It is possible to think logically, of course, without knowing the principles of logic. Though one may be capable of complex reasoning without knowing the principles that underlie it, knowing and having practiced their application in a systematic way can enable one to think more economically and to recognise fallacious argumentation more readily and securely, This applies with greater force to lengthy and intricate chains of reasoning. To be able to recognise and express clearly in exactly what an argument is fallacious is itself part of critical thinking.
Logical thinking itself involves no communication, only the demonstration of arguments require that. Whereas semantic principles apply to communicational interaction, logical principles apply to the internal interactions of the mind. When reasons or arguments are used in communication situations, a more complex level of communication occurs involving both types of principle at once. This will be considered after treating the purely logical principles. One may summarily distinguish semantics and logic as follows:

Semantics is the systematic study of understanding and misunderstanding insofar as this depends upon the use and misuse of language. Semantic theory attempts to discover and state the rules upon which effective communication by way of language depends.

Logic is the systematic study of the validity or invalidity of arguments insofar as this depends upon the correctness or fallaciousness of reasoning (thought). Logical theory thus attempts to discover and state the rules upon which correct reasoning depends.

Theories of logic can be divided into syllogististic (or ‘traditional’) and predicate (or symbolic/mathematical) logic. It is the former variant which features in this book. Syllogistic logic – also known as text logic - was superceded by Russell and Whitehead’s mathematical logic. However, this new ‘predicate logic’ abstracts from texts to such a degree that it is unsuited to explaining the nature of logical thinking in practical language usage, especially in respect of many logical and rhetorical fallacies. The logician V.W. Quine pronounced symbolic (predicate) logic to be "Procrustean", using an artificial language of function and argument, quantifier and bound variable. Besides, there are theoretical problems with it’s use of  empty names and identity statements.

A condition facing any demonstration of logical thinking is that we must begin with elementary materials before more involved problems can be solved. This easily makes for tediousness at the outset because examples must be simple and transparent enough to demonstrate the elements of theory most clearly. The value of this groundwork does not become apparent until more difficult and interesting material can be dealt with.

Note: Oxford philosopher Gareth Evans has criticised predicate logic as follows: “"I come to semantic investigations with a preference for homophonic theories; theories which try to take serious account of the syntactic and semantic devices which actually exist in the language ...I would prefer [such] a theory ... over a theory which is only able to deal with [sentences of the form "all A's are B's"] by "discovering" hidden logical constants ... The objection would not be that such [Fregean] truth conditions are not correct, but that, in a sense which we would all dearly love to have more exactly explained, the syntactic shape of the sentence is treated as so much misleading surface structure" (Evans 1977)

Working definitions of Key Terms and Distinctions (Classes of Statement)

Books on logic, grammar and philosophy abound, with different types of distinction that can be drawn between different classes of statement. (Statements are sometimes also called 'propositions'). There is no perfectly satisfactory or thoroughly accepted system of classifying statements, partly because schools and traditions vary with the purposes they imply, partly because language itself is so flexible as always to make exceptions possible from any rule. On this background, I have selected four basic and quite securely founded distinctions that are common in some form or another to many schools of philosophy and logic, having proven to have wide application in logical analysis, In the lack of one common terminology, different terms are used by various authors for the same distinction, while the same term can sometimes be defined in different ways, giving rise to many nuances of distinction.
The working definitions adopted here are those I find best in practical application, least confusing and quite highly operational. For the orientation of those acquainted with a different terminology, I mention some often used terms explaining the terms I shall otherwise adhere to throughout this section.

Particular and General Statements

Note: It is common to distinguish between particular and general terms in logic. Applied to statements, this distinction facilitates an elementary presentation of valid reasoning).

Particular statements are those that assert something of specific individuals, objects, events etc.
For example, ' The house is on fire', ' The centre of "London is no longer very safe', 'One of the persons present enjoyed himself' (Note that particular statements can contain general terms).

General statements are those that assert something of a class common to individuals, objects, events, etc.
For example, 'Some houses easily catch fire', 'Streets are unsafe places', ' Everyone envoys themselves when they can'. The last example is a special case of a general statement that is termed 'universal' because it includes - or excludes - the entire class involved. Sentences that begin with 'All', 'Every', 'Each' and 'None' are universal statements if they refer to a common class.

