing was real would not be the same thing as to say that it was experienced. That it was real would mean that it was experienced and something else besides: ‘being experienced’ would be analytically essential to reality, but would not be the whole meaning of the term. From the fact that a thing was real we should be able to infer, by the law of contradiction, that it was experienced; since the latter would be part of what is meant by the former. But, on the other hand, from the fact a thing was experienced we should not be able to infer that it was real; since it would not follow from the fact that it had one of the attributes essential to reality, that it also had the other or others.

Now, if we understand esse is percipi in this second sense, we must distinguish three different things which it asserts. First of all, it gives a definition of the word ‘reality,’ asserting that word stands for a complex whole, of which what is meant by ‘percipi’ forms a part. And secondly it asserts that ‘being experienced’ forms a part of a certain whole. Both these propositions may be true, and at all we wish to dispute them. The third issue ist hat ‘real’ is a convenient name for a union of attributes which sometimes occurs, it could not be worth any one’s while to assert: no inferences of any importance could be drawn from such an assertion. Our principle could only mean that when a thing happens to have percipi as well as the other qualities included under esse, it has percipi: and we should never be able to infer that it was experienced, except from a proposition which already asserted that it was both experienced and something else. Accordingly, if the assertion that percipi forms part of the whole meant by reality is to have any importance, it must mean that the whole is organic, at least in this sense, that the other constituent or constituents of it cannot occur without percipi, even if percipi can occur without them.

Let us call these other constituents x. The proposition that esse includes percipi, and that therefore from esse percipi can be inferred, can only be important if it is meant to assert that percipi can be inferred from x. The only importance of the question whether the whole esse includes the part percipi rests therefore on the question whether the part x is necessarily connected with the part percipi. And this is (3) the third possible meaning of the assertion esse is percipi: and, as we now see, the only important one. Esse is percipi asserts that wherever you have x you also have percipi; that whatever has the property x also has the property that it is experienced. And this being so, it will be convenient if, for the future, we may be allowed to use the term ‘esse’ to denote x alone. Thus what what we commonly mean by the word ‘real ‘ does or does not include percipi as well as x. The definition of ‘esse’ to denote x, should be regarded merely as an arbitrary verbal definition.

Answer : The proposition which Moore disputed is: esse is percipi. This is a very ambiguous proposition, but, in some sense or other, it has been very widely held. That wherever you can truly predicate esse you can truly predicate percipi, in some sense or other, is, a necessary step in all arguments, properly to be called Idealistic, and, what is more, in all arguments hitherto offered for the idealistic conclusion. If esse is percipi, this is at once equivalent to saying that whatever is, is experienced; and this, again, is equivalent, in a sense, to saving that whatever is, is something mental. But this is not the sense in which the Idealist conclusion must maintain that Reality is mental.

The Idealist conclusion is that esse is percipere; and hence, whether esse be percipi or not, a further and different discussion is needed to show whether or not it is also percipere. And again, even if esse be percipere, we need a vast quantity of further argument to show that what has esse has also those higher mental qualities which are denoted by spiritual. There are three very ambiguous terms in this proposition, and he began by distinguishing the different things that may be meant by some of them. And first with regard to percipi: it was, perhaps, originally used to mean ‘sensation’ only; but the only Idealists to whom the term should now be applied without qualification — as to hold that, if they say esse is percipi, they mean by percipi sensation only. On the contrary he quite agrees with them that, if esse be percipi at all, percipi must be understood to include not sensation only, but that other type of mental fact, which is called ‘thought ‘; and, whether esse be percipi or not, he considers it to be the main service of the philosophic school, to which modern Idealists belong, that they have insisted on distinguishing ‘thought’ and on emphasising the importance of the latter. Against Sensationalism and Empiricism they have maintained the true view. For, in whatever respects they differ, they have at least this in common, that they are both forms of consciousness or, to use a term that seems to be more in fashion just now, they are both ways of experiencing Accordingly, whatever esse is percipi may mean, it does at least assert that whatever is, is experienced. And since what he maintains is, that even if this is untrue, the question whether it be experienced by way of sensation or thought or both is for my purpose quite irrelevant. If it be not experienced at all, it cannot be either an object of thought or an object of sense. It is only if being involves ‘experience’ that the question, whether it involves sensation or thought or both, becomes important.

