The Origins of Thought

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The origins of thought

A jou rn ey of thou ght in to tho ught

Galtons bean machine

Anti-prologue: The grand human illusion

People in the beginning were no more intelligentthan the other creatures. At this stage, there was

no meaning ofa notion such as divine entity, and every aspect of human activity was focused

on mere survival, even if there had already existed some idea ofa super-natural world, with

respect to nature and the stars. It was then that the instinctive, unconscious brain gave its place to

the moral, logical brain.

What was the cause of this shift? Some would say that it had to do with purely random processesof evolution. Some others would attribute it to some sort of divine intervention. Id rather say

that, according to the anthropic principle, the appearance of intelligent life at some stage in the

universe was somewhat programmed from the beginning. However, one way or the other, all

these assumptions fall into the category of the moral-logical brain- as it is important we realize

that logic is part of ethics, and vice versa.


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Why are meaning and cause so important for us (even within the strict context of survival)? Is it

just because of our mortal nature so that we all need an ethical-metaphysical basis to rely on?

The world of miracles mainly belongs to the gods, so that cause and meaning seem to transcend

the sphere of our everyday-material world. But again this is just the interpretation of our moral

mind, suggesting or even imposing on nature what sheshouldbe and how she should behave. Is

there another way that we may prove or, better, agree that human morality corresponds to some

kind of universal ethics?

Not only morality but also the other fundamental questions of our being- such as those of the

type: Where do we come from? or how did the universe begin? or is individual existence

preserved after death?- may be considered only according to a generalized notion ofcorrespondenceprinciple, or principle of analogy. In simple words, our thoughts, our beliefs

and our sentiments or feelings should correspond (or be analogous) to natures respective

properties. If they didnt then we would be like castaways, with respect not only to any ethical

and logical validity but, literally, we would seem to live outside nature and the universe. But the

fact that, one way or the other, we are part of this world, forms, if not a proof by itself, at least a

confirmation that what takes place in the world, also takes place in ourselves.

According to this realization, a complete understanding of the world may seem not impossible,

even if it may be proved very difficult and effort consuming to be achieved- even if it would take

an infinity to be accomplished. It teaches us that if we grasp the totality of the world, if we

consider ourselves as parts of a larger whole which consists of mutually related parts, we may

understand the meaning of life and of the universe at the largest scale and highest level.

But what about the smallest parts? Would it be enough to divide, lets say, wholeness, into a

dozen different, fundamental blocks of matter, and accordingly build a theory of the universe,

based on the interactions between the fundamental entities? I guess that this is not enough. The

indivisibility of natural processes, as implied by the notion of wholeness itself, prevents us from

doing so. Even if we tried to reconstruct wholeness, the resulting object would look like a

reassembled broken glass, not as fabulous as the original, anyway.


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One way or the other, the clue is that when we construct a theory about facts, objects, even about

ourselves and reality in general, we have to pay attention both to the individual parts we use and

to the totality of the final object. We cant do this simultaneously, at least not consciously, but

from time to time we have to consult the general idea in order not to make a mess with the pieces

of the puzzle to be solved.

There is a final preliminary remark I would like to make here. When we construct a theory about

reality, that is more than a vague idea about what it might look like, the formal language we use

in connection with our methodological procedure is very important. We chose some particular,

abstract symbols, and we use them consistently and universally as patterns or modes of the whole

process. For example, all poets know that as soon as they start to write, writing itself guides

them in what they intended to write.

The same goes for mathematics. Since the time of classical physics, a whole new set of rules and

symbols has been invented in order to express new notions corresponding to new discoveries

about nature- which according to the new rules also includes ourselves. These symbols still

preserve their algebraic, arithmetical character, although now they seem to act or project

themselves to other symbols, while this sort of interaction obeys more matrix algebra than

classical addition.

Is this new kind of formal reasoning enough to describe nature, or do we need a far more

advanced non additive or non-commuting basic structure of a mental language in order to

better and higher communicate with a more complex reality? An intriguing aspect, which is also

very comforting, is that, according to the aforementioned principle of analogy, nature evolves as

much as we evolve. But is nature as we know it all that nature can be, anywhere and anytime? I

believe the answer is yes, and the reason has already been mentioned above- we are parts of

nature, even if not the most intelligent ones. But we are getting on, and this progress is parallel to

evolution. Now, if intelligence in the universe grew at a faster (or slower) rate than ours, this

would be irrelevant because even so there would be another species, the more advanced one, to

overtake us. So the real problem has to do not only with our thought, but also with the fact of


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intelligent life at a universal scale and level. And I personally feel that this remarkable aspect

should be granted to everything and to everyone.

The logical- ethical world of reasoning

Whether logic includes the whole sphere of thought is a question that needs an answer. How

much different, for example, is logic from an instinctive mental response? It may be shown that

we are far more instinctive than what we think we are. Is the existence of God in our thoughts a

proof that there is something divine in them so that we are different from all other creatures?

When a dog obeys its master, is this act of worship fundamentally different from a human being

praying to a god? The main point here is that we should realize that, one way or the other, logic

is submitted to the ethics of our mental character. For example, any kind of our considerations

about right or wrong, our origins in the cosmos or our destination (a meaning and a cause),

betray the ethical dimension of our minds. This dimension cannot be simply explained by

instinctive fears or material pain. Animals do experience fear and pain and they may suffer from

the loss of one of their members. But they dont bury their dead , nor do they have any notion

about an afterlife. What makes us so special is an aspect of continuity ad infinitum, in other

words the capacity to go far beyond ourselves and to gain access into a universal mind.

If we were asked to mention just one thing that could be considered objective, we would realize

that there isnt any. There are different gods for different religions, different theories and

opinions about our origin and our cause, and even if we think about ourselves we realize that

there isnt any certain common picture about who we are. We always project our view of the

world and ofothers so that what we see is a personal aspect about an objective reality. We are

subjects dealing with other objects,even if these objects are other beings, and we will never

come into their place.

However, not only will we never really know how others feel and what they think, but also we

may not find any clue that what we think or how we feel about ourselves consists an objective,

absolutely personal reality. It seems more likely that we share a common experience that takes


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place in the world with other beings and people, and that we just choose or individualize facts

and processes which we consider that they belong to us and nobody else.

Furthermore, even ifwe have taken possession of a part of the collective experience and begin

the processes of analyzing it, the logical conclusions that we come to just confirm the external

origin of the fundamental assumptions we have used. This incompleteness of our logic forms a

well-known theorem which will be stated further down. It reveals the self-referential nature not

only of our basic logical procedures, but also of our own existence with respect to a wider

process of being which is revealed to us infinite and primal.

We gather here the first two conclusions of the processes and origins of our thoughts as follows:

1) No experience can be claimed to be personal.2) No logical sentence can be proved by logical assumptions.

And we may see the respective consequences:

1) Personal consciousness is part of a collective information process which becomesfamiliarized and individualized.

2) Logic is based on truths which therefore should be of spiritual origin.

The fact how fragmented the continuity by which we perceive and understand the external

world can be summarized in the following sentences-processes:

Process one: Mental perception of the object: Its image (A) becomes perceived by consciousness

(B).

Process two: Physical appreciation of the object: Consciousness (B) analyzes its physical

properties (C).

A = B

B = C

Therefore


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A = C

The process is cyclic and self- referential: If B is the object, both A (perception) and C

(cognition) are representations, even if C corresponds to a direct perception (e.g. physical

contact).