Note that a common class can occur in the logical predicate of a statement without thereby making it general. For example, 'This cat is a mammal' or, when the logical predicate comes first, eg: 'Secure fire-proofing has not been carried out on this house'. (The logical predicate here is 'secure fire-proofing').

In a majority of cases this distinction can be applied without much difficulty, but cases occur in which the definition fails to distinguish clearly between the one or other class of statement. For example, 'London has many streets' or 'London's streets are many' can make two particular statements, yet the particular term 'London' can sometimes be used generally, such as 'London and her streets will always be bustling with mysterious incidents in my imagination, whatever era they appear in'. From this we can conclude that to decide whether a statement is particular or general we must sometimes know the context or situation in which it is used.

The purposes to which the above distinction can be put are various. It has importance in philosophy as the basis of a long-standing debate on whether general or universal classes exist as ideas or ideals independently of the particular things they include. Though this seems to be a sort/of philosophical idealism, it is called (ontological) 'realism' in that abstract general classes or universals are held to be real. This standpoint is denied by nominalism , which deny them 'ideal' reality. For logical theory, however, the difference between particular and general statements has consequences for what can and cannot be deduced with logical necessity. In the philosophy of science and in methodology the distinction is of importance because one here attempts to make clear the relations between particular statements of fact and the universal or general statements of theory.

Categorical and Hypothetical Statements

Categorical statements are those that make a definitive assertion about alleged states of affairs. They may be either true or false.
(Also known as 'unconditional propositions' because their assertions are absolute or direct, being unqualified.)
Examples are 'The Prime Minister went back on her word' and 'Some nations suffer from excessive material wealth'. They do not have to be true to be categorical. Also under categorical statements come those called 'Alternative statements' such as have the structure ' Either a or b' ( eg : 'Either materialistic goals or elevated purposes dominate a nation') and 'Disjunctive statements' having the structure 'neither a nor b' ( eg ; 'Neither can one take one's material wealth with one when one dies nor can one live for ever').

Hypothetical statements are those that assert a relation of dependence between (actual or possible) states of affairs. They can be true or false.

(Also called 'conditional statements', 'implicative propositions' or simply 'hypotheses'). Hypothetical statements have the logical structure 'If a then b'. Examples are 'If the Prime Minister went back on his word, then he is not infallible', and 'If nations become excessively wealthy, they suffer from its less visible ill-effects' (where 'then' is understood but not stated).

As is the case with all statements, the class can appear to be different when different contexts and situations are taken into account. A statement which is categorical when taken by itself, such as 'The victim is not likely to die' can be made hypothetical by the context such as 'This is only the case if he takes it easy for some time'. Including the context in the statement, its hypothetical form is made apparent 'If the victim takes it easy for some time, then he is not likely to die'. This distinction is fundamental in logic as will become evident when we study the principle of valid implication.

Descriptive and Prescriptive Statements (also known respectively as 'referential' and 'normative' statements).

Descriptive statements are those that can be either true or false. As the term suggests, they describe something. Because they refer to something allegedly existent, some object or state of affairs that pertains. Their truth depends upon the description being correct, so that what they refer to can be shown to pertain. (Wittgenstein's translators termed true descriptive statements 'propositions with sense' in that they make sense). Egs : 'The earth is nearly spherical', 'The earth is not a disc'. False descriptive statements are those which refer to some object or state of affairs which does not pertain, the statement is not in accordance with the facts. Egs ; ' Kierkegaard was a great Texan preacher', 'Light travels more slowly than sound'.

Another class of statement that are generally regarded as descriptive are those often called 'predictive'. They predict some future state of affairs. Eg: 'The number of cars on the road in year 2000 will exceed the number of people on earth'. There is as yet no means of establishing the truth or falsity of this (pessimistic?) prediction, so it cannot be definitively judged to be descriptive. Yet in principle it would be judged true or false, which is sufficient to class it as descriptive.

Prescriptive (or Normative) statements are those that cannot be either true or false.
As these statements prescribe or order something rather than describe, it is not meaningful to say they are either true or false. Commands, orders, suggestions and expressions of the 'ought', 'should', and 'could' type are all usually prescriptive. For example 'Quick march!' 'You should try Epsom salts', 'Thou shall not covet thy neighbour's wife'. Prescriptive statements are also widely known as 'normative statements' because they set a norm. A norm is a rule of behaviour given by someone.

