For example, in the first half of the 19th century, astronomers were observing the path of the planet Uranus to see if it conformed to the path predicted by Newton's law of gravitation; it didn't. There were an indeterminate number of possible explanations, such as that the telescopic observations were wrong because of some unknown factor; or that Newton's laws were in error; or that God moves different planets in different ways. However, it was eventually accepted that an unknown planet was affecting the path of Uranus, and that the hypothesis that there are seven planets in our solar system was false. Le Verrier calculated the approximate position of the interfering planet and its existence was confirmed in 1846. We now call the planet Neptune.
There are two aspects of confirmation holism. The first is that interpretation of observation is dependent on theory (sometimes called theory-laden). Before accepting the telescopic observations one must look into the optics of the telescope, the way the mount is constructed in order to ensure that the telescope is pointing in the right direction, and that light travels through space in a straight line (which Einstein demonstrated is not so, except as a possible approximation). The second is that evidence alone is insufficient to determine which theory is correct. Each of the alternatives above might have been correct, but only one was in the end accepted.
That theories can only be tested as they relate to other theories implies that one can always claim that test results that seem to refute a favoured scientific theory have not refuted that theory at all. Rather, one can claim that the test results conflict with predictions because some other theory is false or unrecognised (this is Einstein's basic objection when it comes to the uncertainty principle). Maybe the test equipment was out of alignment because the cleaning lady bumped into it the previous night. Or, maybe, there is dark matter in the universe that accounts for the strange motions of some galaxies.
That one cannot unambiguously determine which theory is refuted by unexpected data means that scientists must use judgements about which theories to accept and which to reject. In practice, these judgements are made according to the outcomes of statistical hypothesis tests. As these have their foundation in mathematical statistics, the methods scientists use to accept or reject theories may be regarded as rigorous.
Suppose some theory T implies an observation O (observation meaning here the result of the observation, rather than the process of observation per se):
![T \rightarrow O]()
The required observation (result), however, is not found, i.e.
![\sim O]()
So by Modus Tollens,
![\sim T]()
All observations make use of prior assumptions, which can be symbolised as:
![O \equiv \left( p_1 \wedge p_2 \wedge p_3 \wedge \cdots \wedge p_n \right)]()
and therefore
![\sim O \equiv \sim \left( p_1 \wedge p_2 \wedge p_3 \wedge \cdots \wedge p_n \right)]()
which is by De Morgan's law equivalent to
![\sim \left( p_1 \wedge p_2 \wedge p_3 \wedge \cdots \wedge p_n \right) \equiv \left( \sim p_1 \vee \sim p_2 \vee \sim p_3 \vee \cdots \vee \sim p_n \right)]()
.
In other words, the failure to make some observation only implies the failure of at least one of the prior assumptions that went into making the observation. It may be possible to reject an apparently falsifying observation by claiming that only one of its underlying assumptions is false, and not the one intended to be tested by the observation; if there are an indeterminate number of such assumptions, any observation can potentially be made compatible with any theory.
Similarly, a theory consists of some indeterminate conjunction of hypotheses,
![T \equiv \left( h_1 \wedge h_2 \wedge h_3 \wedge \cdots \wedge h_n \right)]()
and so
![\sim T \equiv \sim \left( h_1 \wedge h_2 \wedge h_3 \wedge \cdots \wedge h_n \right)]()
which implies that
![\sim \left( h_1 \wedge h_2 \wedge h_3 \wedge \cdots \wedge h_n \right) \equiv \left( \sim h_1 \vee \sim h_2 \vee \sim h_3 \vee \cdots \vee \sim h_n \right)]()
In words, the failure of some theory implies the failure of at least one of its underlying hypotheses. It may be possible to resurrect a falsified theory by claiming that only one of its underlying hypotheses that had been previously ignored is false; again, if there are an indeterminate number of such hypotheses underlying a particular theory, it can potentially be made compatible with any particular observation. Therefore it would be in principle impossible to determine if that theory is false by reference to evidence.
The framework of a theory (formal conceptual scheme) is just as open to revision as the "content" of the theory. The aphorism that Willard Quine uses is: theories face the tribunal of experience as a whole. This idea is problematic for the analytic-synthetic distinction because (in Quine's view) such a distinction supposes that some facts are true of language alone, but if conceptual scheme is as open to revision as synthetic content, then there can be no plausible distinction between framework and content, hence no distinction between the analytic and the synthetic.
One upshot of confirmational holism is the underdetermination of theories: if all theories (and the propositions derived from them) of what exists are not sufficiently determined by empirical data (data, sensory-data, evidence); each theory with its interpretation of the evidence is equally justifiable or, alternatively, equally indeterminate. Thus, the Greeks' worldview of Homeric gods is as credible as the physicists' world of electromagnetic waves. Quine later argued for ontological relativity, that our ordinary talk of objects suffers from the same underdetermination and thus does not properly refer to objects.
While underdetermination does not invalidate the principle of falsifiability first presented by Karl Popper, Popper himself acknowledged that continual ad hoc modification of a theory provides a means for a theory to avoid being falsified (cf. Lakatos). In this respect, the principle of parsimony, or Occam's Razor, plays a role. This principle presupposes that between multiple theories explaining the same phenomenon, the simplest theory – in this case, the one that is least dependent on continual ad hoc modification – is to be preferred.
In recent philosophical literature, starting with Kant, and perhaps related most popularly with Strawson, attempts have been made at transcendental arguments. This form of argument attempts to prove a proposition from the fact that said proposition is the precondition of some other well-established or accepted proposition(s). If one accepts the validity of this sort of argumentation, then these arguments may serve alongside the Razor, and may perhaps be more conclusive, as a heuristic for selecting between competing, under-determined theories.