Thus percipi may be understood, in what follows, to refer merely to what is common to sensation and thought. The next thing to be considered is the next ambiguity in the statement: Esse is percipi. What does the copula mean? What can be meant by saying that Esse is percipi? There are just three meanings, one or other of which such a statement must have, if it is to be true; and of these there is only one which it can have, if it is to be important. (1) The statement may be meant to assert that the word ‘esse’ is used to signify nothing either more or less than the word ‘percipi’: that the two words are precise synonyms: that they are merely different names for one and the same thing: that what is meant by esse is absolutely identical with what is meant by percipi. Here the principle esse is percipi is not thus intended merely to define a word; nor yet that, if it were, it would be an extremely bad definition. But if it does not mean this, only two alternatives remain. The second is (2) that what is meant by esse, though not absolutely identical with what is meant by percipi; yet includes the latter as a part of its meaning. If this were the meaning of ‘esse is percipi,’ then to say that a thing was real would not be the same thing as to say that it was experienced. That it was real would mean that it was experienced and something else besides: ‘being experienced’ would be analytically essential to reality, but would not be the whole meaning of the term. From the fact that a thing was real we should be able to infer, by the law of contradiction, that it was experienced; since the latter would be part of what is meant by the former. But, on the other hand, from the fact a thing was experienced we should not be able to infer that it was real; since it would not follow from the fact that it had one of the attributes essential to reality, that it also had the other or others.

Now, if we understand esse is percipi in this second sense, we must distinguish three different things which it asserts. First of all, it gives a definition of the word ‘reality,’ asserting that word stands for a complex whole, of which what is meant by ‘percipi’ forms a part. And secondly it asserts that ‘being experienced’ forms a part of a certain whole. Both these propositions may be true, and at all we wish to dispute them.The third issue ist hat ‘real’ is a convenient name for a union of attributes which sometimes occurs, it could not be worth any one’s while to assert: no inferences of any importance could be drawn from such an assertion. Our principle could only mean that when a thing happens to have percipi as well as the other qualities included under esse, it has percipi: and we should never be able to infer that it was experienced, except from a proposition which already asserted that it was both experienced and something else. Accordingly, if the assertion that percipi forms part of the whole meant by reality is to have any importance, it must mean that the whole is organic, at least in this sense, that the other constituent or constituents of it cannot occur without percipi, even if percipi can occur without them.

Let us call these other constituents x. The proposition that esse includes percipi, and that therefore from esse percipi can be inferred, can only be important if it is meant to assert that percipi can be inferred from x. The only importance of the question whether the whole esse includes the part percipi rests therefore on the question whether the part x is necessarily connected with the part percipi. And this is (3) the third possible meaning of the assertion esse is percipi: and, as we now see, the only important one. Esse is percipi asserts that wherever you have x you also have percipi; that whatever has the property x also has the property that it is experienced. And this being so, it will be convenient if, for the future, we may be allowed to use the term ‘esse’ to denote x alone. Thus what what we commonly mean by the word ‘real ‘ does or does not include percipi as well as x. The definition of ‘esse’ to denote x, should be regarded merely as an arbitrary verbal definition.

Answer : Russell’s philosophy of logical atomism is attributed to the influence of Wittgenstein. Russell belonged to a tradition in contemporary philosophy called logical analysis. This tradition was developed as a challenge to the dominant Hegelian system in the British/American universities at the turn of the century. Logical analysis was a revival of British empiricism, though, with a strong emphasis on logic unprecedented in British empiricism prior to and including John Stuart Mill. Russell did not consider metaphysical assumptions as a prerequisite to his logical doctrine. His first suggestion of logical atomism was: “I shall try to set forth...a certain kind of logical doctrine and on the basis of this a certain kind of metaphysics.