Prescriptive statements usually attempt to influence someone, and though not necessarily by emotive expressions, they frequently are intended to persuade on non-cognitive grounds. Commonly they state a general value (eg: 'Kindness is best') or else a specific injunction (eg: 'Keep off that grass' or 'Stop making such a fuss!'). There occur borderline cases where one cannot, without additional information about the communication situation, decide which case applies. Consider the example "Those who wish to attain excellence have to try and try again'. Does it state a norm or is it a description of a state of affairs that pertains in our experience? It is based on observation of states of affairs, which can lead one to regard it as descriptive, yet it does set a rule for behaviour. The deciding factor must be whether it can be either true or false. If so, it is a descriptive statement.

The problem arises how to judge its truth or falsity. We can recognise many statements as potentially true or false without knowing definitely which they are or how one would set about establishing it. In this case one could at best subjectively judge the likelihood of it being true in the lack of scientific methods of establishing whether it is true or false. Or one could refer to the communication situation to see how the statement was intended. If it were clearly intended as a norm to follow, its possible truth or falsity would be secondary. For example, if it were said by a sergeant to make his soldiers continue at target practice, it would function normatively. On the other hand, as an answer to the question 'who are those who attain excellence?' it would be descriptive in intent. Another example of a statement that has a descriptive form yet a clearly normative intent is the sign one often sees upon entering buses 'The conductor is always paid upon entering'. The intention is probably better expressed as 'The conductor must always be paid upon entering'. Prescriptive statements cannot meaningfully be said to be either 'true' or 'false'. Yet in asserting a norm they can appear to lay claim to being true. For example, 'we ought to accept the only alternative of limiting national population growth everywhere if humanity is to survive on this planet's resources'. This statement, when taken as a whole, is clearly prescriptive, which is indicated by the tern 'ought to'. Had the tern 'must' been used instead of 'ought to', doubt as to whether the statement is prescriptive or descriptive arises, for 'must' can also refer to necessity, which would make the statement a prediction (whether tenable or not).

A statement must be regarded as a whole, preferably also within the context and situation that applies, in order to decide whether it is prescriptive or descriptive. Further, one should beware of deciding purely on the strength of normative verbs like 'ought to'. In common usage "That ought to be true' or ' That should be so' can often mean "That will most likely hold true', which is descriptive. The distinction between descriptive and prescriptive (normative) statements has since Hume's tine been regarded as fundamental in philosophy, logic and science. They are often spoken of as either 'is' or 'ought' statements. Scientific knowledge is often regarded as exclusively consisting in descriptive statements, and many scientists hold that normative statements which express values must be eliminated in favour of the descriptive 'facts'. Whether this is actually so in science is a controversial issue, for reasons that cannot be examined at this stage. In logic too, normative statements have long been regarded as being illegitimate for all deductive purposes, for one cannot deduce values from facts or vice-versa. Even this is contested by modern logicians developing logical theory to accommodate the logical relations between general norms (values) and specific values which can be logically derived from them.

Analytic and Synthetic Statements

The language of philosophy abounds with different usages of the words 'analytic' and 'synthetic'. Statements are variously classified under these terms according to a variety of definitions of them. The definition given here is essentially the semantically oriented definition of Arne Næss, as it allows of a wider practical application of the classes than other such definitions do.

Analytic statements are those whose validity or invalidity follows respectively from the correct or incorrect usage of a language convention.
A 'language convention' here includes an accepted usage or rule of usage, such as a definition.

Valid analytic statements are those the validity of which follow from correct use of a language convention.

Eg : 'All heavy bodies have weight.' Such statements are often said to be self-evidently true (though the term 'valid' is more appropriate than 'true' in the context of logic, as will be explained). The validity of the example statement depends upon the correct usage of the words 'heavy', 'bodies' and 'weight'. That is, according to the normal language convention for the use or meanings of these words, the statement is 'obviously valid of itself'.
(Note: The philosopher Immanuel Kant, incidentally, used the term 'analytical judgement ' of those sentences where the concept expressed by the logical predicate is already contained in the concept expressed by the logical subject. This is so only of some of what here are classed as 'valid analytic statements', nor does it always apply to invalid ones, Likewise, Wittgenstein referred to then as 'tautologies', which are self-evidently valid propositions or statements and thus would be classed under 'valid analytical statements' here.)

