It may be that Karl Popper’s Logic of Scientific Discovery (1959) is not the last word in epistemology, but, as someone said about Kant not very long ago, you cannot go far wrong by studying it. Bearing this in mind, let us say a few words about Popper’s conception of various statements which make up scientific theories. Though the implications of the views briefly presented here are extracted and examined throughout the entire book, I will only touch upon the theoretical outset, which corresponds roughly with Chapters 3 and 4 of the Second Part (pp. 37-73)
Any theory which tries to account for some phenomenon in the external world has to be comprised of two kinds of statements: a singular statement [SS] (sometimes called ‘initial condition’) which describes a specific event in question and a universal statement [US] (sometimes called ‘hypothesis’, or ‘natural law’). This resembles the better known structure of a categorical syllogism, with its minor and major premise of the sort: “All un-suspended objects fall”, corroborated with “This ball is un-suspended” renders a prediction of a kind “The ball will fall”. Singular statements always contain, in some form or another[1], individual names and accordingly, universal statements are statements in which only universal names occur.
Within the class of universal statements[2], further distinctions could be made. First, Popper separates the numerical universal statements [NUS] from the strictly universal statements [SUS]. A numerical universal statement of the kind “All Finns speak Swedish” could in principle be verified by enumerating (hence the term ‘numerical’) all the elements in the class which makes the subject of the statement (i.e. all Finns). That is why, in a precise sense, the numerical universal statement is actually a singular statement, although it speaks of all the members in a class. It is singular because the class – ‘all Finns’, cannot be defined without reference to singular names (e.g. Finland), or the other way around, the statement could be defined by a conjunction of all the singular statements to which the “all-statement” refers.
Strictly universal statements, the ones which make up the so-called ‘laws of science’, can be described by no other means than references to universal names. One must be careful with this affirmation, for ambiguous nouns such as ‘mammal’ or ‘dog’ can be understood both as singular and universal names or concepts “it depends upon whether we wish to speak of a race of animals living on our planet (an individual concept), or of a kind of physical bodies with properties which can be described in universal terms” (Popper, 1959, p. 44). Strictly universal statements claim to be true regardless of spatio-temporal coordinates. To me, this is the fairly obvious distinction between what we normally designate by ‘any’ and ‘all’ respectively. ‘Any-statements’ (in reference to which we need not assume a bounded universe of elements) and ‘all-statements’ (in reference to which we must, as shown above, make reference to some spatio-temporal coordinates) are not mutually replaceable and would therefore serve one’s purpose. Popper makes no attempt to dissolve the ambiguity in ‘all’ by such distinction, so I will not use it any further.
With all this being said, a third distinction, arguably the most important one, is introduced: that between strictly universal statements [SUS] and strictly existential statements [SES]. This time, the statements are both, in the above sense, universal statements. The strictly existential statements are however significantly different: they assert that some event exists, e.g. “There are white ravens”. This statement could be described without reference to individual names, but could hardly be left under the same roof with a SUS. Popper calls them “there-is” statements, but most importantly, calls them non-empirical or “metaphysical”. Why?
With this, one must remember (or leaf back to page 17 for) the criterion of demarcation, i.e. falsifiability: a theory is empirical if it is possible for it to be refuted by experience. Can “there-is” statements, SES’s, be refuted by experience? They can’t: “[n]o singular statement (that is to say, no ‘basic statement’, no statement of an observed event) can contradict the existential statement, ‘There are white ravens’. Only a universal statement could do this” (p. 48) The explanation for this (although I feel the contention is quite sensible, if not self-evident) is that SES’s describe the existence of an event[3], while SUS describe the non-existence, i.e. ‘prohibit’ or ‘rule out’ the existence, of one. The negation of an SUS (‘All ravens are black’) is ‘Not all ravens are black’, and thus a SES, i.e. ‘There are non-black ravens’. This leads Popper to posit that “Whenever it is found that something exists here or there, a strictly existential statement may thereby be verified, or a universal one falsified.” (p. 49)
Short summary:
- singular (basic) statements = individual names (at least one)
universal statements = universal names (all of them) - numerical universal statements (NUS) = ‘All X’s [of a given place and time] are Y’s’ (in fact singular)
strictly universal statements (SUS) = ‘All [i.e. any] X is Y’ (empirical)
strictly existential statements (SES) = ‘There is at least one Y which is X’ (metaphysical) - The negation of a strictly universal statement is always equivalent to a strictly existential statement and vice versa. = the non-SUS ‘Not all X are Y’ is the same as the SES ‘There is a non-Y X’
- SUS’s are falsifiable and SES’s are verifiable
“You’re overthinking this, man…”
[1] Note that „individual names that occur in the singular statements of science often appear in the guise of spatio-temporal co-ordinates. This is easily understood if we consider that the application of a spatio-temporal system of co-ordinates always involves reference to individual names. For we have to fix its points of origin, and this we can do only by making use of proper names (or their equivalents). The use of the names ‘Greenwich’ and ‘The year of Christ’s birth’ illustrates what I mean.” (Popper, 1959, p. 43)
[2] We are, of course, talking about various kinds of synthetic statements, for “All women are women”, though universal by logical form, is not of much interest when we speak of empirical sciences.
[3] An event, in Popper terms, is seen as a class of occurrences. An occurrence is, in its turn, a class of basic (or singular) statements. So an event would be a class of classes of basic statements. If two basic statements are part of the same occurrence, they are equivalent. If they are part of the same event, they are homotypical (see pp. 67-71).
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