Having established pluralism as the general outlook of the nature of the world, the next step for a philosophical system is to discover the structure of the world. How logical atomism tackled this problem. The most basic elements of the world, as claimed by logical atomism, are things, relations, qualities and atomic facts. Russell explains what he means by facts in this way: “the things in the world have various properties and stand in various relations to each other. That they have these properties and relations are facts and the things and their qualities or relations are quite clearly in some sense or other components of the facts that have these qualities or relations.

Although facts are complex, they are ultimate and cannot be reduced to the simple constituents. He says that there are particulars and qualities and relations of various orders, a whole hierarchy of different sorts of simples, but all of them, if we were right, have in their various ways some kind of reality that does not belong to anything else. The only other sort of object you come across in the world is what we call facts and facts are the sort of things that are asserted or denied by propositions, and are not properly entities at all in the same sense in which their constituents are. That is shown in the fact that you can not name them. You can only deny or assert, or consider them, but you can not name them because they are not there to be named, although in another sense it is true that you can not know the world unless you know the facts that make up the truths of the world. In other words, the subjective notion of truth is objectified when he claims that the truth of the world can be reduced to “facts that make up the truths of the world.” This was very similar to monadology where the subjective notion of mind was objectified by monads. The atoms relating to the truth in the objective world, according to logical atomism, are not particulars, relations, or qualities; but a unique unity of them corresponds to the truth, i.e. the atomic facts.

Thus, these atomic facts, though complex, are not reducible to their parts as if the objectification of truth is a ghost holding them together. If irreducible unities of atomic facts are admitted as above, then there is no reason to prefer considering the relations, as external relations between things, rather than internal relations of atomic facts. Actually, the latter is more suitable because it does not separate truth and relations. Moreover, there is no need to recognize particulars separate from facts, since their truth cannot be established independent of atomic facts. In other words, virtually the ultimate is only atomic facts and things, relations, and qualities are aspects of facts. But Bradley objects his proposition and says that even if we accept the theory of types, we are still faced with the problem of objective correspondence of truth to ultimate complexes, rather than the simples and simples are still devoid of truth. This way the simples will become like Kant’s things-in-themselves, with the difference that for Kant these ultimate simples are not knowable, whereas for Russell their objective truth can not be established except in complexes. Theory of types is only the acknowledgement of simples as a type of things whose truth can not be established independent of complexes. The peculiarity of the atomic facts and my criticism above, therefore, remain intact by the theory of types. I propose the following notions to elucidate the problem. Aristotle’s eight to ten categories of the objects of thought and his studies of their relations to each other provided better concepts in discovering the structure of the world for a pluralist than Russell’s categories.

Actually, Russell only mentions three categories, i.e., things, relations, and qualities, and finding it hard to build a system corresponding to the real world based on these categories, he introduces a new category of objects of thought (atomic facts) as an objectification of truth to fill in the gap in explaining the real world. In fact, only this category would suffice and even the three simple categories are redundant, since atomic facts already furnish all the basic elements, to establish the truth in the world. In this way, he departs from pluralism to a great extent without noticing it. This mistake was done due to Russell’s oversight in not appreciating the significance of categories of the objects of thought in philosophical systems. He continued these mistake even years after giving up logical atomism. Contrary to Russell’s view, categories do affect the structure of philosophical systems and this is why all-sided philosophers like Aristotle and Hegel have emphasized the elaboration of their accepted categories of objects of thought. Clarity about accepted categories can help prevent unnoticed categories to unobtrusively slip into a philosophical system without justification.