Eg: 'A rose is a flower'. A valid analytic statement. Its validity depends upon the language convention that the class of plants called 'flowers' always includes the class of plants .known as 'roses'. Further, the term 'rose' is intuitively assumed to refer to a bloom and not, say . to 'a perforated nozzle attached to watering cans' as the context indicates.

Egs: '1 + 1 - 1 = 1'. The validity of this depends upon following the symbolic language conventions of mathematics, as do all mathematically correct statements.

The definition of analytic statement includes examples that cannot be included under Kant's or Wittgenstein's categories (see footnote), yet which function analytically in thought. For example: "When 'Middle Ages' means that period between the fall of the Roman Empire and the rise of Protestantism, eight century philosophy was Middle Age philosophy."
The validity of the main sentence depends upon the language convention stated by the first phrase of the statement. Yet it is also necessary to know that the 8th century A.D. fell within the period indicated, so it is not clearly analytical until the definition of 'Middle Ages' is supplemented to include this.

Eg : "When 'Middle Ages' means that period between the fall of the Roman Empire in the 5th century A.D, and the rise of Protestantism from the 16th century A.D. onwards, 8th century A.D. European philosophy was Middle Age philosophy." This is clearly valid, provided that 'Middle Age philosophy' refers to philosophy in the said period and does not refer to its other characteristics such as its being oriented towards Christian values or the like. The chief point is that the validity of the assertion about 8th century A.D. European philosophy depends upon a language convention and not upon actual investigation of that philosophy or the historical period in case. Had it done so, the statement would he classed as synthetic (see below).

Invalid analytic statements are those the invalidity of which follows from misuse of a language convention. Thus, all self-contradictory statements are invalid analytic (Wittgenstein used the term 'contradictions' to refer to this class).

Eg : 'The area of a triangle is not equal to the space enclosed by its three sides.' This is a contradiction, taking into account the usual meanings of the terms used, (see examples also under 'The Principle of Non-Contradiction'). It is analytic and invalid,

Eg ; "As the farmer said when buying battery eggs from a supermarket: ' Nowadays eggs is not eggs, nowadays!' The assertion one may interpret from this is self-contradictory, yet in the context it is likely that what was meant is expressed by 'Nowadays eggs are not like eggs used to be'. This makes a synthetic statement which is probably true, whereas the first statement, regarded out of context, was analytic and invalid.

Synthetic statements are those whose truth or falsity is established by other means than reference to a language convention. They can only be established (as true) by some sort of investigation, whether of actual states of affairs by observation and experiment, or by other forms of evidence such as testimony from other observers and reading of authentic texts.

Eg: 'If friction is disregarded, bodies of equal weight fall with the same velocity'. This is a true synthetic statement as proven by Galileo's well-known experimental observations. Synthetic statements are not necessarily general statements as in: 'The elephant is not the cause of this mess', or 'The Bishop of New York ordered a campaign for city cleanliness'. In each of the above cases, their truth or falsity are not decided by their dependence on any language convention, although language conventions are of course necessarily involved in understanding the assertions made by them,

Eg: 'The philosopher Kant was a great world traveller '. As Kant is known to have lived all his life in Konigsberg apart from some years in East Prussia in his earlier days and a visit to Sweden in his old age, the statement is false. That it is synthetic is indicated by the method of establishing its falsity by research into the historical facts and testimony about Kant. Unverifiable statements cause no real problem under this distinction for they are invariably synthetic, even though their truth or falsity cannot be established. What matters is how they are established in principle.

As noted introductorily, some sorts of sentence cannot be classified either as analytic or synthetic. These include questions, various comments and jokes, incoherent statements or meaningless expressions (which make no assertion) and statements that are too vague for accurate interpretation. Prescriptive statements that set a norm for the future cannot strictly be classified, though their chief import may be synthetic. Prescriptive definitions present a peculiar ease in that they may be synthetic or they may be neither analytic nor synthetic. She actual statement of any fully explicit prescriptive definition will often make a synthetic statement, such as when it states an intention to follow its rule of usage, such as in "By the term 'fright train' I will always refer to 'the trains that carry nuclear waste through North London every week'. The truth or falsity of this statement will depend upon whether the term 'fright train' is or is not actually used in just that meaning as the definer predicted it would. Thus it is a descriptive statement and synthetic. However, if a prescriptive definition states: 'We ought in future to use the term 'fright train' to refer to 'all trains that carry nuclear waste through populated areas', it becomes a prescriptive statement and is neither analytic nor synthetic.

