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Aristotle’s logic -
Why Aristotelian logic
does not work

Pourquoi la logique aristotélicienne ne fonctionne pas

New translation, the Magna Carta

go to Sums will set you free - the maths zone

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Why Aristotelian logic does not work is the fundamental essay within a group of documents that show how to reason clearly, and so to function more effectively in society.
sociology - the structure of analysing belief systems

Note: this document is optionally non-linear, the position of text and boxes relative to other text and boxes is not definitive.Thus it may be read either linearly or by dodging about, which ever manner best suits your style. Some may find the text outside the boxes difficult to follow at first. In which case, it may help to examine the boxes first.

Because the topics being discussed often interact, for clarity of reasoning some information is repeated in different sections. Thus the section headings are not intended as ‘separate’ categories, but as a help to organisational referencing. For further comment see below.

connecting text

major empiric errors

empirically sound structures

  introduction   the error of the verb ‘to be’   box I – iteration
  reality   the error called ‘equality’   box II - relativity
  categories   the error called ‘zero’ or ‘not’ or ‘negative’  
  words   the error called ‘infinity’ pragmatic/useful structure
  counting is not simple   the error called ‘complete’   box III – inside/outside
  numbers or objects      
  universals and individuals      
  the world of thought as ‘immaterial’    
  essence, meaning and empathy    
end notes and bibliography


By Aristotelian logic, I mean category logic, excluded-middle logic, on/off logic, either/or logic.
No greys – only black and white. This false ‘logic’ lies at the heart of authoritarianism, conflict, and a great deal of inadequate ‘science’.

You are either for us or against us. He ‘is’ ‘good’ or he ‘is’ ‘bad’ . You did, you didn’t. Dyslexia’ is caused by ‘genetics’ or ‘brain trauma’.

Aristotelian logic is also called by some, ‘Descartian logic’.

The problems caused by Aristotelian logic are legion and accumulate. They include the mis-use of ‘properties’, as well as a failure to match ‘theory’ to the real world. Those who take a pragmatic/empirical approach are less likely to be caught by the consequences of this theoretical paradigm. There is much more on the ‘property’ problem in the MetalogicA series of documents – the Confusions of Gödel.

In this document, the elements in the green and yellow boxes refer to the fundamentals of rational communication. Much of the rest of the document is given over to describing the fundamental errors in Aristotelian logic.


You have been raised in an unsane culture. Driving that unsanity is a slavery to words. For sanity, you must learn to attend to reality outside yourself. The woods and the trees are real. To discuss them adequately, you must learn to communicate with clarity. That means understanding the confusions of language that are rife in western culture.

Every time you use a word you make a choice, you form a category to which only you have access.

The errors of Aristotelian logic are so pervasive that they cannot be sorted by one or two simple fixes. Thus I must tackle them in parallel until you may grasp the problems as a gestalt, or else take a leap of faith in completely revising your expressive mental set. Until that point, you are liable to attempt to drive a broken cart that will not go.

It is not enough to attempt to fix Aristotelian logic if you are to cogently discuss issues such as mathematics, politics, philosophy, psychology, economics and the like in a sane and rational manner. For the invasive elements of Aristotelian logic make rational discussion of subtle real-world issues effectively impossible.

It is not what you think that causes the majority of problems in communication,
it is the way in which you think and the manner in which you communicate.

The major part of this document lists the fundamental problems with Aristotelian logic. It is produced for those who need to understand why they should consider revising a system that has contributed to such considerable gains for humans over the last two and a half millennia. This document is also for those who need to understand where the problems lie in the standard cultural paradigm. By understanding this, people may be persuaded to release their grip on an old familiar comfort blanket, preparatory to reorganising their thinking and to considering a more rational model. Further, this document is for those who wish to understand the teaching process.

There are other errors, which are intrinsic to the use or misuse of Aristotelian logic, that have been studied down the centuries. I have listed a couple of sites that provide summaries of these internal problems on my links page. This document is concerned with the fundamental, extrinsic errors of Aristotelian categorical logic, these underlying Aristotelian assumptions may be regarded as empirical falsehoods.

These Aristotelian falsehoods are empiric errors. Aristotelian logic simply does not conform to, or express, the nature of the world as it is. Aristotelian logic engenders a simplistic but erroneous model of reality.

To add to difficulties, as long as the Aristotelian errors, listed and linked in this document, are so pervasive and habitual in the language of our culture, I am to a degree, constrained to use common words, which words may easily be misread. Therefore, as I move from section to section here in this document and highlight the various fundamental errors of the Aristotelian language structures, keep in mind that a degree of ‘relaxation of rigour’ is necessarily inherent if I am to be spared endless qualification of each detailed use of each term.

For example, when I refer to ‘a’ word, keep in mind that each usage is new (see also following section) and further that neither ‘the’ word, nor its referent, is entirely separate in reality. It is merely convenient to treat it thus at a particular ‘point’ in the text. The wide use of quotation marks is used to keep you alert to these problems.

Aristotle had trouble deciding whether ‘the sitting man’ was a different object from ‘the standing man’. The reality is that there are no separate objects, just our choices at individual times to treat the world in terms of separate ‘objects’. Thus we may treat the sitting man as a new object, or as a continuum with the standing ‘object’, entirely at our whim. Separations are made by our personal decisions for our particular purposes, at ‘all’ ‘times’.

Because of the interactive quality of the difficulties presented by Aristotelian (on/off or digital) semantics, I have repeated many of the ideas to some degree in various of the sections of this document.

It is more than possible that various readers may find some phrases ambiguous. Such problems differ from individual to individual; it is therefore not possible for me to remove ‘all’ these difficulties without feedback from readers. If you do find difficulties understanding parts of this document, it would help if you e-mail me with your difficulty. I will attempt to answer your queries and to improve the text where, to me, that appears to be useful.return to index

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I—iteration [4a]

We may iterate to obtain as much accuracy as we require, or have the energy or patience to pursue, but we may never obtain completion or certainty. In reality, such absolutist objectives are illusory for humans. See also the logic of ethics

Each individual has their own notions and intentions. As with any object or objective, the purpose of communication becomes one of negotiating with others to achieve mutually satisfactory outcomes.