Actually, Russell himself is introducing a new category when he postulates atomic facts and if he were aware of this fact, probably he would have recognized that categorically there was no essential difference between his atomic propositions, that were supposedly picturing atomic facts, and the atomic facts themselves, which were nothing but a new category of speech like relation, substance, quality, etc. Also the lack of categories like time and space were problematic in Russell’s logical atomism. In summary, the limited number of categories of the objects of thought, ‘objectifying’ the notion of truth, in the absence of clarity about the importance of categories in philosophical systems, formed the fundamental shortcomings of Russell’s scheme for understanding the structure of the world. Consequently, in his metaphysics, pluralism was undermined by accepting unanalyzed complex unities: atomic facts. Also, in his epistemology, realism was undermined when atomic propositions gained supremacy in his philosophical system.

Answer : An important aspect of Moore’s rejection of idealism was his affirmation of a ‘common sense’ realist position, according to which our ordinary common-sense view of the world is largely correct. Moore begins by listing a large number of ‘truisms’ such as that ‘the earth had existed also for many years before my body was born’. Concerning these truisms he then asserts, first, that he knows them for certain, second, that other people likewise know for certain the truth of comparable truisms about themselves and, third, that he knows this second general truth (and, by implication, others do too). So the truth and general knowledge of these truisms is a matter of common sense.

Having set out these truisms, Moore then acknowledges that some philosophers have denied their truth or, more commonly, denied our knowledge of them (even though, according to Moore, they also know them) and he attempts to show that these denials are incoherent or unwarranted. These claims might seem to leave little space for radical philosophical argument. But in the last part of the paper Moore argues that his defence of common sense leaves completely undecided the question as to how the truistic propositions which make up the common sense view of the world are to be analysed; the analysis may be as radical as one likes as long as it is consistent with the truth and knowability of the propositions analysed. Thus, for example, he is content to allow that philosophical argument may show that a phenomenalist analysis of propositions about the physical world is correct.

This last point shows that Moore’s defence of common sense is not as much of a constraint on philosophical theory as one might at first have thought; for philosophical analysis can reveal to us facts about the ‘principal or ultimate subject’ of a truistic proposition which are by no means what common sense supposes.

Answer : Bertrand Russell described several different definitions and philosophical analyses as treating certain entities and expressions as “logical constructions”. Examples he cited were the Frege/Russell definition of numbers as classes of equinumerous classes, the theory of definite descriptions, the construction of matter from sense data, and several others. Generally expressions for such entities are called “incomplete symbols” and the entities themselves “logical fictions”.

The notion originates with Russell’s logicist program of reducing mathematics to logic, was widely used by Russell, and led to the later Logical Positivist notion of construction and ultimately the widespread use of set theoretic models in philosophy. Russell’s most specific formulation of logical construction as a method in Philosophy comes from his essay “Logical Atomism”: With the concept of Occam’s Razor when some set of supposed entities has neat logical properties, it turns out, in a great many instances, that the supposed entities can be replaced by purely logical structures composed of entities which have not such neat properties. In that case, in interpreting a body of propositions hitherto believed to be about the supposed entities, we can substitute the logical structures without altering any of the detail of the body of propositions in question.

This is an economy, because entities with neat logical properties are always inferred, and if the propositions in which they occur can be interpreted without making this inference, the ground for the inference fails, and our body of propositions is secured against the need of a doubtful step. The principle may be stated in the form: ‘whenever possible, substitute constructions out of known entities for inferences to unknown entities’. Russell was speaking of logical constructions in this memorable passage from his Introduction to Mathematical Philosophy: “The method of ‘postulating’ what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others and proceed with our honest toil.” The notion of logical construction appears frequently with the idea that what is defined is a “logical fiction”, and an “incomplete symbol”.