Booles laws of thought

Clarke and Spinoza

Consciousness in some sense is a process of realizing what we perceive. In other words we could

say that it is thought squared. The mathematical approach of our mental processes was an

inescapable outcome after the foundations of mathematical reasoning were established. George

Boole was one of the first to realize the mathematical aspect of reasoning. But logic is what

mathematics is all about. Because whatever the objective harmony in the world may be, we se t

our own rules of analogy according to the way we perceive the world and based on the functions

of our own system of logic. Therefore, the way we think and understand the world is

fundamentally logical, consisting of basic units of yes and no answers relative to some natural

phenomenon, so that it is really remarkable how from this simplicity of brain function emerges

complex and multilateral thought.

We will refer now to George Booles Laws of thought. Firstly, we will mention a logical

dilemma about the existence of God, keeping in mind how important the moral or divine aspect

of reasoning seems to be. Secondly, we will dive deeper into the realm of our own thought and

take a glimpse at its properties which may reveal a fundamental characteristic oforder.

With respect to Clarkes Demonstration of the Being and Attributes of God, Boole says that,

(it) consists of a series of propositions or theorems, each of them proved by means of premises

resolvable, for the most part, into two distinct classes, viz., facts of observation, such as the

existence of a material world, the phenomenon of motion, &c., and hypothetical principles, the

authority and universality of which are supposed to be recognized `a priori Though the trains


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of argument of which it consists are not in general very clearly arranged, they are almost always

specimens of correct Logic, and they exhibit a subtlety of apprehension and a force of reasoning

which have seldom been equaled, never perhaps surpassed. We see in them the consummation of

those intellectual efforts which were awakened in the realm of metaphysical inquiry, at a period

when the dominion of hypothetical principles was less questioned than it now is, and when the

rigorous demonstrations of the newly risen school of mathematical physics seemed to have

furnished a model for their direction.

Then Boole mentions the fundamental propositions:

Proposition I.

Something has existed from eternity.

For since something now is, tis manifest that something always was. Otherwise the things that

now are must have risen out of nothing, absolutely and without cause. Which is a plain

contradiction in terms. For to say a thing is produced, and yet that there is no cause at all of that

production, is to say that something is effected when it is effected by nothing, that is, at the same

time when it is not effected at all. Whatever exists has a cause of its existence, either in the

necessity of its own nature, and thus it must have been of itself eternal: or in the will of some

other being, and then that other being must, at least in the order of nature and causality, have

existed before it.

Proposition II.

Some one unchangeable and independent Being has existed from eternity.

As Boole comments,

It may be observed, that the impossibility of infinite succession, the proof of which forms a

part of Clarkes argument, has commonly been assumed as a fundamental principle of


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metaphysics, and extended to other questions than that of causation. Aristotle applies it to

establish the necessity of first principles of demonstration; the necessity of an end (the good), in

human actions, &c. There is, perhaps, no principle more frequently referred to in his writings. By

the schoolmen it was similarly applied to prove the impossibility of an infinite subordination of

genera and species, and hence the necessary existence of universals. Apparently the impossibility

of our forming a definite and complete conception of an infinite series, i.e. of comprehending it

as a whole, has been confounded with a logical inconsistency, or contradiction in the idea itself.

Boole goes on enumerating Clarkes logical propositions concerning the existence of God:

Proposition III.

That unchangeable and independent Being must be self-existent.

Boole goes on to comment on the previous proposition:

In Dr. Samuel Clarkes observations on the above proposition occurs a remarkable argument,

designed to prove that the material world is not the self-existent being above spoken of. The

passage to which I refer is the following: If matter be supposed to exist necessarily, then in thatnecessary existence there is either included the power of gravitation, or not. If not, then in a

world merely material, and in which no intelligent being presides, there never could have been

any motion; because motion, as has been already shown, and is now granted in the question, is

not necessary of itself. But if the power of gravitation be included in the pretended necessary

existence of matter: then, it following necessarily that there must be a vacuum (as the

incomparable Sir Isaac Newton has abundantly demonstrated that there must, if gravitation be an

universal quality or affection of matter), it follows likewise, that matter is not a necessary being.

For if a vacuum actually be, then it is plainly more than possible for matter not to be.

According to Clarkes syllogisms, if there is a force of gravity then there must be a vacuum

because otherwise motion cannot take place. And it follows that matter is not a necessary being. I


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would say that this is a proof by contradiction that mattershould exist, otherwise gravity

wouldnt exist. But it is supposed that gravity do exist. So matter must exist too. That means that

a unchangeable and independent Being cannot be self-existent, unless it is not composed of

matter. But even if there exists a purely spiritual state of being, the existence of matter shows the

dependence between the former and the latter, so that any form of existence should depend on

both.

Anyhow, Boole goes on to mention the rest of Clarkes demonstration:

Of the remainder of Dr. Clarkes argument I shall briefly state the substance and connexion,

dwelling only on certain portions of it which are of a more complex character than the others,

and afford better illustrations of the method of this work. In Prop. IV. it is shown that the

substance or essence of the self-existent being is incomprehensible. The tenor of the reasoning

employed is, that we are ignorant of the essential nature of all other things,much more, then, of

the essence of the self-existent being.

In Prop. V. it is contended that though the substance or essence of the self-existent being is

itself absolutely incomprehensible to us, yet many of the essential attributes of his nature are

strictly demonstrable, as well as his existence.

In Prop. VI. it is argued that the self-existent being must of necessity be infinite and

omnipresent; and it is contended that his infinity must be an infinity of fullness as well as of

immensity. The ground upon which the demonstration proceeds is, that an absolute necessity of

existence must be independent of time, place, and circumstance, free from limitation, and

therefore excluding all imperfection

In Prop. VII. it is argued that the self-existent being must of necessity be One. The order of the

proof is, that the self-existent being is necessarily existent, that necessity absolute in itself is

simple and uniform, and without any possible difference or variety, that all variety or

difference of existence implies dependence; and hence that whatever exists necessarily is the

one simple essence of the self-existent being.


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In Prop. VIII. it is argued that the self-existent and original cause of all things must be an

Intelligent Being. The main argument adduced in support of this proposition is, that as the cause

is more excellent than the effect, the self-existent being, as the cause and original of all things,

must contain in itself the perfections of all things; and that Intelligence is one of the perfections

manifested in a part of the creation

In Prop. X. it is argued, that the self-existent being, the supreme cause of all things, must of

necessity have infinite power. The ground of the demonstration is, that as all the powers of all

things are derived from him, nothing can make any difficulty or resistance to the execution of his

will. It is defined that the infinite power of the self-existent being does not extend to the

making of a thing which implies a contradiction, or the doing of that which would implyimperfection (whether natural or moral) in the being to whom such power is ascribed, but that it

does extend to the creation of matter, and of an immaterial, cogitative substance, endued with a

power of beginning motion, and with a liberty of will or choice. Upon this doctrine of liberty it is

contended that we are able to give a satisfactory answer to that ancient and great question,

, what is the cause and original of evil? The argument on this head I shall

briefly exhibit,

All that we call evil is either an evil of imperfection, as the want of certain faculties or

excellencies which other creatures have; or natural evil, as pain, death, and the like; or moral

evil, as all kinds of vice. The first of these is not properly an evil; for every power, faculty, or

perfection, which any creature enjoys, being the free gift of God,. . . it is plain the want of any

certain faculty or perfection in any kind of creatures, which never belonged to their natures is no

more an evil to them, than their never having been created or brought into being at all could

properly have been called an evil. The second kind of evil, which we call natural evil, is either a

necessary consequence of the former, as death to a creature on whose nature immortality was

never conferred; and then it is no more properly an evil than the former. Or else it is

counterpoised on the whole with as great or greater good, as the afflictions and sufferings of

good men, and then also it is not properly an evil; or else, lastly, it is a punishment, and then it is

a necessary consequence of the third and last kind of evil, viz., moral evil. And this arises wholly


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from the abuse of liberty which God gave to His creatures for other purposes, and which it was

reasonable and fit to give them for the perfection and order of the whole creation. Only they,

contrary to Gods intention and command, have abused what was necessary to the perfection of

the whole, to the corruption and depravation of themselves. And thus all sorts of evils have

entered into the world without any diminution to the infinite goodness of the Creator and

Governor thereof.

