Gottlob Frege and modern logic


Gottlob Frege (1848 – 1925) was a German intellectual whose work in the fields of mathematics and logic led to the development of modern predicate logic and sowed the seeds for contemporary analytic philosophy. Frege was largely ignored by his peers, but was to become influential upon and through the next generation of popular thinkers such as Bertrand Russell and Whitehead.

The importance of Frege’s work arises from the inadequacy of Aristotelian and Stoic logic in dealing with mathematical statements, for example Euclid’s theory of the infinite amount of prime numbers. This was a problem for Frege because he contended that all the truths of arithmetic simply were truths that were both logical and analytic. In this way, Frege’s work is more in the rationalist tradition of Leibniz than in Kant’s transcendental idealism.

Frege set about clarifying logic by doing away with the typical subject/predicate analysis and replacing it with function and argument. Many will be familiar with a mathematical function such as f(x) = x + 3, where the function is equal to the numerical value of x + 3. Frege radically applied the function to arguments, such as “all cats have tails”, expressing them as f(x), where x is a cat, then x has a tail.

Fregean logic allowed the dissolution of the problem of multiple generality. For example, prior to Frege the distinction between statements such as “every person loves some city” and “every city is loved by some person” could only be represented artificially.

Alfred Whitehead: process philosophy and scientific materialism

Whitehead_PaintingAlfred Whitehead (1861 – 1947) was an English thinker best known in his early life for his work in the logic of mathematics, and in later life for his contribution to the metaphysical school of thought of process philosophy. Whitehead co-wrote with his former student Bertrand Russell the largely influential Principia Mathematica, one of the 20th centuries most important works in mathematical logic.

Whitehead’s philosophical works were, like most great thinkers, a response to a crisis. The early 20th century saw the full throes of Enlightenment optimism, in which the development of metaphysical systems was regarded as futile due to their lack of subjectivity to the mechanistic scientific method. However, Whitehead contended that rather than abandoning metaphyiscs entirely, the thinkers of his generation had instead imported a type of Cartesianism that went unscrutinised. He called this “scientific materialism”.

There persists … [a] fixed scientific cosmology which presupposes the ultimate fact of an irreducible brute matter, or material, spread through space in a flux of configurations. In itself such a material is senseless, valueless, purposeless. It just does what it does do, following a fixed routine imposed by external relations which do not spring from the nature of its being. It is this assumption that I call ‘scientific materialism.’ Also it is an assumption which I shall challenge as being entirely unsuited to the scientific situation at which we have now arrived.

Alfred North Whitehead, Science and the Modern World

Whitehead’s primary criticism of viewing reality, in the mechanistic tradition, as discrete and independent pieces of matter was that under this schema knowledge of causation is impossible. Whitehead argues that two things that are separate from each other in space simply cannot bear a causal relationship between them. Whitehead says that knowledge of a cause will give full knowledge of all its effects, but this is impossible if pieces of matter are truly distinct from one another. In essence, Whitehead is arguing that efficient causality is unintelligible if scientific materialism is true.

While the Aristotelian tradition turns to final causality to solve this problem, Whitehead instead jettisons the relevance of static things such as substance, form and matter. Whitehead like Hegel envisions reality as a type of organism or process, which consists in its most primary form as interrelated events. For Whitehead, the universe just is a series of occasions that are causally affected by all other occasions and the idea that there could be objects existing separate and distinct in space and time is deeply mistaken.

Freud, antitheism and the genetic fallacy

freud2When Freud’s writings touch upon the issue of religion and the divine, there lies a fascinating intersection of modern ideas. While Charles Darwin had provided the scientific theory of the mechanistic origin of man from simpler life, Freud’s great contribution to the Enlightenment secular edifice was to psychologise man’s religious activities.

If one wishes to form a true estimate of the full grandeur of religion, one must keep in mind what it undertakes to do for men. It gives them information about the source and origin of the universe, it assures them of protection and final happiness amid the changing vicissitudes of life, and it guides their thoughts and motions by means of precepts which are backed by the whole force of its authority.