If statements about possible future states of affairs are predictions, they can be regarded as synthetic, though their truth or falsity cannot be established in practice until the prediction is proven to hold true or otherwise. Therefore, all descriptive statements must be either analytic or synthetic and no prescriptive statements can be synthetic.

Note on the practical application of the above classes of statement

If we go only by statements taken in isolation from their context or communication situation we can decide to which class they belong as expressions without difficulty. This procedure, quite common in some books of logic, has the evident weakness that the assertion is not taken properly into account. As assertions are interpreted from expressions by taking context into account, we find on occasion that one having the form of a general statement must nevertheless be interpreted as expressing a particular statement. Likewise with categorical and hypothetical, descriptive and prescriptive, analytical and synthetic statements. Therefore the above will apply to classes of statement (an expression plus its intended assertion) rather than to either an 'expression' or an 'assertion' alone. Going by expressions alone would give many borderline cases which cannot be judged as clearly belonging to the one class or the other.

Referring to the communication situation so as to interpret the assertion intended is thereby a means of deciding the class in borderline examples, making the classes more highly operational in practical application. Even so there are certain types of expression that cannot be classified at all under the various logical classes of statement. These include most questions, interjections, brief comments, many insufficiently precise expressions, incoherent and senseless utterances and emotive expressions.

The purpose in distinguishing analytic from synthetic statements is often fundamental to understanding their meaning properly. As has become evident, analytic statements are basically about what it is or is not meaningful to say while synthetic statements are not about this but about what is true or false. It can lead to confusion if one interprets an expression wrongly as to its nature as analytic or synthetic. Suppose a person suffering from hallucinations and sudden bursts of anger visits a psychiatrist and is told "Hallucinations and sudden bursts of anger are symptoms of schizophrenia". When the person has got over the shock of it, he or she may ask "Is schizophrenia a disease?" The psychiatrist might truthfully answer, "There is no known disease called schizophrenia, it's only a term we use for brevity to refer to certain sorts of symptom that arise together and cause people problems." In this latter the psychiatrist points out that his statement was essentially about language, about the term used to classify the particular symptoms and not about any definitely known 'disease'. Doubtless this difference would be of importance to the sufferer; it may even alleviate anxiety to know that ' schizophrenia' may be little more than psychiatric jargon, despite the reality of his or her problems and suffering.


1) Consider whether each of the following statements is general or particular. Indicate the logical subject and the logical predicate in each case:-
a) 'The increases in large populations are slowing down'
b) 'The earth is the only one we have'
c) 'There'll always be rises in prices.
d) 'A general breakdown of the world commodity market is already on the way'
e) 'Charlie Brown is not on form today'
2) Consider whether each of the following statements is categorical or hypothetical, giving reasons :
a) 'Hands up!'
b) 'Suppose you want to get rich quickly, then it's not advisable to rob a bank'
c) 'As some chickens do lay eggs and some reptiles do to, then some chickens must be reptiles'
d) 'If some people can be fooled most of the time, then most can be fooled some of the time'
3) Decide which of the following statements are analytic or synthetic, explaining why you so decide:-
a) 'Not all sorts of liquorice sweets are sweets'
b) ' We are actually considering whether we will consider your application'.
c) 'Every sixth person born is Chinese'
d) 'The real distance between New York and London is increasing due to growing delays at airports at both ends'
e) 'a plus b equals b plus a'
f) 'The square root of nine is two'
4) Consider which of the following statements are descriptive and which are prescriptive, giving a brief account of the grounds for your decisions,
a) 'One does not ignore people's feelings'
b) 'I hope the war will not reach us'
c) 'In 2000 A.D, very few of the present nuclear power plants will still be in operation'
d) ' Aggressive behaviour is unacceptable in public places'
e) 'The moral law 'Love thy neighbour as thyself expresses an almost unattainable moral standard'.