Theprevious results of Booles reasoning may be stated as follows:

Evils are either absolute evils, which are consequences of the abuse of liberty, or they are

natural evils, which are consequences of imperfection.

This is why we said from the beginning that ethics is the meaningful consequence of logic. The

whole conversation about the existence or non-existence of God ended up to a discussion about

right and wrong. The notion of order as conceived by human thought transforms into a moral

code within our souls. From this point onwards any logical attempt of proof is based on and

biased by truths already established.

As far as the demonstration of Spinoza about the existence of God is concerned, Boole makes the

following remarks:

The Ethics of Benedict Spinoza is a treatise, the object of which is to prove the identity of God

and the universe, and to establish, upon this doctrine, a system of morals and of philosophy. The

analysis of its main argument is extremely difficult, owing not to the complexity of the separate

propositions which it involves, but to the use of vague definitions, and of axioms which, through

a like defect of clearness, it is perplexing to determine whether we ought to accept or to reject.

While the reasoning of Dr. Samuel Clarke is in part verbal, that of Spinoza is so in a much

greater degree; and perhaps this is the reason why, to some minds, it has appeared to possess a

formal cogency, to which in reality it possesses no just claim


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Boole makes an algebraic analysis of Spinozas arguments, and then goes on to wonder if there

really is any chance that humans can understand God:

It is not possible, I think, to rise from the perusal of the arguments of Clarke and Spinoza

without a deep conviction of the futility of all endeavors to establish, entirely a priori, the

existence of an Infinite Being, His attributes, and His relation to the universe. The fundamental

principle of all such speculations, viz., that whatever we can clearly conceive, must exist, fails to

accomplish its end, even when its truth is admitted. For how shall the finite comprehend the

infinite? Yet must the possibility of such conception be granted, and in something more than the

sense of a mere withdrawal of the limits of phenomenal existence, before any solid ground can

be established for the knowledge, a priori, of things infinite and eternal Were it said, that there

is a tendency in the human mind to rise in contemplation from the particular towards the

universal, from the finite towards the infinite, from the transient towards the eternal; and that this

tendency suggests to us, with high probability, the existence of more than sense perceives or

understanding comprehends

There is, however, a class of speculations, the character of which must be explained in part by

reference to other causes,- impatience of probable or limited knowledge, so often all that we can

really attain to; a desire for absolute certainty where intimations sufficient to mark out before us

the path of duty, but not to satisfy the demands of the speculative intellect, have alone been

granted to us; perhaps, too, dissatisfaction with the present scene of things. With the undue

predominance of these motives, the more sober procedure of analogy and probable induction

falls into neglect. Yet the latter is, beyond all question, the course most adapted to our present

condition. To infer the existence of an intelligent cause from the teeming evidences of

surrounding design, to rise to the conception of a moral Governor of the world, from the study of

the constitution and the moral provisions of our own nature;- these, though but the feeble steps

of an understanding limited in its faculties and its materials of knowledge, are of more avail than

the ambitious attempt to arrive at a certainty unattainable on the ground of natural religion. And

as these were the most ancient, so are they still the most solid foundations, Revelation being set

apart, of the belief that the course of this world is not abandoned to chance and inexorable fate.


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Here I would agree with Boole. If God is just the product of formal logical deduction then He

would be subject to all fallacies and expediencies of human necessity. But if we regard God as a

being existing beyond the most pure and advanced thoughts of ours then we submit ourselves to

a process of mental and moral progress. So even if the natural world is subject to a force of

necessity, this force is controlled and guided by the highest considerations of mental awareness.

We will always feel fear and pain but within our thoughts this fear and pain do not exist, not

physically in any sense, so that a greater mental power can guide us through. What is truly

remarkable is not that our thoughts tell us if something is right or wrong, but, considering either

right or wrong as granted, that we have the freedom to choose, even if a wrong choice may lead

us to the absolute evil.

Constitution of the intellect

Next comes the analysis of Boole about the notion of a system, such as that of thought, which is

necessary to make it properly function according to an intrinsic moral faculty:

What I mean by the constitution of a system is the aggregate of those causes and tendencies

which produce its observed character, when operating, without interference, under those

conditions to which the system is conceived to be adapted. Our judgment of such adaptation

must be founded upon a study of the circumstances in which the system attains its freest action,

produces its most harmonious results, or fulfills in some other way the apparent design of its

construction. There are cases in which we know distinctly the causes upon which the operation

of a system depends, as well as its conditions and its end. This is the most perfect kind of

knowledge relatively to the subject under consideration

There are also cases in which we know only imperfectly or partially the causes which are atwork, but are able, nevertheless, to determine to some extent the laws of their action, and,

beyond this, to discover general tendencies, and to infer ulterior purpose. It has thus, I think

rightly, been concluded that there is a moral faculty in our nature, not because we can understand

the special instruments by which it works, but because while, in some form or other, the

sentiment of moral approbation or disapprobation manifests itself in all, it tends, wherever


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human progress is observable, wherever society is not either stationary or hastening to decay, to

attach itself to certain classes of actions, consentaneously, and after a manner indicative both of

permanency and of law. Always and everywhere the manifestation of Order affords a

presumption, not measurable indeed, but real, of the fulfillment of an end or purpose, and the

existence of a ground of orderly causation.

Someone could say that intelligence is a product of chance. Those of course that disagree claim

that the probability of such a coincidence is practically zero. They also tend to regard that only a

supreme and primordial intelligence could have created the natural world and, thus, human

intelligence. Boole, however, follows the middle path. Neither coincidence, according to him,

can lead to intelligence, nor can a supreme entity explain the uniqueness and particularities of

human thought. This is why, as he explains, the search for truth by humans, while they get

overwhelmed by the experience of the external world, must also be accompanied with the study

of their own internal nature and reality:

The particular question of the constitution of the intellect has, it is almost needless to say,

attracted the efforts of speculative ingenuity in every age. For it not only addresses itself to that

desire of knowledge which the greatest masters of ancient thought believed to be innate in our

species, but it adds to the ordinary strength of this motive the inducement of a human and

personal interest. A genuine devotion to truth is, indeed, seldom partial in its aims, but while it

prompts to expatiate over the fair fields of outward.

This way, the experimental basis of modern science is established, and the nature of scientific

truth is attested. Human knowledge, according to Boole, is based on the main facts of scientific

truth, and of the human intellect in general- that we are able to deduce from the partial events of

experience the general conclusions of science, thanks to our inherent capability to perceive order:

Thus the necessity of an experimental basis for all positive knowledge, viewed in connection

with the existence and the peculiar character of that system of mental laws, and principles, and

operations, to which attention has been directed, tends to throw light upon some important

questions by which the world of speculative thought is still in a great measure divided. How,


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from the particular facts which experience presents, do we arrive at the general propositions of

science? What is the nature of these propositions? Are they solely the collections of experience,

or does the mind supply some connecting principle of its own? In a word, what is the nature of

scientific truth, and what are the grounds of that confidence with which it claims to be

received?...