The latter term derives from the use of contextual definitions, providing an analysis of each sentence in which a defined symbol may occur without, however, giving an explicit definition, an equation or universal statement giving necessary and sufficient conditions for the application of the term in isolation. The terms “fiction” and “incomplete symbol” apply with differing aptness to different constructions. Russell’s first use of construction, and the model for later constructions, is the Frege/Russell definition of numbers as classes. This follows the kind of definitions used in the arithmetization of analysis of the preceding century, in particular, Dedekind’s earlier construction of real numbers as bounded classes of rational numbers.

Russell’s logicist programme could not rest content with postulates for the fundamental objects of mathematics such as the Peano Axioms for the natural numbers. Instead numbers were to be defined as classes of equinumerous classes. Russell also refers to this method as “abstraction”, now known as the abstraction of an equivalence class. The definition of equinumerosity, or of the existence of a one to one mapping between two classes, also called “similarity”, is solely in terms of logical notions of quantifiers and identity. With the numbers defined, for example, two as the class of all two member sets, or pairs, the properties of numbers could be derived by logical means alone.

Answer : according to Russell objects (that is, logical constructions) in their relations or with their qualities constitute the various forms of facts. Assuming that what makes a sentence true is a fact, what sorts of facts must exist to explain the truth of the kinds of sentences there are? Russell answers this question by accounting for the truth of several different kinds of sentences: atomic and molecular sentences, general sentences, and those expressing propositional attitudes like belief. So-called atomic sentences like “Andrew is taller than Bob” contain two names (Andrew, Bob) and one symbol for a relation (is taller than). When true, an atomic sentence corresponds to an atomic fact containing two particulars and one universal (the relation). Molecular sentences join atomic sentences into what are often called “compound sentences” by using words like “and” or “or. ”When true, molecular sentences do not correspond to a single conjunctive or disjunctive fact, but to multiple atomic facts. Thus, we can account for the truth of molecular propositions like “Andrew is kind or he is young” simply in terms of the atomic facts (if any) corresponding to “Andrew is kind” and “Andrew is young,” and the meaning of the word “or.” It follows that “or” is not a name for a thing, and Russell denies the existence of molecular facts. Yet to account for negation (for example, “Andrew is not kind”) Russell thinks that we require more than just atomic facts. We require negative facts; for if there were no negative facts, there would be nothing to verify a negative sentence and falsify its opposite, the corresponding positive atomic sentence. Moreover, no list of atomic facts can tell us that it is all the facts; to convey the information expressed by sentences like “everything fair is good” requires the existence of general facts.

Answer : The purpose of philosophical analysis, according to Moore, is merely to explicate the precise implications of the truth of such beliefs, and that is the procedure he followed in “A Defence of Common Sense” (1925).

Moore began with a simple list of “common-sense” beliefs that each of us holds about many things, including my own body, other human bodies, my own experiences, and the experiences of other human beings. He then declared further that we all know that each of these simple beliefs is wholly true in just the (unanalyzed) sense in which they are commonly meant. Philosophers who hold opposing views Moore divided into two groups:

• Some of them deny the truth of the beliefs (as, for example, do idealists who reject the reality of time, space, or self). But this Moore took to be indefensible, self-defeating, and never consistently held as a basis for ordinary life.
• Others deny only that we know the beliefs (as, for example, do skeptics about the external world). This position, Moore argued, is not only self-defeating and impractical but also logically inconsistent.

Thus, Moore concluded that in fact we do really know all of these common-sense beliefs to be true. On the other hand, of course, the correct analysis of these beliefs still remains open to debate. In a parting shot against his idealist teachers, Moore pointed out that “mental facts” about conscious experience are particularly troubling, since they don’t typically have the kind of timeless identity they are supposed to possess. “Physical facts” may be explicable—both logically and causally—without any direct reference to their mental representation. Moore’s own analysis, however, is clearly a version of representation realism with its attendant difficulties about the status of sense-data and their independence of individual acts of sensation. In the later essay, “Proof of an External World” (1939), Moore’s methodology (perhaps influenced by his conversations with Wittgenstein) relied even more heavily on the analysis of ordinary language. Much of his point there seems to rest on an extraordinarily cautious explanation of such phrases as “to be met with in space” and “external to the mind.” Many who have been sincerely troubled by skeptical doubts will find Moore’s “proof” of the existence of physical objects less than satisfying. Perhaps Moore’s extremely careful procedures leave too many legitimate philosophical questions unanswered.