– Sigmund Freud, New Introductory Lectures on Psychoanalysis

Per Freud religion exists in order to placate man’s need for wish fulfillment. Specifically, religion exists because of man’s fears regarding the indifference and power of the natural world and because of its sometimes usefulness in promoting social cohesion and order. Religion is for Freud the attempt of an infantile man to use illusion to create a better world. In Freud’s theory one also finds the progressive anthropology common in the writings of thinkers such as Rousseau and Comte, where it is postulated that the primitive ideas of religion will eventually be shed by a new type of scientific man.

But is what Freud has to offer a refutation of religious ideas or simply a type of historical classification? In this regard Freud seems to take a similar approach to Nietzsche.

Historical refutation as the definitive refutation. — In former times, one sought to prove that there is no God — today one indicates how the belief that there is a God could arise and how this belief acquired its weight and importance:  a counter-proof that there is no God thereby becomes superfluous. — When in former times one had refuted the ‘proofs of the existence of God’ put forward, there always remained the doubt whether better proofs might not be adduced than those just refuted:  in those days atheists did not know how to make a clean sweep.

-Friedrich Nietzsche (1844-1900), Daybreak:  Thoughts on the Prejudices of Morality, Book I, sec. 95

The genetic fallacy is a type of logical fallacy whereby a conclusion is proposed based upon some fact regarding the origins of something. It is a fallacy because the conclusion is unsupported by irrelevant facts regarding the subjects origin. Freud fails to take into account that the truth (or falsity) of his psychological theory regarding the origins of religion are consistent both with the existence and non-existence of the divine.

Sigmund Freud and psychoanalysis

MemoryLearningSigmund Freud (1856 – 1939) was a neurologist whose work in the field of psychology gave birth to the contemporary psychiatric apparatus of psychoanalysis. Freud initially worked as a medical doctor at the Vienna General Hospital, where he undertook research into conditions such as cerebral palsy. The publications of his research would later see him offered a position as a university lecturer specialising in neuropathology.

The intellectual climate in which Freud formulated his theories was shaped largely by the titanic influence of Darwin’s evolutionary theory of common descent and natural selection. Previously, under the Aristotelian and Platonic hierarchies, man was differentiated from animals by his possession of an immaterial intellect or soul i.e. man was a rational animal. One of the consequences of Darwin’s theory was that while man was indeed different from the animals this difference was only in complexity; quantitative rather than qualitative.

Freud was also largely influenced by the development of the physical theory of the conservation of energy. Brücke, a supervisor of Freud in his early career, published a work contending that all living organisms were also governed by the law of energy conservation. Freud’s novelty was to flesh out what Brücke’s theory meant for the human mind; that the human psyche is also a mechanistic system and its various outputs are governed by the laws of physics.

Thus arises psychoanalysis, where mental disorders are treated as physical problems and their symptoms are to be elucidated through an interrogation of the patient by a psychoanalyst. It was Freud’s revolutionary idea to apply the principles of modern science to the treatment of mental disorder, and his legacy looms large over our contemporary intellectual landscape.

Darwin, mechanism and anthropology

indexCharles Darwin (1809 – 1882) was an English scientist best known for his particular theory of special evolution involving common descent and natural selection. Darwin initially found fame for his work in the field of geology and the popular journal of his voyage aboard the HMS Beagle. It was during this time that Darwin first became fascinated by the manner in which the diversification of species seemed to follow a geographical pattern. It was not until 1858 that Darwin published a joint paper outlining his evolutionary theory.

In a way, Darwin’s theorising is the perfect modern archetype. Platonic philosophies outright rejected change in the immutable world of the forms (which includes forms of the species), and for Aristotle whilst there was a gradation in the complexity of living things (inorganic < vegetable < animal < rational) the difference between these categories was clearly defined and not a matter of degree. The most important thing to note is that for Aristotle and Plato the information of matter to a various species takes part as a teleological process. For Plato it is the will of the demiurge and for Aristotle his Divine being of pure actuality.