When from a large number of observations on the planet Mars, Kepler inferred that it revolved in

an ellipse, the conclusion was larger than his premises, or indeed than any premises which mere

observation could give. What other element, then, is necessary to give even a prospective

validity to such generalizations as this? It is the ability inherent in our nature to appreciate Order,

and the concurrent presumption, however founded, that the phenomena of Nature are connected

by a principle of Order. Without these, the general truths of physical science could never have

been ascertained The security of the tenure of knowledge consists in this, that wheresoever

such conclusions do truly represent the constitution of Nature, our confidence in their truth

receives indefinite confirmation, and soon becomes undistinguishable from certainty

Modern writers of high repute have contended, that all reasoning is from particular to particular

truths. They instance, that in concluding from the possession of a property by certain members of

a class, its possession by some other member, it is not necessary to establish the intermediate

general conclusion which affirms its possession by all the members of the class in common. Now

whether it is so or not, that principle of order or analogy upon which the reasoning is conducted

must either be stated or apprehended as a general truth, to give validity to the final conclusion. In

this form, at least, the necessity of general propositions as the basis of inference is confirmed,- a

necessity which, however, I conceive to be involved in the very existence, and still more in the

peculiar nature, of those faculties whose laws have been investigated in this work. For if the

process of reasoning be carefully analyzed, it will appear that abstraction is made of all

peculiarities of the individual to which the conclusion refers, and the attention confined to those

properties by which its membership of the class is defined.

The fact that a conclusion can be greater than the corresponding hypotheses is analogous to the

case when a sum is greater than its parts. This may be due to the fact that a sum also includes the


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binding energy of its constituents. However, many have doubted that the rules of inference are

capable by themselves to capture, beyond the causal relations of the parts, the idea of totality. In

this case, according to this view, human thought must rely on pre-existing and everlasting forms,

or archetypes, that guide our thoughts towards the realization of inescapable, eternal truths. On

the other side, are those who say that the so-called archetypes are partial products of human

thought, which occur by deduction, and thus are doomed to be incomplete. For Boole, truth is

again found somewhere in the middle. He refers to the example of geometrical shapes. The

circle, as a perfect geometrical object, is not found in nature. Instead, we humans imagine the

corresponding process which forms a circle, and which, somehow, becomes perfectly round

within our thoughts. This way, as we approach the notion of an object through a physical process

of thought which is not perfect by itself, we built the truth, and create, thanks to our thought, a

notion about perfection and a form perhaps more ideal than the nature of the phenomenon which

we originally wanted to grasp. In a similar way we built theories in physics. We observe natural

phenomena and, based on previous remarks and experiences, we regard natural laws which are

valid, if not for all cases, for the greater part of similar phenomena:

But besides the general propositions which are derived by induction from the collated facts of

experience, there exist others belonging to the domain ofwhat is termed necessary truth The

question concerning their nature and origin is a very ancient one, and as it is more intimately

connected with the inquiry into the constitution of the intellect than any other to which allusion

has been made, it will not be irrelevant to consider it here. Among the opinions which have most

widely prevailed upon the subject are the following. It has been maintained, that propositions of

the class referred to exist in the mind independently of experience, and that those conceptions

which are the subjects of them are the imprints of eternal archetypes. With such archetypes,

conceived, however, to possess a reality of which all the objects of sense are but a faint shadow

or dim suggestion, Plato furnished his ideal world.

It has, on the other hand, been variously contended, that the subjects of such propositions are

copies of individual objects of experience; that they are mere names; that they are individual

objects of experience themselves; and that the propositions which relate to them are, on account

of the imperfection of those objects, but partially true; lastly, that they are intellectual products


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formed by abstraction from the sensible perceptions of individual things, but so formed as to

become, what the individual things never can be, subjects of science, i.e. subjects concerning

which exact and general propositions may be affirmed.

Now if the last of the views above adverted to be taken (for it is not proposed to consider either

the purely ideal or the purely nominalist view) and if it be inquired what, in the sense above

stated, are the proper objects of science, objects in relation to which its propositions are true

without any mixture of error, it is conceived that but one answer can be given. It is, that neither

do individual objects of experience, nor with all probability do the mental images which they

suggest, possess any strict claim to this title.

It seems to be certain, that neither in nature nor in art do we meet with anything absolutely

agreeing with the geometrical definition of a straight line, or of a triangle, or of a circle, though

the deviation therefrom may be inappreciable by sense; and it may be conceived as at least

doubtful, whether we can form a perfect mental image, or conception, with which the agreement

shall be more exact. But it is not doubtful that such conceptions, however imperfect, do point to

something beyond themselves, in the gradual approach towards which all imperfection tends to

disappear. Although the perfect triangle, or square, or circle, exists not in nature, eludes all our

powers of representative conception, and is presented to us in thought only, as the limit of an

indefinite process of abstraction, yet, by a wonderful faculty of the understanding, it may be

made the subject of propositions which are absolutely true. The domain of reason is thus

revealed to us as larger than that of imagination.

If logic through perception connects the external natural world with the internal intellectual one,

there will be two classes of laws to be faced with: both physical-material and spiritual laws of

our system of thought. If we relate the physical laws with truths, the intellectual laws should be

related to some form of necessity. So this interference between the absolute universal truths

and the inherent necessity of human thoughts can cause what is called a logical error. But while

an absolute subjection to the truths of the universe would deprive us from any freedom of

thought, the recognition of an independent, even if sometimes false, intellectual necessity could

impose its own truths on the universal reality. Boole assumes that the restoration of this


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connection between nature and human thought can be done logically, philosophically, and also

mathematically:

Now what is remarkable in connection with these processes of the intellect is the disposition,

and the corresponding ability, to ascend from the imperfect representations of sense and the

diversities of individual experience, to the perception of general, and it may be of immutable

truths. Wherever this disposition and this ability unite, each series of connected facts in nature

may furnish the intimations of an order more exact than that which it directly manifests. For it

may serve as ground and occasion for the exercise of those powers, whose office it is to

apprehend the general truths which are indeed exemplified, but never with perfect fidelity, in a

world of changeful phenomena

Were, then, the laws of valid reasoning uniformly obeyed, a very close parallelism would exist

between the operations of the intellect and those of external Nature. Subjection to laws

mathematical in their form and expression, even the subjection of an absolute obedience, would

stamp upon the two series one common character. The reign of necessity over the intellectual and

the physical world would be alike complete and universal But while the observation of

external Nature testifies with ever-strengthening evidence to the fact, that uniformity of

operation and unvarying obedience to appointed laws prevail throughout her entire domain, the

slightest attention to the processes of the intellectual world reveals to us another state of things

But while the observation of external Nature testifies with ever-strengthening evidence to the

fact, that uniformity of operation and unvarying obedience to appointed laws prevail throughout

her entire domain, the slightest attention to the processes of the intellectual world reveals to us

another state of things. The mathematical laws of reasoning are, properly speaking, the laws of

right reasoning only, and their actual transgression is a perpetually recurring phenomenon. Error,

which has no place in the material system, occupies a large one here. We must accept this as one

of those ultimate facts, the origin of which it lies beyond the province of science to determine.

We must admit that there exist laws which even the rigor of their mathematical forms does not

preserve from violation. We must ascribe to them an authority the essence of which does not


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consist in power, a supremacy which the analogy of the inviolable order of the natural world in

no way assists us to comprehend.

Which are these laws whose authority brings them into conflict with the laws of intellectual

necessity so that to lead to a logical fallacy? They may be the physical or mathematical laws of

the universe, eternal and undifferentiated truths to whom humans both spiritually and physically

are subject to. It may therefore be a question about our struggle against the will of nature, and, at

the same time, against our own desires or ambitions. But the most intriguing aspect here is that

these absolute laws do not come exclusively from the outside, but they could equivalently

derive from a different secondary level of function of our own thoughts. This may therefore have

to do with the moral dimensions of human thought, independent, up to a certain degree, from

logic, juxtaposing their mutually exclusive consequences. This way, not only are we presented

with the deepest aspect of a perfect harmony with the world and with the natural laws, but also

we are faced with the task to fulfill these laws, at an ethical level, as our own responsibility with

respect to nature, which originally formed them.

