On Necessary and Contingent Truths, With Special Reference to Mt. Kilimanjaro



by Justin E. H. Smith

There is a familiar distinction in philosophy between contingent and necessary truths. Truths of the latter sort are those the negation of which implies a contradiction, or those that are true simply in virtue of the meaning of the words involved. For example, “A triangle has three sides” is true simply in virtue of the meanings of the words ‘triangle’, ‘three’ and ‘side’. If you encounter a figure with four sides, then necessarily you have not encountered a very unusual triangle, but rather a non-triangle.

Contingent truths are those the negation of which implies no contradiction, or, to put this somewhat differently, those that could have been false (whatever that might mean!). Some contingently true statements involve particular cases, e.g., “This swan is white.” A special class of contingent truths are those expressed by empirical claims about how one expects all entities or phenomena of a certain kind to be. These are the sort of truths established by inductive reasoning, and it is characteristic of them that they can always turn out to be falsified by any given case. Thus, “All swans are white” was held to be true for a long time, as the instances of observed swans grew and grew, and in each case, each swan observed turned out, in fact, to be white. This contingent truth however, turned out to be false, as European travelers to Australia, home of the Cygnus atratus, realized toward the end of the 18th century.

Now, any member of the genus Cygnus is a swan, and there was a prior fact of the matter, prior that is to Captain Cook’s expedition, about the color-independent features of an entity that determine whether it is a member of this genus or not. This is what makes “All swans are white” a mere empirical claim rather than an analytic truth, or a truth that can be established simply in virtue of the analysis of a proposition into the meanings of its component parts.

“All triangles are three-sided” is analytic, and so, it is generally supposed, is “All whales are marine mammals.” But the grounds for placing the whales with the triangles rather than with the swans are by no means perfectly clear. What if we found a cetacean population uniquely (and implausibly) adapted to a terrestrial environment? Would they be ipso facto non-whales? We suppose, for now, that “All whales are marine mammals” is true by definition, but this could turn out to be a prejudice supported only by the current imperfect state of our empirical knowledge. In the 17th century, “All swans are white” no doubt appeared true by definition as well.

In that same century, when all swans were white (in Europe), René Descartes argued that existence pertains to God in exactly the same way that three-sidedness pertains to triangles. That is, he thought, you can no more entertain the idea of a non-existent God than you can the idea of a four-sided triangle. If you are thinking, “This ‘God’ is a pretty interesting concept, but I’m still wondering whether he exists or not,” then you are not really entertaining the concept of God at all. You only think you are. Says Descartes.

But what if “God exists” is in fact more like “Swans are white” than it is like “Triangles are three-sided”? What if, as it were, Descartes simply hadn’t encountered, yet, an inexistent God? It is perhaps more telling than it first appears to note that one of Descartes’ preferred examples of a claim that is true by definition, alongside “God exists” and “Triangles are three-sided,” is one that he believes to hold of mountains: a mountain, he claims, is something that has, by definition and of necessity, a valley.


Now a valley is typically defined as a depression that is longer than it is wide, while a depression is any landform that is lower than the area surrounding it. Valleys, it is not hard to see, are therefore typical of mountains that are organized into mountain ranges, such as the Alps. But there are also so-called ‘free-standing mountains’, such as Mt. Kilimanjaro, which is entirely surrounded by a plain, or El Pico Tenerife, which is an island mountain entirely surrounded by water. The surface surrounding these peaks is lower relative to the peaks themselves, but it is in no sense a ‘depression’ relative to the earth’s surface or to sea level, and so neither is it a depression that is wider than it is long.

It was not until 1846 that the German missionary Johann Ludwig Krapf made a journey to the snow-covered mountains of inland East Africa (the other principal peak being Mount Kenya, 200 or so miles away). As E. G. Ravenstein reports 16 years later, it would only be possible to doubt the implausible report of their existence “if we assume the missionaries capable of deliberately advancing false statements.” In his “Precise Account of Geographical Discovery in Eastern Africa,” which serves as a preface to the English translation of Krapf’s Travels, Researches, and Missionary Labours, During an Eighteen Years’ Residence in Eastern Africa (1), Ravenstein disputes some recent claims that as to the location of the African mountains that Ptolemy had described as resembling the Montes Lunae, the mountains of the moon (see here for my treatment of some aspects of the history of lunar topology, which includes among other theories the idea that the visible portion of the moon is in fact a single, massive free-standing mountain). Certain explorers had inferred that these must have been the cresent-shaped chain surrounding Lake Tanganyika, separating modern day Tanzania from the Republic of Congo. But Ptolemy had no knowledge of the Upper Nile and its termination in the African Great Lakes, Ravenstein argues, and so the moon-like mountains to which the Greek geographer refers could only be those freestanding peaks on the inclined plateau to the east, Mounts Kilimanjaro and Kenya.

Krapf himself had complained of a certain Mr. Cooley who, in his Inner Africa Laid Open of 1852 had refused to lend credence to native reports of snow-covered peaks in the region. The locals had told Cooley that “white matter” was “visible upon the dome-like summit of the mountain,” and that “the silver-like stuff, when brought down in bottles proved to be nothing but water.” Cooley finds this detail outlandish, while Krapf blames his fellow explorer for following poor inductive method by failing to recognize the high probability of reports of seemingly insignificant details: “Had Mr. Cooley been accustomed to weigh and sift evidence more closely, he would have argued differently from that very fact; for by its own law evidence is always strengthened by the record of trivial and immaterial circumstances”(2). Here Krapf is echoing some of the themes of the debates held in the Royal Society of London two centuries earlier about the veracity of anecdotal reports.