Effective communication is done by a sequential process of continually refining understanding between individuals. This process includes the settling upon definitions of any approximate objects to be discussed, the objectives to be discussed, and the words with which those objects are to be discussed.

Some may wish to be very careful and precise in their attempts to understand others well. Those who do not wish to put in such effort tend to be called ‘lazy’, while those called ‘lazy’ tend to call the careful, ‘neurotic’! Thus is the intolerance of differences.

If in doubt check, always seek feedback. Is it that plate or this? Do you mean here or here? What do you mean by that word? Show me how you use that word using real objects that I can see, as a means to demonstrate.

Always, always, seek feedback

For effective relationships, negotiation is central. Negotiation is a form of iteration. Often such negotiation becomes a matter of power; I discuss this further in feedback and crowding and in the logic of ethics. return to the index


One day, Manjushri stood outside the gate when Buddha called to him. "Manjushri, Manjushri, why do you not enter?"

"I do not see a thing outside the gate. Why should I enter?" Manjushri replied.

Where is the gate? Are you inside or outside the gate?

The above is a Buddhist koan. [5a] Such ‘stories’ are designed to evoke satori (enlightenment), that is, the realisation that all words are grass.

All categories are arbitrary; categories do not exist ‘out there’. Once your mind is ruled by category, you are in a mind-trap; you are unable to think with clarity or independence. To think clearly, your mind must be still and clear of any words.

"I only think well when my mind is calm," M. Botvinnik.[6]

I don’t wish to be gobbled . For example, frogs dive from predators, and plants produce poison and thorns to discourage others from turning them into dinner.

Categorisation is necessary for life and survival; categorisation is a matter of pragmatism.

The first twelve chapters of Book 7 of Aristotle’s Politics sketch the connection between philosophy and politics: namely, that the highest purpose of a city-state is to secure the conditions in which those who are capable of it can live the philosophical life. Such a life, however, lies only within the capacity of the Greeks, whose superiority qualifies them to employ the non-Greek tribal peoples as serfs or slaves for the performance of all menial labour. Thus, citizenship and service in the armed forces are considered to be the exclusive rights and duties of the Greeks.

At about the same time, Aristotle composed the work, now lost, On Kingship, in which he clearly distinguishes the function of the philosopher from that of the king. He alters Plato’s dictum – for the better, it is said – by teaching that it is not merely unnecessary for a king to be a philosopher, but even a disadvantage. Rather, a king should take the advice of true philosophers; then he would fill his reign with good deeds, not with good words.

Aristotle formalised the categorical thinking that has evolved into a dogma in western society. As a dogma, it has been extremely useful in analysing the world (Aristotle called his logical system ‘analytics’). However, it has also tended to inhibit creative and realistic thinking.

The arrogant and rather dull Bernard of Clairvaux said of Abelard, “you will find something more in the woods than in books. Woods and stones will teach you what you cannot hear from masters.” [7]

Abelard kept discussion of ‘god’ out of his work on logic. In a passage in his commentary on Porphyry, the question of ‘god’s’ intellect arises in the context of the problem of knowledge of the future. ‘god’s’ perception of the future, Abelard says, is most sensibly resolved by saying that: 

His substance, which alone is unchanging and simple, is varied by no conceptions of things nor by any other forms. For; although the custom of human speech presumes to speak of the creator in the same way as of creatures, by calling Him provident or intelligent for example, nevertheless nothing in Him should be, or can be, understood as distinct from Him: neither perception nor any other form. Therefore any question about perception is irrelevant so far as God is concerned. [8]

Abelard also tries to make his contemporaries understand that there is a fundamental difference between talking about ‘god’ and, alternatively, discussing what others have said of ‘god’. It is but a short step to substitute in the writings of the brighter of the scholastics, the term ‘god’ with the word ‘reality’, whence texts that may read as obscurantism and mysticism to a modern starts to make eminent sense.

Thus Abelard, in the 12th century, is concerned with the connectivity of ‘objects’. More recently, Brouwer [9] and others have expressed similar concerns through an attack on the Aristotelian dogma of the excluded middle. By better understanding the varying semantics of considerable thinkers down the ages, it is clear that, despite their different words, their meanings are often rather similar. Again, this is a major concern in Abelard’s monumental Sic et Non.
For more details on the problem of the excluded middle, see the logic of ethics.return to index

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Words are, by their usage and near natural (physical) reality, categories chosen by individuals. The words are not ‘identical’ with the ‘substance’ (real matter) at which individuals point, when they use those words. Reality does not somehow magically split when we choose our usage of categories; category merely helps us to communicate and to mediate our relationships with reality.

We likewise treat the words as separate items and imagine that, in turn, those words are capable of referencing separate items. For further discussion in a more complex context, see Feedback and crowding.

Thus to control our world and to communicate about it, as a pragmatic act we section off reality, in order to enable us to handle complex matters within our very limited understanding. We build up our understanding, first by accumulating rather minor ‘bits’ of information about the world, and then by attempting to synthesise patterns from the cacophony of reality; see also MetalogicB1 – Decision Processes.

So we act as if reality is sectioned into ‘parts’. Reality however, remains universally interconnected. The moment we lose sight of this fact, we move toward hubris and error. As human animals, we further tend to make a strong separation between our ‘individuality’ and the ‘rest of the world’. But again we are connected, we are ‘part’ of the universal reality. Words are ‘part’ of reality. The words that we treat as ‘separate’ are also involved as noises or marks on paper or cathode ray tubes in the universal reality.