Even if human reasoning has the tendency, on one side, to divide things in a way to compare the

opposites, on the other side, it seeks their unification in order to understand the world in its

totality. Human syllogisms move from the part to the whole, composing thus the wholeness of

the world. There may exist in parallel, however, a pre-existing aspect of wholeness, as a sort of

truth in the world, which humans can grasp, perhaps in their own personal way, and built upon it

any logical train of thought. Perhaps such an attempt is highly biased, and may inescapably lead

us to mistakes and absurdities. Nevertheless, it reveals a possible deeper connection between

humans and the world, of human intelligence with the essence of nature, so that by this principle

of analogy we may move on gradually and progressively to compose the unity of the world:

It may be that the progress of natural knowledge tends towards the recognition of some central

Unity in Nature. Of such unity as consists in the mutual relation of the parts of a system there can

be little doubt, and able men have speculated, not without grounds, on a more intimate

correlation of physical forces than the mere idea of a system would lead us to conjecture.

Further, it may be that in the bosom of that supposed unity are involved some general principles


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of division and re-union, the sources, under the Supreme Will, of much of the related variety of

Nature. The instances of sex and polarity have been adduced in support of such a view. As a

supposition, I will venture to add, that it is not very improbable that, in some such way as this,

the constitution of things without may correspond to that of the mind within. But such

correspondence, if it shall ever be proved to exist, will appear as the last induction from human

knowledge, not as the first principle of scientific inquiry. The natural order of discovery is from

the particular to the universal, and it may confidently be affirmed that we have not yet advanced

sufficiently far on this track to enable us to determine what are the ultimate forms into which all

the special differences of Nature shall merge, and from which they shall receive their

explanation.

Were this correspondence between the forms of thought and the actual constitution of Nature

proved to exist, whatsoever connection or relation it might be supposed to establish between the

two systems, it would in no degree affect the question of their mutual independence. It would in

no sense lead to the consequence that the one system is the mere product of the other. A too great

addiction to metaphysical speculations seems, in some instances, to have produced a tendency

toward this species of illusion. Thus, among the many attempts which have been made to explain

the existence of evil, it has been sought to assign to the fact a merely relative character,- to found

it upon a species of logical opposition to the equally relative element of good. It suffices to say,

that the assumption is purely gratuitous

If the study of the laws of thought avails us neither to determine the actual constitution of things,

nor to explain the facts involved in that constitution which have perplexed the wise and saddened

the thoughtful in all ages,- still less does it enable us to rise above the present conditions of our

being, or lend its sanction to the doctrine which affirms the possibility of an intuitive knowledge

of the infinite, and the unconditioned,- whether such knowledge be sought for in the realm of

Nature, or above that realm. We can never be said to comprehend that which is represented to

thought as the limit of an indefinite process of abstraction. A progression ad infinitum is

impossible to finite powers. But though we cannot comprehend the infinite, there may be even

scientific grounds for believing that human nature is constituted in some relation to the infinite.

We cannot perfectly express the laws of thought, or establish in the most general sense the


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methods of which they form the basis, without at least the implication of elements which

ordinary language expresses by the terms Universe and Eternity.

As we saw, logical deduction, as a process of the intellect, permits us to move from the partial

events of everyday experience to the general conclusions about scientific truth. This truth

corresponds to an objective physical reality, which we also perceive as a general pattern upon

which we base our thoughts. The constitution of our intellect, in other words, is relative to the

truth of natural reality, and this relationship can be expressed through the principle of analogy.

The world which surrounds us is not only chaotic and probabilistic; it is also characterized by

lawfulness, origins and direction. These neutral natural properties we perceive and interpret as

moral rules, cause, and destination, respectively. This way, while our conscience gets interested

in this game of contact and understanding of nature, at the same time it is submitted to the sphere

of its duties with respect to the world and its own self:

Refraining from the further prosecution of a train of thought which to some may appear to be of

too speculative a character, let us briefly review the positive results to which we have been led. It

has appeared that there exist in our nature faculties which enable us to ascend from the particular

facts of experience to the general propositions which form the basis of Science; as well as

faculties whose office it is to deduce from general propositions accepted as true the particular

conclusions which they involve. It has been seen, that those faculties are subject in their

operations to laws capable of precise scientific expression, but invested with an authority which,

as contrasted with the authority of the laws of nature, is distinct, sui generis, and underived.

Further, there has appeared to be a manifest fitness between the intellectual procedure thus made

known to us, and the conditions of that system of things by which we are surrounded,- such

conditions, I mean, as the existence of species connected by general resemblances, of facts

associated under general laws; together with that union of permanency with order, which while it

gives stability to acquired knowledge, lays a foundation for the hope of indefinite progression.

Human nature, quite independently of its observed or manifested tendencies, is seen to be

constituted in a certain relation to Truth; and this relation, considered as a subject of speculative

knowledge, is as capable of being studied in its details, is, moreover, as worthy of being so


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studied, as are the several departments of physical science, considered in the same aspect. I

would especially direct attention to that view of the constitution of the intellect which represents

it as subject to laws determinate in their character, but not operating by the power of necessity;

which exhibits it as redeemed from the dominion of fate, without being abandoned to the

lawlessness of chance.

We cannot embrace this view without accepting at least as probable the intimations which, upon

the principle of analogy, it seems to furnish respecting another and a higher aspect of our nature,-

its subjection in the sphere of duty as well as in that of knowledge to fixed laws whose authority

does not consist in power,- its constitution with reference to an ideal standard and a final

purpose. It has been thought, indeed, that scientific pursuits foster a disposition either to

overlook the specific differences between the moral and the material world, or to regard the

former as in no proper sense a subject for exact knowledge. Doubtless all exclusive pursuits tend

to produce partial views, and it may be, that a mind long and deeply immersed in the

contemplation of scenes over which the dominion of a physical necessity is unquestioned and

supreme, may admit with difficulty the possibility of another order of things. But it is because of

the exclusiveness of this devotion to a particular sphere of knowledge, that the prejudice in

question takes possession, if at all, of the mind. The application of scientific methods to the study

of the intellectual phenomena, conducted in an impartial spirit of inquiry, and without

overlooking those elements of error and disturbance which must be accepted as facts, though

they cannot be regarded as laws, in the constitution of our nature, seems to furnish the materials

of a juster analogy.

Finally, Boole makes us wonder what the study of the laws of thought and of their mathematical

expression, in particular, offers us. Definitely, the realization of the fundamental questions which

concern us, such as the definition of our species, our relationship with the rest of the world and

the other people, as well as of the causes for the sake of which nature s functions were designed,

leads us to a self-awareness and to a relationship of harmony between ourselves, the other people

and the rest of the world. This way, our spiritual civilization is being built. Mathematics

comprises a language of rationalization with respect to processes of thought, and, together with

language in the broader sense of communication, helps us to construct a comprehensive system


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of education. Mathematics forms, in a few words, the instrument to make our logic reasonable.