Krapf’s American biographer, Paul Kretzmann, remains stupefied, several decades after the German missionary’s journey, that such a thing as Kilimanjaro exists at all. It seems strange, he writes, “that there should be mountains in Africa, almost beneath the equator, whose foot hills are covered with the palms and the jungles of the tropics, while their summits are covered in everlasting snow”(3). Kretzmann cited the poet Bayard Taylor’s evocative 1855 address to the mountain itself: “Hail to thee, monarch of African mountains / Remote, inaccessible, silent and lone – / Who, from the heart of the tropical fervors, / Liftest to heaven thine alien snows” (4).

Strange, unnatural, alien, moonlike, valley-less: Mt. Kilimanjaro confounds the Europeans, imports disorder into their pat scheme of what must go with what. It is also surrounded, as Kretzmann reminds us immediately after his description of East African topology, by people who have no concept of God:

The Paganism or Fetishism which is the native religion of a large part of Africa is a form of Animism or the worship of spirits. It is a religion of almost unbelievably terrible darkness. It believes in numerous horrible demons, and the Pagan native of Africa thinks of these as surrounding him on every side, continually seeking to do him injury and to bring about his death. These demons are supposed to inhabit every object, whether possessing life or not (5).

Existence belongs to God, just as valleys belong to mountains. Except, it appears, in Africa.

Of course Krapf and Ravenstein were writing two centuries after Descartes, and we cannot expect the French philosopher to have inferred the existence of Kilimanjaro from slight hints in Ptolemy (if that is what they are). But the Canary Islands had been thoroughly navigated by the 14th century, and several descriptions of the Tenerife peak were available by the time Descartes was reading and writing and defining mountains.


 Descartes, it has often been noted, was programmatically uninterested in travel reports, in cultural diversity, in the profusion of knowledge about local divergences that might complicate an attempt to model the world as a rational, ordered whole. He valued geodesy over geography. He had next to nothing to say about the Americas. In all of this he differs radically from the philosophers, such as Francis Bacon, who took the rise in sea travel as the very cause of the birth of modern philosophy, and correlatively took as the principle task of philosophy the ‘laying by of notions’ in order to harvest as many particular facts (“This swan is white,” “So is this one,” …) about the world as possible. Descartes by contrast wished to construe philosophy entirely by appeal to notions, which have the advantage of being indifferent to complications that might arrive from the field, from the soiled notebooks of half-literate travellers.

We should perhaps not make too much of Descartes’ peculiar choice of mountains and valleys as an example of a truth of definition. Perhaps he had a curious understanding of ‘valley’, such that it is simply the area, any area, that surrounds a mountain. But the significance of this example is brought into sharper relief when it is placed in the light of what really interests him: the existence of God. Descartes would never think to survey the globe, and least of all to survey the people later belittled by Kretzmann as backward animists, to find out whether one must in fact accept the existence of God or not. But what if Descartes’ geographical error in fact reveals a shortcoming in the approach to theology?

Black swans were incorporated into European taxonomy with little crisis– even though Australia has generally played a role comparable to that of Africa, as a place where the ordinary rules governing nature begin to break down, and even though marsupials and monotremes would indeed send a strong signal back to Europe of such Antipodean chaos, the black swan itself required only a slight modification. This is because, again, it was understood prior to 1790, when John Latham gave the first natural-historical description of the Atratus species, that Cygnus is a genus term that is not based on feather pigmentation. Now, Descartes could have conceived mountains in similar terms: as the sort of things that, in his experience up until now, have always been accompanied by valleys, but that do not necessarily need valleys in order to be mountains. But he did not proceed in this way. Instead, he took valleys as pertaining to mountains by definition, and he was so committed to this definitional inseparability that he used this example to illuminate his understanding of the ontological argument for the existence of God.

His commitment to this procedure by way of definition, rather than survey, foiled him in the case of mountains. I believe it foiled him in the case of God too: what we need are surveys of the full range of human interpretations of the ultimate ground of our existence and experience –even, or especially, of those interpretations that attribute powers to trees and stones– and not a priori arguments. A Baconian theology, if you will.

Piece crossposted with Justin E. H. Smith’s website


(1) Rev. Dr. J. Lewis Krapf, Travels, Researches, and Missionary Labours, During an Eighteen Years’ Residence in Eastern Africa, Together with Journeys to Jagga, Usambara, Ukambani, Shoa, Abessinia, and Khartum; and a Coasting Voyage from Mombaz to Cape Delgado… With an Appendix respecting the Snow-Capped Mountains of Eastern Africa (London: Trübner and Co., Paternoster Row, 1860).

(2) Krapf, Travels, Researches, and Missionary Labours, 543-544.

(3) Paul Kretzmann, John Ludwig Krapf: The Explorer-Missionary of Northeastern Africa (Columbus, Ohio: The Book Concern, 1909), 7.

(4) Ibid.

(5) Ibid., 15.