Denotation involves the interpretation of denoting phrases such as: a cell, some cell, every cell, all cells, the zygote that developed into Bertrand Russell, the unfertilised ovum that developed into Bertrand Russell. The theory of descriptions, developed by Bertrand Russell beginning with his work On Denoting , provides a means of extracting the logical form of denoting phrases from natural language expressions.
The topic of denotation is important to Russell from a theory of knowledge point of view, that is, theory about what we can know about the world. Russell at the time saw two distinct types of knowledge:
acquaintance:things that we can directly perceive.
knowledge about:things with which we have no immediate acquaintance, but understand by description.
Descriptionsof objects are denoted by phrases composed of words with whose meanings we are acquainted.
Acquaintance is a special type of knowledge about
Many texts on Russell’s theory of descriptions suggest that direct perception and the naming of objects by ostensive definition, by pointing, are unproblematic. This may have been Russell’s view too in his early writings.
However, in Russell’s later writings on human knowledge  he took a pragmatic empirical view that I would summarise as follows:
He accepts Hume’s position that there is no certain knowledge of the real world
However, he believes that there is a pragmatic and practical basis for believing in knowledge that has strong empirical support.
Acquaintance with the name of a thing is gained through a series of events where the name is associated with the physical perception of the thing.
Through this empirical acquaintance we link the name of the thing with the mental description of the object that we keep in our mind and use to recognise the object.
The name of the object is just the short hand link to the mental description of the object we keep. The mental description that is used by our brains to interpret the inbound perceptual information from our senses (for example, information from our eyes delivered by our optic nerve to our brain).
This is essentially the same as the short hand identifier used by a computer to link to a detailed description or model for recognising an object. A model that is used by the computer to interpret inbound information from its sensory devices (for example, information from a camera delivered by binary information to the CPU).
Symbols are used to denote things, usually we think of words, words in any language, but the language could be a computer language of binary bits, those bits physically held in memory, our memories stored in the structure of physical neural networks.
If acquaintance is taken to be empirical as discussed above, then really it is just another form of knowledge about things. Traditionally it is considered to be knowledge gained where there is no intermediate unnatural translation of the description from the “natural world” (light travelling to our eyes from the object) and our perception (the receipt of the light by our eyes). But even in this natural case, the simple name we give to a perceived thing is denoted by the description held in our minds of the object, the description used to recognise the object. This description of the object is an incomplete description and created through imperfect senses and thus empirical in nature.
Even knowledge of our selves is empirical, in that it necessarily involves one part of the self-perceiving another and in the same way this must be incomplete.
Some examples of acquaintance being a special type of knowledge about:
Direct sense perception: Practical medical science provides an opportunity for physical acquaintance with physiological, biological and other medical objects. Names are associated with the physical objects by ostensive definition, pointing out, of objects by demonstrators and peers. As discussed, I argue that even here the objects are being denoted by descriptions in our minds that will be used to link future acquaintances with the name given to the object.
Magnified perception: When our practical science moves to the microscopic level the empirical nature of naming and denotation becomes clearer. Here we don’t have direct perception of the objects and must rely on the images provided by magnification devices. We treat the images as if they were simply the perceptions we would have if our eyes could achieve the same magnification, however this assumption is an empirical one.
Assay perception: At the molecular level, the empirical nature of perception becomes obvious. When we run an assay on a biological sample (eg. ELISA) and interpret the results, it is impossible to treat it as a direct perception of the molecular make-up of the sample. This is acknowledged by the use of statistical analysis to interpret the results and their quality.
I would argue that the direct sense perception of medical objects is, from a theory of knowledge point of view, no different to the perception of assay results. Both rely on the translation of sensory perception into description/denotation/model in our brains that is then linked to a name for the object. The difference being only that the assay perception involves external additional descriptions of the object and the direct sensory perception only involves internal human descriptions of the object in our brains.
This equivalence can further be demonstrated by the following examples:
Instead of a physical practical experience with the object, you could instead learn the name for an object from a textbook where the exact same image that you would have seen in an in person medical practical is provided in the text book. Certainly some of the quality of the acquaintance with the object will be lower (eg. loss of 3 dimensions, you can’t feel it), but it is not a completely different experience and you would gain similar acquaintance and knowledge about the object.
It may be that the image in the textbook was damaged, but there remains an extremely detailed description of the object in the book and you would gain a lower but again somewhat similar acquaintance and knowledge about the object.
Other similar examples would be a high quality replica wax model of the object, a diagram of the object that is drawn to highlight important attributes of the object (good ways of describing or recognising the object), etc
Perception, as it is used here, is simply a name for a type of knowledge about things in the world that doesn’t involve the interposition of descriptions of the object between a human and the object in the real world. However, there remains descriptions within the human, that makes perception a form of knowledge about the object.
Thus all human knowledge is knowledge about the world and is thus subject to Russell’s theory of descriptions and denotation.
Knowledge about is empirical
Knowledge about the world gained by acquaintance or through descriptions is inevitably empirical. In the case of acquaintance, the descriptions of objects that we build for objects in the world are strengthen and refined through the corroboration of our recurring observations of the object and the description we hold for the object. In the case of knowledge gained through descriptions, the descriptions to be useful must have been developed through empirical means by the person or community who created the description. It is possible that a description has been developed without an empirical foundation, but in this case we should not expect the description to be corroborated by our own observations of the world.
Most of our common sense knowledge about the world is established through our acquaintance with the world as we develop. We may not consciously think of this knowledge acquisition as a scientific process, but subconsciously our mind is gaining knowledge through the generation of hypotheses and the testing of these hypotheses in the course of our life.
Science and the scientific method is really just a formalisation of our natural approach to knowledge acquisition with a higher expectation on the required level of corroboration.
The goal of science is to gain high quality and reliable knowledge about specific things in the world, both objects and the processes that effect objects, to be able to describe or denote these specific things in a highly reliable way.
Very good scientific descriptions are those that would allow a person with no direct acquaintance with a thing to identify and make good predictions about that thing in the world.
The quality of the descriptions in science are important. Descriptions that are needlessly complicated or rambling will make their conversion into knowledge about the world difficult for the reader. Ockham’s razor suggests that descriptions should be as simple as possible, but no simpler.
Another goal of science is to make descriptions as broadly applicable as possible where that can be done without excessive additional complexity. Our preference is to create efficient scientific descriptions of “all cells”, rather than just “some cells”.
In physics, many of the descriptions are provided in the form of mathematical equations. On the other hand, in medical science, the majority of descriptions are given in the form of literature. Certainly medicine uses special scientific terminology, but the terminology is presented in natural language. There are some niches of medical science were more formal languages are used: for instance, in biochemical pathway analysis.
Mathematics is just a type of description where the symbols and words are used in a highly formal way. High quality natural language can be somewhat formal, but only to a dramatically lower level than formal languages like mathematics and first order predicate logic.
Our goal is to develop and promote more formal languages for expressing medical science knowledge. We seek to extract medical science knowledge out of the existing natural language literature and into such formal languages. Ideally one-day medical science will be coded directly into such formal languages and we believe that powerful and easy to use tools will be essential to achieving this goal.
Russell, Bertrand. (1905). “On Denoting”, Mind14, pp. 479–493.
Russell, Bertrand. “Human knowledge: Its scope and its limits.” New York: Simon &Schuster (1948).