The human enters the world without language. Because language is so very useful to human progress, a central objective of education is to develop language usage; but the process goes too far. Language is near universally taught in such a manner that it ceases to be merely a tool for communication, but become a straitjacket upon the thinking progress. This extends until most humans cannot think outside ‘the’ mass of words circulating in their consciousness that becomes a substitute for independent, reality-based analysis. That is, humans become addicted to language, they become the servants of local language structures instead of the masters of language. [12]

We are not required to throw all previous knowledge of logic to the winds as useless. But we must considerably increase the rigour of reasoning and, from the earliest age, train different habits of thinking about language if we are to free ourselves from the language trap.

To establish sane habits of language usage, it is necessary to develop usage that is both in accord with the human condition and in accord with the nature of the reality in which we find ourselves enmeshed.

The categories we use for habitual thinking are fundamentally false to reality, as to some degree they are bound to be. They still must conform to reality to such an extent that they are reasonably useful, easily understood and widely acceptable.

Thus for useful language structure, it is essential that I proceed with an assumption that my reader will agree to the categories I establish. The categories are based upon what I have found to work; that is, the categories are pragmatic. They are most definitely not static; they are intended to be demonstrable to reasonable people upon the sole criterion of pragmatism. These categories are assertions about how communication will work in practice. I am widely convinced that the present underlying, unexamined premises abroad in western society do not work in the real world much of the time, particularly when discussion gets complicated. I am convinced that the principles I am stating will and do work, however complex discussion becomes. That is, I am establishing empirically founded assertions that are structurally capable of negation.

If we become caught in the separated construction that we assemble for our own feeble-minded convenience, if we start to ‘think’ in words rather than control the words for our communicative purposes, we move beyond sanity.

Brouwer in 1907 put it thus:

However, in general the consideration of sequences and consequent going back from the end to the means, where intervention appears easier, show themselves very efficient tactics from which mankind derives its power. Man succeeds in discovering regularities in a limited field of phenomena independent of other phenomena, which consequently can remain completely latent in the intellectual consideration of the former. [13]

The development of ‘religion’ is the history of development of world-views among steadily more sophisticated societies. Gradually the world-views have moved from dogma to empiricism, as we gained better understanding. We often hear this called the advance of ‘science’. But ‘science’ is also a form of religion.

Aristotle, in Posterior Analytics, imagined that science could be placed upon fundamental axioms. As understanding has progressed, it has become clear that effective progress is based in empirics. That is, all ideas of our strange home are subject to constant revision as new data is gathered. Step by step, traditional ‘religion’ has been driven out of large areas of human understanding, as empirics advances over dogmatic axiomatics.

Aristotle, in Politics, also imagined humans to be essentially political animals and discussed political systems in terms of the various characters of citizens. That is, he grounded politics in views concerning human psychology. Ever since, the field of human behaviour has been claimed by various axiomatic approaches of differing societies.

Dogmatism has yet to be driven from human concepts of individual and social behaviour.
It is my intention to lay the logical basis for achieving that end.

Naturally the extent of knowledge concerning the human state has steadily grown down the centuries, as it has in all studies of interest to humans. But systematic progress only develops when descriptions that ‘reasonably’ reflect reality are established. Aristotle called the human a rational animal, by which he intended the meaning: an animal that uses language.

Psychological study is so complex that the Aristotelian axiomatic system of itself introduces fundamental errors of ‘thought’.

The wish for any Aristotelian-based ‘theory of everything’ imbibes ‘the’ error.return to index

the error of the verb ‘to be’ [14]

To understand communication, it is essential to understand that each person uses each word differently, both from each other and also on each occasion of usage.

We use the words primarily to point at ‘objects’ in the real world. Words are similar to sticks with which we might choose to point.

The use of the verb ‘to be’ has a high propensity to confuse the word with the object at which we might point. ‘That is a house’ we might say, when what we mean is, ‘I wish you to direct your attention to that house over there.’ The thing to which we point is not a ‘house’. It is an arrangement of real matter in which some may well choose to live. And once again that sneaky word ‘is’ creeps in to our conversation. What is ‘really’ meant is that I call that object over there a ‘house’ and wish to discuss that object with you.

The introduction of the word ‘is’ has a considerable ability to confuse the mind of the humans who spend so much of their focus of attention upon words. For sanity, the focus must be on the real material of nature, not upon the words that describe. One must always attend to observing the ‘objects’ to which the words point.

Unlike Manjushri, the human child is conditioned to think in words as if those words are the reasonable objects of thought. Humans learn to ‘think’ in words, rather than merely acting impulsively in the world. While this brings great benefits, it also brings great confusions and dangers, particularly when situations become complex.

The real world does not sit quietly with our pre-arranged words. The world is in constant flux and change. If we learn to think in words, that process has the undesirable side effect of inclining us to think with in the limited and confused categories we have imbibed through language. Thus language limits our flexibility of thought.

Manjushri has become aware of this, as some humans do. Manjushri is ‘enlightened’.


Most who come to the state of satori have proceeded from the inchoate ‘natural’ state of the newborn who has no language, that is they may be said to be ‘pre-verbal’.


Then they move onward to the ‘verbal’ state of using language upon which they become addicted, and by which they become trapped.


Some few move thence to satori or enlightenment or to a ‘post-verbal’ state, when they become aware that real independent thought must live in a world of silence beyond words.

See also here for more details.

Most never move to stage three. Far better that children were taught in such a manner that they never become addicted to stage two.

This may be achieved by constantly making the child aware of the differences between language and the ‘outside’ world. “I call that object a plate”, “that is a picture of a duck” in place of “that is a duck” or “that is a plate”.

It is not required that one becomes neurotic, just that you establish clearly in the child’s mind the awareness of the nature of language as useful for communication, but deadly and deadening for enlightened thought.

Playing games with words is also useful. Calling the plate a duck and the duck a plate reinforces the separation and flexibility of mind.

