Monthly Archives: August 2019

Frege, his Dad and the Eternal

“By Heaven, can we be ready to believe that the absolutely real has no share in movement, life soul or wisdom? That it does not live or think, but in solemn holiness, unpossessed of mind, stands entirely at rest? That would be a dreadful thing to admit.” (Plato ‘Parmenides’ p.248e)

Philosopher and biographer Ray Monk has written some of the most interesting and informative biographies about a variety of philosophers such as Bertrand Russell and Ludwig Wittgenstein etc. Monk argues that some philosopher’s lives are so dull as to resist any interesting biographies being written about them. Monk singles out philosophers such as Frege and Kant as being people who are so boring as to make a biography of them pointless.

Frege’s life certainly seems to bear out Monk’s negative impressions.  By all accounts Frege was a dull man whose life (outside of his theoretical work), seemed to be very dreary. He was a hard working maths student, who turned out into a hard working associate professor, he had an unremarkable marriage, had one adopted child and eventually he grew old and died. My little summary of Frege’s life may seem harsh, but the biographies written about him reveal little else about the man. There is very little documentary evidence of any kind of personality; no funny anecdotes, no interesting quirks in his personality; just lots of hard work in mathematics.

However as the philosopher Richard Rorty noted, one of the lessons we should have taken from Freud was that there were no truly dull people. If you get anyone on the bench you will discover unconscious motivations, bizarre desires, idiosyncratic behaviours etc. Here is Rorty’s gloss on dull people:

“But there is a difference between Nietzsche and Freud which my description of Freud’s view of the moral man as decent but dull doesn’t capture. Freud shows us that if we look inside the bien-pensant conformist, if we get him on the couch, we find that he was only dull on the surface. For Freud, nobody is dull through and through, for there is no such thing as a dull unconscious. What makes Freud more useful and more plausible than Nietzsche is that he does not relegate the vast majority of humanity to the status of dying animals. For Freud’s account of unconscious fantasy shows us how to see every human life as a poem… (Rorty ‘Contingency, Irony and Solidarity’ p. 35)


One doesn’t have to entirely buy into Freud’s particular views on psychology to agree with the general claim. It is surely indisputable that all humans have day-dreams, fantasies, unconscious beliefs governing their behaviour which they don’t explicitly state. Presumably Frege had sexual fantasies, presumably he had fears about death, growing old, he had passionate hates and passionate loves. Unfortunately there is little documentary evidence indicating any of these subjective states of the great man. In his writing he practically never mentions his emotional world. His output is almost entirely dedicated to his views on the foundations of mathematics. The only time Frege the man is seen in his writing is in a diary written later in his life where he expresses some extreme right wing thoughts. Aside from that Frege the man never emerges in his output of writing.

Frege famously argued against the idea that our grasp of mathematics could be explained entirely interms of our own idiosyncratic psychology. For Frege, mathematics was about an objective Platonic realm, the abstract objects mathematics picks out exist independently of any psychological states. Frege even argued that meaning should not be explained interms of idiosyncratic subjective ideas but instead meanings should be cashed out interms of abstract entities.

As every first year philosophy student knows philosophers such as Locke, Hume, Descartes etc cashed out the meaning of our words interms of their reference to ideas in our mind. Thus the meaning of our word ‘Cat’ would be cashed out in terms of our subjective idea (roughly a mental image) of a Cat. On this representationalist picture when we see a cat in our environment we are seeing it via a mental representation of the cat, and when we think about a cat we conjure up less vivid images of the cat. The meaning of the word ‘cat’ is derived from a combination of our images we conjure up when we think of a cat and the mental representations we use when we interpreting cat like stimuli in our environment.

Frege rejected this view of meaning. Firstly he rejected the view that our words picked out mental representations; for Frege our words picked out mind independent objects[1]. Our words reference was a mind independent object {which he parsed as either the true or the flase}, and the reference was mediated by an abstract sense. In his infamous example two people could be referring to the same object (Venus), but they could pick out that object via different modes of presentations. One person could refer to Venus via a sense {the morning star}, while another person could refer to Venus via the sense {the evening star}, neither person might know that { the Morning Star and The Evening Star both refer to the same thing i.e. Venus}.

Thus far people may find the above unproblematic. Our words pick out mind independent entities via our senses (which can be cashed out interms of descriptions instead of mental images), the overall picture seems a sensible one. However, natural as the above picture is, it is important to not be misled, Frege was explicit on the point that the senses which picked out references shouldn’t be understood as psychological states. Senses are objective modes of presentations they aren’t to be equated with psychological states or ideas.

Tyler Burge correctly argued that Frege claimed that there were three different functions of senses; (1) Senses are modes of presentation, (2) Senses fix reference, (3) they serve as the denotation of expressions in oblique contexts ( Burge ‘Frege on Sense and Linguistic Meaning’ pp.242-243). Furthermore, it is important to note that for Frege Senses are not to be reduced to linguistic meaning. Frege argued that while mathematicians who had written in his time and prior to him used linguistic descriptions of various different mathematical concepts their linguistic descriptions only partially and incompletely captured the abstract senses of the various different mathematical concepts. On Frege’s views senses belonged to a third realm of abstractions that existed independently of any psychological states or of the physical world.