Answer : Bertrand Russell described his philosophy as a kind of “logical atomism”, by which he meant to endorse both a metaphysical view and a certain methodology for doing philosophy. The metaphysical view amounts to the claim that the world consists of a plurality of independently existing things exhibiting qualities and standing in relations. According to logical atomism, all truths are ultimately dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality or multiple simple particulars standing in a relation.

The methodological view recommends a process of analysis, whereby one attempts to define or reconstruct more complex notions or vocabularies in terms of simpler ones. According to Russell, at least early on during his logical atomist phase, such an analysis could eventually result in a language containing only words representing simple particulars, the simple properties and relations thereof, and logical constants, which, despite this limited vocabulary, could adequately capture all truths.

Russell’s logical atomism had a profound influence on analytic philosophy in the first half of the 20th century; indeed, it is arguable that the very name “analytic philosophy” derives from Russell’s defense of the method of analysis. Bertrand Russell introduced the phrase “logical atomism” to describe his philosophy and used the phrase consistently throughout his life. Russell’s logical atomism is perhaps best described as partly a methodological viewpoint, and partly a metaphysical theory. Methodologically, logical atomism can be seen as endorsement of analysis, understood as a two-step process in which one attempts to identify, for a given domain of inquiry, set of beliefs or scientific theory, the minimum and most basic concepts and vocabulary in which the other concepts and vocabulary of that domain can be defined or recast, and the most general and basic principles from which the remainder of the truths of the domain can be derived or reconstructed. Metaphysically, logical atomism is the view that the world consists in a plurality of independent and discrete entities, which by coming together form facts. According to Russell, a fact is a kind of complex, and depends for its existence on the simpler entities making it up. The simplest sort of complex, an atomic fact, was thought to consist either of a single individual exhibiting a simple quality, or of multiple individuals standing in a simple relation.

Answer : Russell’s theory of descriptions was most clearly expressed in his 1905 essay “On Denoting”. Russell’s theory is about the logical form of expressions involving denoting phrases, which he divides into three groups:

1. Denoting phrases which do not denote anything, for example “the present King of France”.
2. Phrases which denote one definite object, for example “the present King of England”. We need not know which object the phrase refers to for it to be unambiguous, for example “the tallest spy” is a unique individual but his or her actual identity is unknown).
3. Phrases which denote ambiguously, for example, “a man”.

Definite descriptions involve Russell’s second group of denoting phrases, and indefinite descriptions involve Russell’s third group. Descriptions typically appear to be of the standard subject-predicate form. Russell proposed his theory of descriptions in order to solve several problems in the philosophy of language. The two major problems are of (1) co-referring expressions and (2) non-referring expressions. The problem of co-referring expressions originated primarily with Gottlob Frege as the problem of informative identities. For example, if the morning star and the evening star are the same planet in the sky (indeed they are), how is it that someone can think that the morning star rises in the morning but the evening star does not? That is, someone might find it surprising that the two names refer to the same thing (i.e. the identity is informative). This is apparently problematic because although the two expressions seem to denote the same thing, one cannot substitute one for the other, which one ought to be able to do with identical or synonymous expressions.