As the child develops language, prior to becoming too fluent, it is common for the child who has learnt the word for daisy to decide that all flowers are daisies, or to call a sheep a little white camel. Children are far more flexible until the addictive forms of language intervene and destroy their flexibility. Our language teaching thus tends to teach the young to think in rigid manner, which then limits their potential. That is, teaching tends to teach how not to think efficiently, the very reverse of any sane objective.

True thinking is silent

Words going around and ‘around in the head’ are destructive of sanity. If this happens to you, you need to learn to refuse words every time they enter your head/‘thinking’. To achieve this, it is an assist to concentrate on looking at and feeling some real-world object of your choice, such as a stone or your favourite teddy bear.

Words are for communicating; they will be there when you need them.return to index

counting is not simple

A great unexamined assumption down the ages has been that counting is some simple process which all can understand; counting is no such ‘thing’. We are taught a series of ordered magical grunts in childhood, ‘one’, ‘two’, ‘three’, etc. We learn to associate these magic noises with what we imagine to be ‘objects’.

No ‘two’ humans ever occupy the ‘same’ space-time. The space-time position currently occupied by one human can never be occupied by another human. Everything each of us sees is necessarily ‘different’ from that seen by others, for we are not the other. We are our ‘separated’ selves. At the core of our language usage is an assumed separateness of individuals and the pragmatic separation of words. That separation includes the words called ‘numbers’ (also see box III).return to index

numbers or objects

The meaning of the word ‘one’ is synonymous with the meaning of
‘thing’ or ‘that’ or ‘the’ or ‘bit’ or ‘object’

Numbers have no magical essence. Numbers are no different in nature or type than any other words. ‘Two’ just means “object and another object”. Numbers are words, they are not more than words and they are not less than words. There is no essential difference between language and mathematics. To attempt to teach mathematics as somehow separated from language is poor and confused pedagogy.

Humans use numbers to point at objects, just as they use other words to point at objects. Words point at objects, just as a stick may be used to point at objects. The words themselves are as much real-world objects as are the objects at which we point. A word is marks on paper, speech causing a mass of air to vibrate, an electro-chemical configuration in our real brains, and so on.

An ‘object’ is just what any individual human decides at that moment is an ‘object’. Objects do not somehow ‘exist in their own right in the world’. As Manjushri is aware, all is one. It just happens to be convenient and useful for humans to separate out and focus upon ‘bits’ of that unified reality.

When a human decides to refer to some ‘section’ of reality, in order to examine ‘it’ or to communicate about ‘it’ with another human (object), it is not possible for either human ever to understand ‘exactly’ what the other human is focusing upon. It is not even possible for humans to ‘fully’ delineate or define anything. The best that may be hoped for is approximations (see section on ‘complete’).

Even the human doing the pointing is limited, to the extent that they cannot focus upon the microscopic detail, nor keep up with the ever-changing movement of the atoms and shifts in space.

Remember, the human doing the pointing is subject to constant change as well. Thus on repeating a word, the human will have changed and the supposed object to which the human points will also have changed.

Every use of every word by every person is different

One might say every object is different at all times, but naturally we cannot pin down any object to make such a statement fully meaningful. Nor can we fully establish a separateness of objects, including a separateness of ourselves.

All ‘objects’ are in flux

Fortunately these difficulties, and differences or changes, are not so great that we cannot use words with pragmatic effect. Despite the problems, we can communicate sufficiently effectively to enable and enhance our everyday life and survival, but we are wise to keep in mind the very real limitations of language.

We may proceed by not worrying too much about the inevitable inaccuracy of all language usage, thus accepting a generalised relaxation of rigour. That is, by accepting sufficient similarity as a replacement for any ambition to some unattainable ‘total accuracy’ or ‘equality’.return to index

II –relativity

The idea of a ‘naughty’ or ‘good’ person or other object, is mis-thinking. What is really meant is that the other person is acting in a way that conflicts with, or alternatively, serves my interests, my ego or my sense of aesthetics. All ‘naughtiness’ or ‘goodness’ is relative to our own individual objectives or interests, there is no absolute (see the logic of ethics) standard written in the stars. We make our own cultural rules according to our power, our comfort and our tastes.

The description of the relationships of objects does not require the use of the concept of space. It requires only measurement of distances between objects. Time is not some phantasm.

Time is movement

The movement of objects, such as the pendulum of a clock, we use to measure what we call time.[14a] Thus does time become a matter of the relativising the movement of one chosen object with another, without a need to refer directly to the qualities of space.

So modern physics attends to Occam and ignores space, and merely measures relative movement and distances. Space does not thereby cease to exist, but attention is not focused on this most difficult aspect of reality.

The movement of a ball thrown across a room may be measured in the framework of the room and tracked by the imagined regularity of a clock. The room, also, may be measured in its movements relative to the earth, as the earth spins and walks around the sun. The individual, likewise, can be measured and tracked as they walk upon the earth. Meanwhile, the heart ticks as a clock within the moving body, as part of the body’s constant internal change or movement.

All change is measured thus. As you speak, your words take a finite time to reach the ears of another. Meanwhile your body is in external and internal motion; so with the body of your communicant; so with the objects you have chosen for your discourse.

Thus there is no ‘absolute’ ‘static’ framework, just sufficient stability for much everyday discussion. Such limited stability is not reliable and within complex conversation the instability can confuse. For sanity it is well to keep this in mind.

five blocks, each containing four 'similar' objects. Each block is rotated 90 degrees.Thus, in the fifth block the positions of the objects 'look' 'the same' as in the first block.

Consider four blocks. Consider an experimenter and a subject. Consider the blocks going around step by step in a ‘circular’ clockwise motion. Consider the subject exiting from sight of this ‘clock’. After an interval the subject returns to find the blocks which appear, to the subject, to be in the original position. If the subject depends upon this ‘clock’ for their sense of ‘time’ and if the subject is unable to distinguish any difference in the position of the components of the block clock, to all intents and purposes, ‘time’ is static for that subject relative to that clock. Of course they still have their own heart-beat and a remembrance of moving out and into the presence of the clock. Without such remembrance, in the absence of an external clock, time effectively ceases for that person.