Frege’s views on the subject were brilliantly argued for and to this day stand out as one of the best explanations we have for mathematical knowledge. His reasons for dismissing psychological states and subjective ideas are nicely summarised by Jacqquette:

“Frege wanted to distance himself from including meaning factors in the third level of associated mental content. He did not deny their existence. That is important. He nevertheless found no place for transitory ideas in objective non-psychologistic semantics. He concluded that an associated mental image, connotation, and “poetic” but nonetheless real “colouring” may sometimes accompany a thought’s reference to an intended objected by means of a word’s or sentence’s sense, what the symbol is being used to express and the thinker trying to say. However, Frege did not believe that these accidental subjectively variable associations occur in any lawlike way.” ( Jacquette ‘Frege: A Philosophical Biography’ p. 335)

Frege’s views on the above topic have influenced the likes of Quine, Wittgenstein, and Skinner. Frege’s argument in the above piece is pretty convincing. Whatever, the subjective colour provided by our idiosyncratic experiences as we do math; if we want to engage in law like inferences we need to move beyond our psychology and into the normative level.

From a logical point of view Frege’s attack on a naive psychologism is a sensible attack; without the attack we are in a quandary in explaining our normative judgements in logic and our law-like explanations of natural phenomena. Nonetheless, there was at times something unbalanced in Frege’s reaction to psychological explanations.

In his philosophical biography of Frege, Dale Jaquette documented the almost universal bad reviews or indifferent uncomprehending reviews that Frege’s work received throughout his life. Up until Russell acknowledged Frege’s work in his 1903 ‘Principles of Mathematics’ few mathematicians were impressed with Frege’s Logicism. On philosopher who was impressed with Frege’s work was Edmund Husserl; Husserl contacted Frege and they communicated about their respective research into the foundations of mathematics. Husserl even presented Frege with his ‘The Philosophy of Arithmetic’. The evidence from their correspondence seemed to indicate that the younger Husserl hoped to initiate a collaboration with Frege.

However, Frege’s review of ‘The Philosophy of Arithmetic’ put an end to any hope of collaboration between them (though they did communicate with each other after the review). Frege’s review of Husserl’s book was a sustained attack on Husserl for engaging in psychologism in mathematics. What is odd about the review is that Husserl wasn’t attempting to reduce mathematics entirely to psychological states. Nothing in ‘The Philosophy of Arithmetic’ argued that against giving a logical foundation for mathematics. Husserl was just interested in describing the phenomenology of arithmetical thinking (Jacquette p. 434). Husserl was quite clear in the philosophy of arithmetic that he was not trying to reduce arithmetic to psychological processing.

So one wonders why Frege could have misjudged Husserl’s intents so badly and in the process alienate one of his few allies? A plausible explanation is that Frege’s sensible arguments against psychological reductions of the timeless world of mathematics stemmed from an emotional source. And that any attempt to explain math in psychological terms was triggering for him; even if the psychological explanation wasn’t intended to be reductive.

One of Frege’s contemporaries was Bertrand Russell. Russell along with Frege helped to found the discipline of analytic philosophy. Russell often speculated that his early obsession with the world of abstract Platonic entities stemmed from a fear of the contingencies of reality. In the real world things are changeable and sometimes frightening. Russell knew about the contingencies of reality only too well. Both of his parents died when he was still a young child; parents are foundational for children. They are their child’s whole world. From the moment a child is born they are entirely dependent on their parents help to survive. Eventually, typically post adolescence, children become (partially) independent of their parents. But prior to that their parents are their whole world. In his book ‘The Philosophers their Lives and the Nature of their Thoughts’ Ben-Ami Scharfstein noted that a disproportionate amount of philosophers had lost a parent when they were young:

“The table shows what must appear to be a high frequency of early separations from parents, whether by death or by other causes…Of the twenty-two philosophers listed, two had lost both parents and eleven at least one by the age of six. In only six cases did both parents survive till the philosopher was fifteen…Painful separations are no doubt common in early life, but it seems nevertheless notable that at least twenty of the twenty two philosophers may of undergone them…a parent’s death might leave the philosopher in fear that he had inherited some vulnerability or even death from the parent.” (The Philosophers pp 347 -348)

Frege is one of the great philosophers who fits into the above category, he lost his father when he was just reaching adolescence, and he was a sickly child. It is not hard to imagine a weak child terrified with the contingencies of existence, who has lost his father, and who is sickly and acutely aware of his own mortality being fascinated by the universal rules of logic and mathematics. Frege being naturally brilliant at mathematics would have been constantly reinforced in its pursuit when he was developing as a young man. The eternal truths he was discovering would have seemed to have been an anchor that would remain true no matter what the contingencies of life would bring.

It is possible that Frege’s attack on Husserl was an unconscious defensive attack on someone who he unconsciously believed was attacking the only secure foundation he believed possible in the world he found himself in.

However, even if it is true that Frege had an unconscious emotional attachment to Logicism that led him to uncharitable attacks on people who attempted psychological explanations, this hardly makes his life a poem (in the Rortian sense). At best we have a dull professor who feared death and vulnerability and who as a result was overly attached to a particular philosophy.

Frege the human exemplar of a poem it seems is lost to biographers. To understand Frege in the Rortian sense we need artistic representations. Frege’s diary revealing extreme right wing comments and pushing for emotional expression in political gestures reveals a less sympathetic human. A man who flees from psychology and ideas as explanatory tools but who argues for emotional expression is a much more interesting man. But he is a man hidden in shadows. It will take an artist to render this Frege flesh and blood.

[1] Frege didn’t provide much by way of justification for his views on words referring to mind independent entities as opposed to referring to mental representations.