The problem of non-referring expressions is that certain expressions that are meaningful do not seem to refer to anything. By “the present King of France is bald” it is not meant that there is some individual, namely the present King of France, who has the property of being bald (France is no longer a monarchy, so there is currently no King of France). Thus, what Russell wants to avoid is admitting mysterious non-existent entities into his ontology. Furthermore, the law of the excluded middle requires that one of the following propositions, for example, must be true: either “the present King of France is bald” or “it is not the case that the present King of France is bald”. Normally, propositions of the subject-predicate form are said to be true if and only if the subject is in the extension of the predicate. But, there is currently no King of France. So, since the subject does not exist, it is not in the extension of either predicate (it is not on the list of bald people or non-bald people).

Thus, it appears that this is a case in which the law of excluded middle is violated, which is also an indication that something has gone wrong. Russell says in his paper, in a typically sly dig at a school of philosophy with which he disagreed, that “Hegelians, who love a synthesis, will probably conclude that he wears a wig.” Russell analyzes definite descriptions similarly to indefinite descriptions, except that the individual is now uniquely specified. Take as an example of a definite description the sentence “the present King of France is bald”. Russell analyzes this phrase into the following component parts (with ‘x’ and ‘y’ representing variables):

• There is an x such that x is the King of France.
• There is no y, other than x, such that y is the King of France (i.e., x is uniquely the King of France).
• x is bald.

Thus, a definite description becomes the following existentially quantified phrase in classic symbolic logic (where ‘x’ and ‘y’ are variables). This analysis, according to Russell, solves the two problems noted above as related to definite descriptions: First, “The morning star rises in the morning” no longer needs to be thought of as having the subject-predicate form. It is instead analyzed as “there is one unique thing such that it is the morning star and it rises in the morning”. Thus, strictly speaking, the two expressions “the morning star...” and “the evening star...” are not synonymous, so it makes sense that they cannot be substituted (the analysed description of the evening star is “there is one unique thing such that it is the evening star and it rises in the evening”). Second, since the phrase “the present King of France is bald” is not a referring expression, according to Russell’s theory it need not refer to a mysterious non-existent entity.Take as an example of an indefinite description the sentence “some man is being obnoxious”. Russell analyzes this phrase into the following component parts (with ‘x’ and ‘y’ representing variables): First, there is an x such that x is a man. Second, x is being obnoxious.

Thus, an indefinite description becomes the following existentially quantified phrase in classic symbolic logic (where ‘x’ and ‘y’ are variables) This analysis, according to Russell, solves the second problem noted above as related to indefinite descriptions. Since the phrase “some man is being obnoxious” is not a referring expression, according to Russell’s theory, it need not refer to a mysterious non-existent entity. Furthermore, the law of excluded middle need not be violated (i.e. it remains a law), because “some man is being obnoxious” comes out true: there is a person that is both a man and obnoxious. Thus, Russell’s theory seems to be a better analysis insofar as it solves several problems.

P. F. Strawson argued that Russell had misrepresented what one means when one says “The present King of France is bald.” According to Strawson, this sentence is not contradicted by “No one is the present King of France,” for the former sentence contains not an existential assertion, but attempts to use “the present King of France” as a referring (or denoting) phrase. Since there is no present King of France, the phrase fails to refer, and so the sentence is neither true nor false.

Answer : Wittgenstein’s view of what philosophy is or should be changed little over his life. In his book Tractatus he says that philosophy is not one of the natural sciences. It aims as the logical clarification of thoughts. Philosophy is not descriptive but. elucidatory. Its aim is to clear up middle and confusion. It follows that philosophers should not concern themselves so much with what is actual keeping up with the latest popularizations of sciences say which Wittgeinstein despised. The philosopher’s proper concern is with what is possible, or rather with what is conceivable. This depends on our language and the ways they fit together as ocean in language. What is conceivable and what is not what makes sense and what does not depends on the rules of language, of grammar.

Wittgenstein says that our investigation is grammatical one. Such an investigation sheds light on our problem by clearing misunderstanding away. Misunderstanding concerning the use of words, caused, among other things, by certain analogies between the forms of expression in different regions of language is the main problem. The similarities between the sentences “I will keep it in mind” and “I will keep it in box”, for instance, can lead one to think of the mind as thing something like a box with contents of its own.