Remember, separations of space and time are likewise arbitrary.return to index

the error called ‘equality’

To understand words, it is necessary to understand that words
have no fixed or certain meaning

Heraclitus said, “You cannot step into the same river twice”.

You live on a surfboard, the world is constantly shifting around you and within you. To be effective, you must learn to ride the surf and to keep your balance, not attempt to stop the river, or even fuss to speed it up.

Most attempts to understand words thereby miss all useful understanding or meaning.

Poincare stated “Mathematics is the art of giving the same name to different things”. [15]

Skolem writes “The use of the equal sign in what follows is always to be understood in the sense that two names or expressions mean or designate the same thing”. [16]

Jefferson declared, “all men are created equal”. [17]

Knowledge proceeds by empirics. Empirics is the true arbiter of useful knowledge. ‘Theories’ are current best available descriptions. Theories are pragmatic patterns of communication. ‘Theories’ are perhaps the most efficient, common means of communicating our current knowledge in a particular area available at this time. Theories do not exist as ‘objects’ or ‘things’ in some mysterious hyperspace.

No ‘two’ usages of a word are the ‘same’. The very ideas of ‘same’, or ‘equality’, are false to reality. Human use of the term ‘same’, when used rationally, means, ‘sufficiently similar that I do not care about the differences’ or even, ‘I cannot discern the differences’. Realise that ‘theories’ are, at all times, subject to the different word understandings of the participants in those communications.

If I fit the pistons into the cylinder block of an engine, it matters not which piston goes in which cylinder. Each cylinder has relatively small variations and each cylinder is formed from differing masses of metal. For the purpose of an engine this does not matter. So, we say loosely, all cylinders are ‘the same’, but of course they are not.

[See also ‘equality’]return to index

the error called ‘zero’ or ‘not’ or ‘negative’

‘This nothing is a very important something, since it is that out of which god created everything’.[18]

‘Whereof one cannot speak, thereof one must be silent’.[19]

Zero has no existence or meaning outside of context. It is possible to have no elephants in a room.
It is not possible to have no unicorns in a room, for there are no unicorns not to be in the room.

There is no object called the empty set. A set is a collection of objects. Without objects, there is no set.

In both situations, there is a pre-supposition of individuals in the real world available to be placed in the collections. One might imagine a set as a collection of items in a box, in which case there is a real-world box in which to place the collection. If the box is emptied of elements, the real box remains.

If there is to be a mental set, it exists as a real encoding in the brain, ready and available to take up a list of real-world items. Either the set/box exists in the real world or it does not. If the box does not exist, there is no set, empty or otherwise.

The legal right to silence grows from an awareness that no legitimate inference may be drawn from that which does not exist. Therefore, in less educated societies, such rights do not exist. [20] Likewise, what cannot be counted is best treated with caution. It is very difficult to count that which cannot be seen, whether it be gods or unicorns.[21]

The asymmetry of not. To tell you that I have no high explosives in my pocket does not give you any information about ‘items’ that may reside in my pocket. All it tells you is what I say about one kind of object not being in my pocket. Likewise, to tell you that I don’t call the four-wheeled vehicle that is resting outside my cave a dog, does not give you information about what I do call it. On the other hand, if I do tell you that I have a hat upon my head, you have a clear idea of a real-world fact. In the first case, you are left with a myriad ‘possibilities’. In the second case, the possibilities are much constrained. Thus, negative statements give far less information than positive statements. Negative statements and positive statements are not symmetrical. Yes and no are not ‘opposites’, they are ‘different’ (see here for more detail).

Note that a form of zero is used as a marker in the number 101 and on many scales such as for the measurement of temperature. For example, the centigrade scale zero measures the temperature at which water freezes, that is 273 degrees above ‘absolute zero’, which is a point at which localised movement (and thus time) ceases. Such conveniences are not at issue at this point.return to index

the error called ‘infinity’

We have a system of counting that allows continuation from any point. Likewise an engine has the means of continuation from any position. Eventually the engine wears out and fails, likewise the counter.

What we may call a table eventually ‘wears out’ or rots away. At some point, we cease to recognise it as a table; it becomes compost or smoke. Categories are not permanent. There is no ‘infinity’ that goes on for ‘ever’. Wherever such fictions are used, they may be replaced with some suitable, very large number.

Another form, sometimes referred to as ‘infinite’, is but an open system where no decision as to a stopping point has yet been chosen or occurred.return to index

the error called ‘complete’

Much of superstitious ‘religion’ is built upon ‘concepts’ of ‘perfection’. There is great fear among humans that analysis will lead to a removal of wonder in a world where wonder is surely appropriate. It is difficult for fearful humans to adjust to the reality that insecurity is inherent in uncertainty and wonder. We live in a wonderland that is both far beyond our comprehension and our control. Many seek some unattainable ‘certainty’, or a ‘complete’or ‘absolute’ or ‘precise’ understanding, such are not available. For peace and equanimity, we needs must accept our reality and limitations, not seek opiates or escape. Thus the great ‘theologians’ emphasise the unknowability of ‘god’.

We may always increase our precision, but we can never be precise.

The notion of some imaginary ‘perfect’ circle is but a statement about the limited acuity of human visual equipment. The lack of precision does not amount to the possibility of some potential ‘perfection’, or ‘certainty’, somewhere ‘out there’ on some sky-hook. Once again, it is a matter of maintaining silence when being tempted to speak of that which does not exist or, at the least, not introducing entities without cause.[21a]

Similarly, ‘all’ is only used with legitimacy in the context of a pre-defined set of ‘objects’.return to index

universals and individuals

For a person to think with flexibility and realism, it is essential that they learn to think outside words.