There was nothing novel, or even modern, in Darwin’s rejection of teleology. After all, prior to Aristotle Leucippus the Atomist had asserted that “nothing in the body is made in order that we may use it. What happens to exist is the cause of its use”. Following the work of Newton and Descartes, mechanical explanations of natural phenomena had begun to displace classical and medieval dualistic views. However, while Newton and Descartes seemed to favour natural laws as manifestations of divine will, Darwin favoured Schopenhauer’s view that life is imbued with a will that manifests itself as a struggle to survive.

Darwin’s novel insight was not that one species was generated from another, but rather that the method for this generation was natural selection. In this way, Darwin provided a way to account for the diversity of species (and the origin of man himself) in a purely mechanistic manner. Darwin’s theory radicalised not only biology, but also anthropology – as before the Aristotelian hierarchy had rendered man wholly other to the animal kingdom. Now with Darwinian evolution, man was only different from animal and vegetable life by degree.

Definitions of sex, naturalism and the marriage debate

The definition of sex is surprisingly hard to pin down. There are a few common tropes such as that which produces orgasm or that which is pleasurable. But neither of these will do because sex can be sans orgasm and pleasure can be induced in other ways. One may say it’s the insertion of a penis in certain orifices, but of course this won’t do either for obvious reasons. Consent is also insufficient.

The traditional western definition is the coming together of two distinct individual organisms as one organism for the production of a new life. However, this takes something like a Platonic or Aristotelian realism and a fundamentally teleological view of nature for granted.  This just begs the question: can a society that is essentially naturalistic (i.e. no forms and no teleology) produce a meaningful definition of sex?

The naturalist position is the reverse of the realist position. For the realist, the man as substance is both more real than and is the final cause of his various accidents (such as his appendix for example). This view can most simply be thought of as wholes causing parts. For the naturalist-cum-atomist, atoms are the substance and man is the accident – parts causing wholes. This is the problem of the one or the many. When the naturalist view is fleshed out, not only is the definition of sex problematic but also the principles by which distinct individuals (which are necessary for sexual intercourse) have their being.

Therein is one of the potential sources for confusion in the modern debate regarding sex and marriage. The cart has gone well and truly before the horse; the question of the morality of sex must be subsequent to inquiry into the nature of sex itself. We don’t know what to do with sex and by extension marriage, simply because as a society the west has no understanding of what these things are.

Nietzsche: the death of God and cultural criticism


God is dead. God remains dead. And we have killed him. How shall we comfort ourselves, the murderers of all murderers? What was holiest and mightiest of all that the world has yet owned has bled to death under our knives: who will wipe this blood off us? What water is there for us to clean ourselves? What festivals of atonement, what sacred games shall we have to invent? Is not the greatness of this deed too great for us? Must we ourselves not become gods simply to appear worthy of it?

— Nietzsche, The Gay Science, Section 125

“God is dead” – the oft quoted, but seeming as oft misunderstood, idea of Nietzsche. These words are often casually dropped in conversation, as if a soundbite, but rarely does the mournful gravity of Nietzsche’s contention break through.

The mourning comes from recognising the crisis that the death of God will bring upon the individual and  Europe as a whole, and whether Nietzsche meant death as literal or figurative doesn’t change this point. For Nietzsche, when one gives up the credulity of the existence of God, one also necessarily relinquishes one’s right to Christian morality. Furthermore, one is left with a universe absent of objective values and truth – a disorderly place that at first glace seems to evoke the only natural response of nihilism. Nietzsche’s solution to this nihilistic tendency was the ubermensch and his will to power.

Thus arises Nietzsche’s vehement criticism of “the herd”. Nietzsche saw the popular culture as embracing the false Christian morality in order to avoid the use of their own will. As Marx held that religion holds man back from the sanctity of his labour, so Nietzsche criticises the herd for holding back the rise of the ubermensch, culminating in their own damnation.