However, as Boole himself wisely notices, mathematics is not enough to reveal and describe all

the phenomena of the human soul. The ethical dimension of human intelligence, together with

emotions and instincts, drives us to thoughts and actions which seek a wider and deeper aspect of

the world, and obliges us to accept higher causes, which have never been searched for before in

the natural history of the world. If mathematics offers us the quantification and rationalization of

our natural functions, a sort of insight, on the other hand, which co-exists within our intellectual

system, asks us to extend the process of intellectual anticipation, expanding and bringing to

perfection our own system of thought!:

If it be asked to what practical end such inquiries as the above point, it may be replied, that

there exist various objects, in relation to which the courses of men's actions are mainly

determined by their speculative views of human nature. Education, considered in its largest

sense, is one of those objects. The ultimate ground of all inquiry into its nature and its methods

must be laid in some previous theory of what man is, what are the ends for which his several

faculties were designed, what are the motives which have power to influence them to sustained

action, and to elicit their most perfect and most stable results. It may be doubted, whether these

questions have ever been considered fully, and at the same time impartially, in the relations here

suggested. The highest cultivation of taste by the study of the pure models of antiquity, the

largest acquaintance with the facts and theories of modern physical science, viewed from this

larger aspect of our nature, can only appear as parts of a p erfect intellectual discipline

The laws of thought, in all its processes of conception and of reasoning, in all those operations of

which language is the expression or the instrument, are of the same kind as are the laws of the

acknowledged processes of Mathematics. It is not contended that it is necessary for us to

acquaint ourselves with those laws in order to think coherently, or, in the ordinary sense of the

terms, to reason well. Men draw inferences without any consciousness of those elements upon

which the entire procedure depends. Still less is it desired to exalt the reasoning faculty over the

faculties of observation, of reflection, and of judgment. But upon the very ground that human

thought, traced to its ultimate elements, reveals itself in mathematical forms, we have a

presumption that the mathematical sciences occupy, by the constitution of our nature, a


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fundamental place in human knowledge, and that no system of mental culture can be complete or

fundamental, which altogether neglects them.

But the very same class of considerations shows with equal force the error of those who regard

the study of Mathematics, and of their applications, as a sufficient basis either of knowledge or

of discipline. If the constitution of the material frame is mathematical, it is not merely so. If the

mind, in its capacity of formal reasoning, obeys, whether consciously or unconsciously,

mathematical laws, it claims through its other capacities of sentiment and action, through its

perceptions of beauty and of moral fitness, through its deep springs of emotion and affection, to

hold relation to a different order of things. There is, moreover, a breadth of intellectual vision, a

power of sympathy with truth in all its forms and manifestations, which is not measured by the

force and subtlety of the dialectic faculty. Even the revelation of the material universe in its

boundless magnitude, and pervading order, and constancy of law, is not necessarily the most

fully apprehended by him who has traced with minutest accuracy the steps of the great

demonstration. And if we embrace in our survey the interests and duties of life, how little do any

processes of mere ratiocination enable us to comprehend the weightier questions which they

present! [1]

Gdels incompleteness theorem

The point made previously, that the system of thought may be considered efficient to include

both deduction in the form of logic and truth in the form of ethics, can be further expanded and

more rigorously expressed with Gdels incompleteness theorem:

Suppose you build a computing machine, and you give the order: You will never say if this

sentence is true. If the sentence is true, then the machine should say that the sentence is false. If

it is false, the machine can tell the truth that the sentence is false. So we will never know thecorrect answer. This is a problem that Gdel introduced, showing that logic is not immune to

inconsistencies. Logic is not a perfect machine of truth. Gdel even quantified his theorem,

which simply says that for each theory there is a sentence G which states that G cannot be

answered by theory . If G could be proved by the axioms of, then would have a theorem


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G, which is contradictory, so would be inconsistent. But if is consistent, then G cannot be

proved by T, thus T is incomplete.

As Solomon Feferman notes, Actually there are two incompleteness theorems, and what people

have in mind when they speak of Gdels theorem is mainly the first of these. Like Heisenbergs

Uncertainty Principle, it has captured the public imagination with the idea that there are absolute

limits to what can be known. More specifically, its said that Gdels theorem tells us there are

mathematical truths that can never be proved. Among postmodernists its used to support

skepticism about objective truth; nothing can be known for sure. And in the Bibliography of

Christianity and Mathematics its asserted that theologians can be comforted in their failure to

systematize revealed truth because mathematicians cannot grasp all mathematical truths in their

systems either. Not only that, the incompleteness theorem is held to imply the existence of God,since only He can decide all truths. [2]

Anyway, Gdels theorem does not prove the existence of God. It proves that some things are

truths beyondthe realm of logic. What is more fundamental in Gdels theorem is the property of

self- reference, i.e. a sentence whose truth relies on the existence of the sentence itself. This is

exactly what would happen in the case of the aforementioned computer- it would face a program

with an infinite loop. But how come we may accept something as true if we cannot prove it? In

fact, the most fundamental questions about ourselves, such as the existence of God, life after

death, the moral codes in general are common everyday truths which we accept even if they

cannot be proved by facts happening in the real world.

Feferman also notes that, Among those who know what the incompleteness theorems actually

do tell us, there are some interesting views about their wider significance for both mind and

matter. In his 1960 Gibbs Lecture, Gdel himself drew the conclusion that either mind infinitely

surpasses any finite machine or there are absolutely unsolvable number theoretic problems. A

lot has been written pro and con about the possible significance of Gdels theorem for

mechanical models of the mind by a number of logicians and philosophers. One of the most

prominent proponents of the claim that Gdels theorem proves that mind is not mechanical is

Roger Penrose: there must be more to human thinking than can ever be achieved by a


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computer. However, he thinks that there must be a scientific explanation of how the mind

works, albeit in its non-mechanical way, and that ultimately must be given in physical terms, but

that current physics is inadequate to do the job. But Stephen Hawking and Freeman Dyson,

among others, have come to the conclusion that Gdels theorem implies that there cant be a

Theory of Everything.

If our logic in particular or our thought in general were not sufficient to grasp the totality of

information in the universe, we wouldnt be able to realize the incompleteness theorem in the

first place. So what we have here is a fundamental logical paradox about logic itself. Logic

seems to lead sometimes to a contradiction which seems to nullify logic but at the same time it

reveals its combinatory power. Consider for example: Light sometimes blinds us because of its

reflection, but simultaneously it makes as see. So the whole problem is, as I have already

mentioned, a question about how self- reference works.

Impossible objects

Gdels incompleteness theorem is a problem of formal logic. However, it can be extended into

any field of science or of everyday life. Many times our thought is led to paradoxes and

absurdities without any obvious logical reason. We accept some facts as personal or universal

truths which are self-evident, so they dont need to be proved or disproved. Furthermore, modern

physics seeks for the so-called theory of everything, a set or rules by which any natural

phenomenon could be explained. But if Gdels theorem is true then any such attempt is doomed

with failure.

Penroses triangle

As an object we may define anything that can be perceived or conceived as having a form or/and

a content. In this sense, objects include mountains, lakes, clouds, thoughts, feelings, logical

problems, notions, properties, everything. An object doesnt need to be composite or well-

defined. Intelligent living objects could be us, for example.


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Impossible triangle sculpture as an optical illusion, East Perth, Western Australia [3]

The previous picture depicts Roger Penroses triangle, which is an impossible object. The object

in both three pictures is exactly the same although seen from different angles. What the brain

does is to try to perceive the object in its totality. This is why we seem to be tricked by this

optical illusion. We will return later on to the unconscious properties of our mind.

Escher and non-Euclidian geometries

Waterfall


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A painter who expanded the perspective of impossible objects is M.C. Escher. His waterfall,

depicted in the previous image, is an example of an impossible machine which carries water

from the bottom to the top without any mechanical work.

Escher occupied himself with the so-called non-Euclidean geometry, as depicted in the previous

figures. Impossible objects in general may be said not to be able to be represented by common 3-

D space. Non-Euclidean geometries are regarded those in which the so-called Euclids 5th

postulate is violated. This postulate can be simply stated as follows:

Euclids 5th postulate


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If a line segment intersects two straight lines forming two interior angles on the same side that

sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side

on which the angles sum to less than two right angles. [4]

In more simple words, two parallel lines dont meet each other. Of course this is wrong in the

case, for example, of geodesics. We know that all the meridians of the Earth meet both at the

South and at the North Pole. Earths geometry is spherical, not Euclidean-flat. But we may

define a non-Euclidean geometry in general, as depicted by Lobachevsky (1840):


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All straight lines which in a plane go out from a point can, with reference to a given straight line

in the same plane, be divided into two classes- into cutting and non-cutting. The boundary lines

of the one and the other class of those lines will be called parallel to the given line.