Much human communication is through words. There is no such thing as the opinion of a country, or of any other group or organisation. Only individuals have opinions. All else is confusion or rhetoric. People may act in alliances, but there is no possible guarantee that the objectives of various individual allies who seek alliance are coherent. Each individual acts entirely to their own agenda, whatever the appearances a confused individual may generate or imagine.

There is much confusion between the idea of an act, and the idea of an object. Reality is that the terms ‘act’ and ‘object’ are synonyms. That is,

actions are objects.

An action is an object moving over a chosen time-period. For example, Aristotle sitting on a chair for two minutes ‘is’ an object we may decide to call Aristotle. Archimedes running down the street starkers ‘is’ the object we may decide to call Archimedes. Any object is changing through time. Referenting an object with a word, such as ‘a stone’, is fundamentally not different from referenting the running object called Archimedes. The common distinction ‘between’ noun and verb is therefore empirically dubious. The difference is merely that our attention, in the case of the stone, is not upon the movement or change of the stone. I will leave it to you to think about where our attention may lie in the case of Archimedes.

Individual purposes are not publicly available, only the acts of individuals are public. Acts are not aims. To imagine that aims may be subject to full examination is both irrational and futile. Trust actions, not words is the very sound advice of Machiavelli. However, words are also actions.

Words are noises made by real mouths vibrating air and by the writing of real marks on real substrate by real actions. An empirical approach may be applied to test for habitual coherence between the real words and the real acts of individuals, and some view to consistency may be drawn. However, keep clearly in mind the multiple layers of potential misreading and misunderstandings to which words are inherently subject.

(117) Priscian [(111)] [22] calls these common conceptions “general” or “specific” because, in one way or another, they suggest general or specific names to us. He says universal terms are themselves, so to speak, proper names for these conceptions. Even though they are of confused signification as far as the named essences are concerned, they do immediately direct the listener’s mind to the common conception, just as proper names do to the one thing they signify.[23]

Problems have arisen in human communication for thousands of years because of what are called universals. Universal words (or ‘universals’) are words that are applied to general conceptions, words such as ‘table’ or ‘person’. These words do not apply to single objects that are immediately available to the senses such as John or Jill, [24] or the approaching ’bus, or the spoon on your plate, but are words which are applied by humans to a variety of supposedly similar objects. There is more on this in The Confusions of Gödel, part 1.

Humans are widely confused into imagining that because a word may be said, a real singular object must exist associated with that word, but that does not follow. Universals may be imagined as little mental programmes that differ from human to human.[24a] These programmes exist in the brains of individuals, and they also differ subtly from individual to individual. The differences are also unavailable for any ‘complete’ investigation. (See also Iteration (box I).

A ‘universal’ is an ‘individual’ residing in a particular human brain.

‘The’ and ‘a’ as prefixes tend to qualify words as ‘individuals’ or as ‘universals’. They are often used to lend a false air of authority. Be cautious to ensure that a likely ‘object’ exists when a word is thus prefixed,as in a ‘bargain’, the ‘set of unicorns’ or the ‘wonderful government’.return to index


Assessment of human veracity is a statistical study made by observers. Such observances can only be applied after the events, they are never very reliable for future events.

The perception of the correlation between words and acts may vary wildly between actor and observer, and among various observers. Certainties are mere illusion and self-delusion.

Mind-reading [25] is not an option. Most humans, in their vanity, imagine far more diagnostic power in understanding acts and motives than is rational. If an individual is not ‘emotional’, others tend to make wild guesses at the internal state of the quiet individual. People may even become most peeved when a person does not exhibit emotional noise, which state is still often read as ‘emotion’, attributing the quietude to all manner of paranoid interpretation (i.e. guesses). Humans are disturbed by a lack of ‘clues’, they often react with fear and then with aggression. Hence, many labelled ‘normal’ exhibit a cacophony of emotional noise, as part of their attempt to convince or gain acceptance from others, or from sheer panic and habitual agitation.

Individuals apply their internal understanding of various words in accord with their individual differing experiences. The widely held assumption that the word that you may use has some ‘accepted’ definition is false. Nor are your internal meanings understood with reliable certainty by those others who may hear your words. Likewise, your understanding of the words of others is at best approximate.

Dictionaries, at most, can give some approximation of common usage; those definitions have no external static certainty. Dictionaries are not authorities, they are guide-books. It is common to imagine that ‘definitions’ in dictionaries are authoritative in everyday conversation. This is in error for, as stated, all usages of words at all occurrences are new. A dictionary merely attempts to give an averaged ‘common’ usage, it can not do more. Dictionaries provide approximate relationships between words, not some static certainty. All such forms of dogmatism do not meet empirical reality tests. Words, of themselves, do not have meanings; words are dynamically assigned meanings by local varying individual inclinations. return to index

the world of thought as ‘immaterial’

A major confusion arising from Aristotelian categories is the ‘idea’ of the ‘immaterial’. There is no (see also comments on the ontological argument and authority elsewhere) useful ‘meaning’ to ‘the world of the immaterial’. If ‘such a world’ is ‘immaterial’, how, one may ask, is such a world to be detected, let alone be demonstrated to another ‘individual‘? As Aristotle seemed to realise, and as certainly did Occam, all knowledge is first in the senses. Aristotle and others have managed down the ages to convince themselves that ‘things’ that are ‘immaterial’, in some sense, ‘exist’, or exist in the ‘mind’.

Now, as with Occam, in order not to multiply entities without cause, I will take the mind to be an expression of the brain in action. However, this is a more recent understanding.

The ‘sort’ of ‘entity’ that was considered ‘immaterial’ would be: ‘the’ ( see to be)‘perfect’ (see ‘perfect’) circle.