The nature of this box and its mental contents can then seem very mysterious. Wittgenstein suggests that one way, at least, to deal with such mysteries is to recall the different things one says about minds, memories, thoughts and so on, in a variety of contexts. What one says, or what people in general say can change. Ways of life and uses of language change, so meanings change, but not utterly and instantaneously. Things shift and evolve, but rarely if ever so drastically that we lose all grips on manning. So there is no timeless essence of at least some and perhaps all concepts, but we still understand one another well enough most of the time.

When nonsense is spoken or written, or when something just seems fishy, we can swift it out. The road out of confusion can be a long and difficult one, hence the need for constant attention to detail and particular examples rather than generalizations, which tend to be vague and therefore potentially misleading. The slower the route, the surer the safety at the end of it will be. That is why Wittgenstein said that in philosophy the winner is the one who finishes last. But we cannot escape language or he confusions to which it gives rise, except by dying. In the meantime, Wittgenstein offers four man methods to avoid philosophical confusion, as described by Norman Malcolm: describing circumstances in which a seemingly problematic expression might actually be used in everyday life, comparing out use of words with imaginary language games, imaging fictitious natural history, and explaining psychologically the temptation to use a certain expression inappropriately. The complex, intertwined relationship between a language and the form of life that goes with it means that problems arising from language cannot just be set-aside they infect our lives, making us live in confusion. We might find our way back to the right path, but there is no guarantee that we will never again stray. In this sense there can be no progress in philosophy.

Moreover, Wittgenstein says that for a large class of cases though not for all in which we employ the word “meaning” it can be defined thus: the meaning of a word is its use in the language” It is quite clear that Wittgenstein is not offering the general theory that “ meaning is the”, as he is sometimes interpreted as doing the main rival views that Wittgenstein warns against are that the meaning of a world is some object that it means in which case the meaning of a word could be destroyed, stolen or locked away, which is nonsense- and that the meaning of a word is somepsychological feeling in which case the meaning of a word could be destroyed, stolen or locked away, which is nonsense- each use of a word could mean something different by it, having a different feeling, and communication would be difficult if not impossible.

Knowing the meaning of a word can involve knowing many things: to what objects the word refers, whether it is many or not what part of speech it is, whether if carries overtones, and if so what kind they are, and so on. To known all this, or to know enough to get by, is to know the use. And generally knowing the use means knowing the meaning. Philosophical questions about consciousness, for example, then, should be responded to by looking at the various uses we make of the word “consciousness”. Scientific investigations into the brain are not directly relevant to this inquiry.

The meaning of any word is a matter of what we do with our language, not something hidden inside anyone’s. It is merely distinguishing philosophy (which is properly concerned with linguistic or conceptual analysis) from science (which is concerned with discovering facts). Besides, Wittgenstein says that “the word” ‘is’ is used with two different meanings (as the copula and as the sign of equality)” but that its meaning is not its use. That is to say, “is” has not one complex use (including both “water is clear” and “water is H2O”) and therefore one complex meaning, but two quite distinct uses and meanings. It is not an accident that we use the world “car” to refer to both Fords and Hondas. But what is accidental and what is essential to a concept depends on us, on how we use it.

This is not completely arbitrary, however depending on one’s environment, one’s physical needs and desires, one’s emotions, one’s sensory capacities, and so on. Different concepts will be more natural or useful to one. This is why “forms of life” are so important to Wittgenstein. What matters to you depends on now you live and this shapes your experience. So if a lion could speak, Wittgenstein says, we would not be able to understand if. We might realize that “roar” meant Zebra, or that “roar, roar” meant lame zebra, but we would not understand Lion ethics, politics, aesthetic taste, religion, humor and such like, if lion have these things, the moral of the story is that philosophy is not a doctrine, and hence should not be approached dogmatically.