More simply put:

There exist two lines parallel to a given line through a given point not on the line. [5]

What Lobachevsky says is that at the point in the previous figure there may exist more parallel

lines to BC (not only EE). Logic of course says that something like this seems impossible. If

there exist such lines then they shouldnt pass from point A. Otherwise A is not unique. Or A

could be even seen as a line which seems like a point from an extra-dimension. What we face

here is another impossible object. If two parallel lines meet each other then they are not straightlines but curves. On the other hand, we have already assumed the axiomatic existence of a line

and a point. When is a line straight? The question seems much more difficult to answer. If a

line is a collection of infinite points, still it may represent a curve, or a plain, or even space itself.

This difficulty in the definition of a line in contrast to a curve led Einstein to use the notion of a

geodesic cosmic line instead of a straight line. Everything in the universe must then move

along geodesics. So in the real cosmos motions and the corresponding shape of space and things

are far from being ideal. All things, including space and time, are subject to deformations caused

by forces. In other words, geometry cannot be irrelevant to the nature of things it wants to

describe.

So what goes on in our minds? Is there such a thing as an empty mind, or do all thoughts, even

the fainter ones, deform, in some sense, the mental space-time of our brain? By the action of a

very strong force space-time may bend as much as to form a closed loop. Near black holes such

an event can take place. Is there a black hole in our minds, a spiritual kind of singularity, which

may wind up our thoughts in such a way as to give birth to what we commonly refer to as

ingenuity, creativity, or inspiration? Are these loops within our minds spontaneous

phenomena of thought creation, little time-machines which manage to produce the future of our

thoughts even before we conceive them? And is there any connection with what we refer to as


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impossible objects, or does the whole thing fall into the category of a mere optical, or mental in

general, illusion?

Strange loops

The notion of an infinite loop is portrayed in a vivid way by Douglas Hofstadter in his book I

am a strange loop:

And yet when I say strange loop, I have something else in mind- a less concrete, more elusive

notion. What I mean by strange loop is- here goes a first stab, anyway- not a physical circuit

but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a

shift from one level of abstraction (or structure) to another, which feels like an upwards

movement in a hierarchy, and yet somehow the successive upward shifts turn out to give rise to

a closed cycle. That is, despite ones sense of departing ever further from ones origin, one winds

up, to ones shock, exactly where one had started out. In short, a strange loop is a paradoxical

level-crossing feedback loop.

The Penrose stairs is a two-dimensional depiction of a staircase in which the stairs make four 90 turns as they

ascend or descend; yet form a continuous loop so that a person could climb them forever and never get any higher.

As Wikipedia says, a strange loop is technically called tangled hierarchy consciousness and

arises when, by moving only upwards or downwards through a hierarchical system, one finds

oneself back where one started. Strange loops may involve self-reference and paradox. The

paradox arises when what we perceive comes into conflict with common sense. The staircase, for


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example, in the previous figure depicts the endless journey of someone ascending and

descending forever. [6]

So the greatest paradox of thought is that it seems to be born spontaneously, like a strange loop,

and then, as the mind tries to understand how this thought came into existence, the validity of

such a syllogism stands as a self- evident and self-referring truth. I guess that this points towards

something more than just a theorem of incompleteness. Its more like a theorem or axiom of self-

consistency. We have talked before about the moral aspect of our logic. But here ethics takes on

a more universal meaning. Its not just the story of right and wrong but it is more like an insight

into the moment of creation of our mental processes. This is why absurd conclusions or

impossible objects are not mere faults of logic or illusions of perception, respectively. They hide

a deeper and primal aspect of the nature of our intellect, a kind of spontaneous action which is

based on strange loops and which is revealed unfolding through the process of analytical

reasoning.

The impossibility of thought

Bertrand Russell, by co-authoring with A. N. Whitehead Principia Mathematica,

attempted to ground mathematics on logic. He believed that all propositions of

mathematics could be proved. Curt Gdel showed that truths in a logical system are not

provable by its own premises. So Gdels theorem has given an end to our ambition that

there could be any complete logical system, as Russell in his Principia would have

expected.

Infinite regress

When we try to demonstrate a truth we use syllogisms until we find a contradiction:


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P0: Logic is true.If P0is true thenP0 P1 (if P1true)P1 P2 (if P2true)P

2 P3

(if P3true)

Pn Pn+1

We can repeat this process until we find a wrong proposition. Then the whole syllogism

collapses. But if our first argument is quite strong (or just axiomatic) then it could hold

true for ever. In this case, we assume that we are satisfied with an adequate number of

repetitions which support our primary argument more and more

This is what we call an infinite regress. If P0 is our first proposition then it is true if P1 is

true, and P1 is true if P2 is true, and so on:

Pn+1 = Pn + I

(where I stands as the next

step in the series.)

If the first proposition P0stands as truth (like the sentence logic is true) then we will

never end with a contradiction or with an affirmation.

Infinite loops

Another name for an infinite regress is an infinite causal chain. An infinite causal chain

has no beginning or end. We can use any means of logical deduction but we can never

reach an end or a first cause. Infinite causal chains are logically valid but, lets say,

incomplete with regard to common experience. There is a fast way to escape from a

causal chain. For example, if we ask how the universe started, we can simply reply that


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the universe has always existed. So a previous state loses any meaning. This is an

example of an infinite (causal) loop. But here we have to face a problem: If an infinite

loop can explain its existence as its own cause, then logical reasoning loses any sense.

Because logic will have to ask: What lies outside an infinite loop?

This is why Richard Hanley has argued that causal loops are not impossible but their only

possibly objectionable feature they all share is that coincidence is required to explain

them. Therefore infinite causal loops are in fact acausal.

There still remains an important question: Does nature thinks the same way humans do?

Are all human problems also problems of nature? If humans are nature then the obvious

answer is yes. But this answer is still an answer of logic. Could nature have a more

sophisticated way of thinking above human logic? But again the previous question is a

question of logic. And so on

Our logic moves on using an infinite regress procedure. We can stop this procedure any

time but if we want to give a definite answer then we have to start again. We may admit

that logic is insufficient for the understanding of the world but if we abandon logic then

we lose any ability of common sense. Is there a function within the limits of themind

which, if found, could lead us to a new way of reasoning and thinking? Perhaps this

question is just another question of logic. But since logic and our common sense have

proved worthy of understanding or at least having access to incredible things outside

their realm, there is a final question left: Why do we understand? We may not be able

to reply but I guesswe can keep our mind open to the possibility of miracles.

We cannot demonstrate truths, we just accept them. On the other hand, by demonstration

we cannot prove a truth. As Aristotle put it forward:

Some hold that, owing to the necessity of knowing the primary premises, there is no

scientific knowledge. Others think there is, but that all truths are demonstrable. Neither

doctrine is either true or a necessary deduction from the premises. The first school,


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assuming that there is no way of knowing other than by demonstration, maintain that an

infinite regress is involved, on the ground that if behind the prior stands no primary, we

could not know the posterior through the prior The other party agrees with them as

regards knowing, holding that it is only possible by demonstration, but they see no

difficulty in holding that all truths are demonstrated, on the ground that demonstration

may be circular and reciprocal. Our own doctrine is that not all knowledge is

demonstrative: on the contrary, knowledge of the immediate premises is independent of

demonstration. Such, then, is our doctrine, and in addition we maintain that besides

scientific knowledge there is its originative source which enables us to recognize the

definitions.

The previous statement by Aristotle beautifully summarizes the nature of human thought.