Consider that the human brain is a digital device; essentially, either neurons fire or do not fire, rather as with transistor switches in computers. However, the world ‘outside’ the human brain ‘is’ essentially ‘continuous’. The human brain tends to elide differences that become too fine for the discrimination of its peripheral systems and its digital system. Thus, a circle is so round or continuous that the brain cannot distinguish the small real world variations that factually exist. In the same way, it becomes very difficult to discriminate whether the moon is ‘full or not a few minutes or hours before ‘precise’ ( see ‘perfect’) fullness.return to index

III   inside/outside and separateness

There is no inside/outside, but it pays to maintain such a distinction for the purposes of communication. At the same time, you must keep clearly in mind that you are engaged in a pragmatic strategy, you are not ‘saying’ something very meaningful about reality.

Remember that no person ‘out there’ can see your thoughts, they can only hear your words and watch your behaviour. Their input is your output, while your output is their input.

For each word you use, others will have different meanings than your own; their meanings are drawn out of their experiences, which experiences are always different from your own. Similarly, each time you hear the words of other people, be cautious that you understand their meanings adequately for your current needs.

Look at the people outside yourself and imagine what they can see and understand, as they look at and listen to you. Remember, their understanding of you is severely limited, their purposes and experience differ from your own.return to index

essence, meaning and empathy

The ‘idea’ of ‘empathy’ is another error of thought. We cannot know the mind of another, we may only make crude guesses and do our best to understand the messages that others signal to us. That we may at times guess correctly the needs of another, does not turn a guess into knowledge.

Guessing right is not being right.

Nor can we ‘understand’ the ‘essence’ of some ‘other’ object (see box III) that exists outside our bodies (compare with ontology section and The error of ‘qualities’ or ‘properties’). We may only interact with such bodies. Objects do not have ‘meaning’; objects only have relevance or use to us as individuals. Frogs legs have an entirely different meaning to a French gourmet than their meaning to the frog. We may see a stone, or interact with a stone, but to talk of the ‘essence’ of a stone is quite without meaning. ‘Essence’ is an introduction of a redundant entity: taking Occam’s advice, it is better that this primitive notion is allowed to go into silence.

Guessing is not ‘knowledge’, but it is the best we have.
Therefore, tolerance and patience is an essential to any sane communication.

As individuals, we may intend meanings or signals to others by our acts. Such gives us no strong grounds that others will understand our intended meanings. Only by experience and constant experiment can we build a data bank of what will probably work for us in any given new situation. To rail and fuss when not understood is irrational; patience and caution are necessary to attain useful and sane communication. (see box I). ‘Mind-reading’ is not a verifiable human attribute.

Relationships are not ‘symmetrical’ or simply countable; ‘falling in love’ does not guarantee reciprocity. Relationships are trades, what is value to one may be without value to another. Of course, some are dishonest enough to suggest the value of an object or service is far below their real reactions. As usual, experiment and caution are the means of progress.

You cannot read the purposes of another, only understand as best you may. Likewise, others cannot entirely understand you and your purposes. Tolerance of such difficulties and differences is basic to sanity.

Tolerance and patience are not some sign of grace or a message from the ‘immaterial’ world. Tolerance and patience are essential to sane communication, by the nature of reality and the human condition within that reality.return to index

Related further reading

the confusions of Gödel (in four parts) The logic of ethics
Decision processes Feedback and crowding
    For related psycho-logical documents, start with Intelligence: misuse and abuse of statistics

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End notes and bibliography

  1. unsane:
    a form introduced by Korzybski.

    abelard uses this term to refer those who are not in contact with reality, who are unrealistic. We can also say, "not of sound mind."

  2. gestalt:
    to view as an organised whole that which is perceived to be ‘more than’ the sum of its parts.

    For example, to take the view that a ‘car is an object which hurls us around the planet’ is to view it as a gestalt. To view it as a bunch of tyres, seats, carburettors and the like would be to view it as a sum of ‘parts’.

  3. empiric:
    relying upon reality feedback / experiment.

  4. referent:
    that to which a word refers.
    The word ‘stick’ refers to an object ‘out there’ in the real world.
    To say ‘the word stick’ refers to the word, ‘stick’.
    Both the word ‘stick’, and the object ‘out there’ are ‘objects’.
    If this is a little confusing to you, worry not, it will seep in over time.

4a   For greater detail, see feedback and crowding.
  1. satori:
    the term implies no element of praise.
Zen illustrations used to bring attention to the insufficiencies of verbal communication, and to show the dissonance between language and the real world (‘objects’).
  1. Botvinnik, Mikhail Moiseyevich
    (b. 17 Aug. [4 Aug., Old Style: the Gregorian calendar was not introduced to Russia until the revolution!] 1911, St. Petersburg, Russia—d. 5 May 1995, Moscow),
    Soviet chess master who held the world championship three times (1948 – 57, 1958 – 60, 1961 – 63).

    Abelard, a medieval life by M.T.Clanchy
  2. Clanchy, M. T., Abelard, a Medieval Life
    pbk, 1999, Blackwell Pub, 0631214445
    £23.74 [amazon.co.uk] {advert} / $44.95 [amazon.com] {advert}.
    This publication lacks the rather pompous tone of much historic writing and the author is not afraid to guess a little. It therefore gives a good feel for the times.

  3. Clanchy, 1999, p.106 from Logica Ingredientibus p.27, lines 9-15. (See translation by Spade, §140 on p.50.)

    From Brouwer to Hilbert by Paolo Mancosu
  4. Brouwer’s language is sophisticated and personal. It takes some getting to understand. As a starting point for those wishing to plunge into this more deeply, see for example: Paolo Mancosu, From Brouwer to Hilbert, pp.40 – 44 
    1997, OUP, pbk, ISBN-10: 0195096320 / ISBN-13: 978-0195096323
    £23.99 [amazon.co.uk] {advert} / $42.95 [amazon.com] {advert}

  5. pragmatic:
    what works in reality.