One the one hand, there is reasoning, which leads us to the knowledge of the world by

demonstration. On the other hand, there are truths, on which our whole reasoning is

based, truths that have to do not only with the physiological properties of our brain but

also with the fundamental way the process of thought evolves. In other words,

inconsistency or impossibility is not necessarily a fault of our weak minds but instead a

reality which our minds are powerful enough to conceive and utilize. [7]

The truth of the unconscious

We saw that truths are logically impossible objects or elusive targets of intelligence, which

seems to be amazed by the inexplicable character of its own fundamental aspects. Our thoughts

seem to be drifted away and carried off by processes beyond our mental powers. Is our fate

already written somewhere in our genes and in our minds, expressed through our instincts and

predispositions? It seems that many functions of our brain lie in the unconscious, so that they

pass unnoticed by analytical reasoning and uninfluenced by free will.


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The facts of perception

Hermann von Helmholtz, who introduced the meaning of free energy in physics, was a polymath

who also wrote about the way we perceive the world. He wondered how objective the

information we get by the senses and process with our brain could be in order to form the picture

of the external world:

The problems which that earlier period considered fundamental to all science were those of the

theory of knowledge: What is true in our sense perceptions and thought? And in what way do

our ideas correspond to reality? Philosophy and the natural sciences attack these questions from

opposite directions, but they are the common problems of both. Philosophy, which is concerned

with the mental aspect, endeavors to separate out whatever in our knowledge and ideas is due to

the effects of the material world, in order to determine the nature of pure mental activity. The

natural sciences, on the other hand, seek to separate out definitions, systems of symbols, patterns

of representation, and hypotheses, in order to study the remainder, which pertains to the world of

reality whose laws they seek, in a pure form. Both try to achieve the same separation, though

each is interested in a different part of the divided field...

Shortly before the beginning of the present century, Kant expounded a theory of that which, in

cognition, is prior or antecedent to all experience; that is, he developed a theory of what he calledthe transcendentalforms of intuition and thought. These are forms into which the content of our

sensory experience must necessarily be fitted if it is to be transformed into ideas. As to the

qualities of sensations themselves, Locke had earlier pointed out the role which our bodily and

mental structure or organization plays in determining the way things appear to us. Along this

latter line, investigations of the physiology of the senses, in particular those which Johannes

Mller carried out and formulated in the law of the specific energies of the senses, have brought

(one can almost say, to a completely unanticipated degree) the fullest confirmation. Further,

these investigations have established the nature of - and in a very decisive manner have clarified

the significance of - the antecedently given subjective forms of intuition. This subject has already

been discussed rather frequently, so I can begin with it at once today.


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Among the various kinds of sensations, two quite different distinctions must be noted. The most

fundamental is that among sensations which belong to different senses, such as the differences

among blue, warm, sweet, and high-pitched. In an earlier work I referred to these as differences

in the modality of the sensations. They are so fundamental as to exclude any possible transition

from one to another and any relationship of greater or less similarity. For example, one cannot

ask whether sweet is more like red or more like blue.

The second distinction, which is less fundamental, is that among the various sensations of the

same sense. I have referred to these as differences in quality. Fichte thought of all the qualities of

a single sense as constituting a circle of quality; what I have called differences of modality, he

designated differences between circles of quality. Transitions and comparisons are possible only

within each circle; we can cross over from blue through violet and carmine to scarlet, for

example, and we can say that yellow is more like orange than like blue.

Physiological studies now teach that the more fundamental differences are completely

independent of the kind of external agent by which the sensations are excited. They are

determined solely and exclusively by the nerves of sense which receive the excitations.

Excitations of the optic nerves produce only sensations of light, whether the nerves are excited

by objective light (that is, by the vibrations in the ether), by electric currents conducted through

the eye, by a blow on the eyeball, or by a strain in the nerve trunk during the eyes' rapid

movements in vision. The sensations which result from the latter processes are so similar to those

caused by objective light that for a long time men believed it was possible to produce light in the

eye itself. It was Johannes Mller who showed that internal production of light does not take

place and that the sensation of light exists only when the optic nerve is excited

It is apparent that all these differences among the effects of light and sound are determined by

the way in which the nerves of sense react. Our sensations are simply effects which are produced

in our organs by objective causes; precisely how these effects manifest themselves depends

principally and in essence upon the type of apparatus that reacts to the objective causes. What

information, then, can the qualities of such sensations give us about the characteristics of the

external causes and influences which produce them? Only this: our sensations are signs, not


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images, of such characteristics. One expects an image to be similar in some respect to the object

of which it is an image; in a statue one expects similarity of form, in a drawing similarity of

perspective, in a painting similarity of color. A sign, however, need not be similar in any way to

that of which it is a sign. The sole relationship between them is that the same object, appearing

under the same conditions, must evoke the same sign; thus different signs always signify

different causes or influences.

To popular opinion, which accepts on faith and trust the complete veridicality of the images

which our senses apparently furnish of external objects, this relationship may seem very

insignificant. In truth it is not, for with it something of the greatest importance can be

accomplished: we can discover the lawful regularities in the processes of the external world. And

natural laws assert that from initial conditions which are the same in some specific way, there

always follow consequences which are the same in some other specific way. If the same kinds of

things in the world of experience are indicated by the same signs, then the lawful succession of

equal effects from equal causes will be related to a similar regular succession in the realm of our

sensations. If, for example, some kind of berry in ripening forms a red pigment and sugar at the

same time, we shall always find a red color and a sweet taste together in our sensations of berries

of this kind.

What Helmholtz tells us is that our brain does not perceive the external objects directly but

instead it reconstructs them using signs it receives from the senses. The image of external objects

is reconstructed on the retina by spots of light which comes from the objects. The example of a

photo of an object may convince us that what we see is a good representation of reality. Still, the

image of the object in the photo remains a representation of the image of the object in our brains.

What is also intriguing is that, except from the fact that perception of colors and sounds is highly

subjective, space-time itself may be an internal representation of an external order of things,

which helps us arrange them in our minds in a helpful way, but which may have little or none

physical significance:

Thus, our physiological make-up incorporates a pure form of intuition, insofar as the qualities

of sensation are concerned. Kant, however, went further. He claimed that, not only the qualities


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of sense experience, but also space and time are determined by the nature of our faculty of

intuition, since we cannot perceive anything in the external world which does not occur at some

time and in some place and since temporal location is also a characteristic of all subjective

experience. Kant therefore called time the a priori and necessary transcendental form of the

inner, and space the corresponding form of the outer, intuition. Further, Kant considered that

spatial characteristics belong no more to the world of reality (the dinge an sich) than the colors

we see belong to external objects. On the contrary, according to him, space is carried to objects

by our eyes.

Even in this claim, scientific opinion can go along with Kant up to a certain point. Let us

consider whether any sensible marks are present in ordinary, immediate experience to which all

perception of objects in space can be related. Indeed, we find such marks in connection with the

fact that our body's movement sets us in varying spatial relations to the objects we perceive, so

that the impressions which these objects make upon us change as we move. The impulse to

move, which we initiate through the innervation of our motor nerves, is immediately perceptible.

We feel that we are doing something when we initiate such an impulse. We do not know directly,

of course, all that occurs; it is only through the science of physiology that we learn how we set

the motor nerves in an excited condition, how these excitations are conducted to the muscles, and

how the muscles in turn contract and move the limbs. We are aware, however, without any

scientific study, of the perceptible effects which follow each of the various innervations we

initiate

From this point of view, space is the necessary form of outer intuition, since we consider only

what we perceive as spatially determined to constitute the external world. Those things which are

not perceived in any spatial relation we think of as belonging to the world of inner intuition, the

world of self-consciousness. Space is an a priori form of intuition, necessarily prior to all

experience, insofar as the perception of it is related to the possibility of motor volitions, the

mental and physical capacity for which must be provided by our

The Origins of Thought

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