  6. as if:
    Hans Vaihinger wrote an enormous and tedious treatise in 1911, titled
    The Philosophy of ‘As If’, in which he proposed that pragmatism is served by proceeding on false but workable assumptions. The idea is useful, but it did not need 370 pages! For more detail see box III.

  7. Alice through the looking glass by Lewis Carroll [UK]‘There’s glory for you!’
    ‘I don’t know what you mean by “glory”,’ Alice said.
    I meant, “there’s a nice knock-down argument for you!” ’
    ‘But “glory” doesn’t mean “a nice knock-down argument”,’ Alice objected.
    ‘When I use a word,’ Humpty Dumpty said in a rather scornful tone, ‘it means just what I choose it to mean—neither more nor less.’

    ‘The question is,’ said Humpty Dumpty, ‘which is to be master—that’s all.’
    Alice through the looking glass, with Alice in Wonderland, by Lewis Carroll [USA]
    Lewis Carroll, Through the Looking-Glass (1872, Ch. 6)
    1994 reprint, ISBN-10: 0140620877 / ISBN-13: 978-0140620870, £1.80 [amazon.co.uk] {advert}
    1999 reprint ,Wordsworth Editions, pbk, ISBN-10: 0760716196/ISBN-13: 978-1853261183, $4.99 [amazon.com] {advert}

  8. L. E. J. Brouwer, Collected Works, Volume 1, written in 1907,
    (ed. by A. Heyting, 1975, 0720420768, out of print), p.53.

  9. See also E-Prime.
14a   For more on time, see time 2 box in Metalogic B1: Decision processes.
  1. Men of Mathematics 2 by E.T. BellPoincare, J.H.—see Bell, E.T., Men of Mathematics 2 (1965, Pelican Books), p.609.
    Reprinted by Simon & Schuster as Touchstone Ed (1986, 067162818, $13.60)
    ISBN-10: 0671628186 / ISBN-13: 978-0671628185
    $13.50 [amazon.com] {advert} / £9.45 [amazon.co.uk] {advert}

  2. Skolem, T.A., ‘The foundation of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains’,
    From Frege To Gödel, A Source Book of Mathematical Logic, Harvard U.P.translation in Heijenoort, J. van, From Frege To Gödel, A Source Book of Mathematical Logic 1971, Harvard University Press, p. 303

    2002 reprint, Harvard University Press
    ISBN-10: 0674324498 / ISBN-13: 978-0674324497
    $31.50 [amazon.com] {advert}

  3. Jefferson, T., see opening lines of the American Declaration of Independence, 1776.

  4. Fridugisus, 9th century. From
    ‘Carolingian debates over Nihil and Tenebrae: A Study in Theological Method’,
    Speculum, 59, (1984), pp. 757-795.
    Tractatus Logico-Philosophicus by Ludwig Wittgenstein
  5. Wittgenstein, L., Tractatus Logico-Philosophicus, 1922, preface.

    1981 reprint, Routledge
    ISBN-10: 041505186X / ISBN-13: 978-0415051866
    £14.24 [amazon.co.uk] {advert} / $28.00 [amazon.com] {advert}

  6. A Man for all Seasons by Robert BoltFor an excellent dramatisation of the right to silence see
    Bolt, Robert, A Man for all Seasons, 1960
    (reprinted 1990, Vintage Books, 0679728228A main for all seasons, 1966 DVD
    $9.95 [amazon.com] {advert} / amazon.co.uk

    This play has been made into two films. The better (and very good it is) is the original 1966 version, which won 6 Oscars. Play first performed in 1954
    $10.99 [amazon.com] {advert} / £3.99 [amazon.co.uk] {advert}

  7. “Science begins when you can measure what you are talking about and express it in numbers.”,
    W.T. Kelvin, ‘Electrical Units of Measurement’ in W.T. Kelvin, Popular Lectures and Addresses, vol. 1 [486pp .pdf], p.66 (1889, Macmillan)
21a   Key name for further investigations: Occam ( also spelt as Ockham).

An example:
a suggestion that a tree spirit animates a tree.

The implications of this idea is not simple as it may seem. Part of the success of quantum physics is to develop a model in which there are no hidden variables, equations are developed from actual data and encorporate only actual data. The equations just describe the present, known situation. The equations do not tell us what is going on, they just describe the situation and calculate probabilities.

Using the example above: all you see is the tree growing, that is therefore all you say. In due course, you collect more real-world data, eventually you reach DNA.

The tree is still ‘alive’. You do not really understand what that means, but you do not attribute it to an extra variable like ‘god’, or the spirit of the trees, or individual spirits in each tree, to ‘explain’ the aliveness! Nor do you even use the phrase, ‘the quality of treeness’, as some sloppy romantics now babble about! Thus, entities are not multiplied (or added!) “without cause”.
  1. Reference numbers point to paragraph numbers in Spade.

  2. Five Texts on the Medieval Problem of Universals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham translated by P.V. Spade From Abelard’s Glosses on Porphyry in his Logica ‘Ingredientibus’
     in translation by Spade, P.V., Five Texts on the Mediaeval Problems of Universals,
    p.46., 1994, Hackett Pub Co Inc
    ISBN-10: 0872202496 / ISBN-13: 978-0872202498
    £8.54 [amazon.co.uk] {advert} / $15.25 [amazon.com] {advert}

  3. Such words are often called ‘individuals’.
24a   Compare with averages and universals in intelligence: misuse and abuse of statistics.
  1. Soal and Bateman, and Rhine and Platt, published books suggesting that ‘mind-reading’ or ‘telepathy’ was part of reality. However, the more rigour is increased, the more such supposed ‘effects’ approach zero. One of the workers on the Rhine and Pratt study eventually admitted fraud 17 years later. Turing was taken in by this fraud. (See Turing gloss, not yet issued, and the logic of ethics.)
    Similar dubious claims are made for mechanical ‘lie detection’, as if measures of stress are means of ‘mind-reading’.return to index

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