Lecture 6 - Explanation Flashcards
Explanatum = explanandum + explanans
- Explanandum: description of observed phenomenon or established regularity
- Explanans: f.e. lecture, not mere deduction (but deduction from laws of nature)
- Explanation is answer to a why question (or how question), what-questions are answered by description or explication
Deductive-nomological explanation (Hempel) :
- Set of sentences implies explanandum
- Premises are only laws of nature, mathematical theorems and particular facts
- Set of sentences is consistent
- Explanandum can’t be deduced from facts and math, laws are needed
- No premise in set can be deduced from explanandum
- Deduction is slender: throw out any premise and explanandum no longer follows (throw out redundant premises)
Lawlike regularity
Hempel: contingent regularity does not explain, only law-like regularity will do
Three types of problems for DN explanations:
- Redundancy problem: we can add arbitrary sentences to the premises in Γ without invalidating the deduction of the conclusion
- Tacking problem: We can add disjuncts to the explanandum ad libitum and every added disjunct will hurt, because the explanans has nothing to do with the added disjuncts
- Symmetry problem: Struggles to capture causal asymmetry—the one-way relationship where causes explain effects but effects don’t explain causes, does not offer genuine explanation (solved by adding causality)
Inductive-nomological explanation:
- Set of sentences consists of laws of nature, of which at least one is probabilistic, mathematical theorems and particular facts
- Set of sentences implies probability of explanandum close to 1
- Conclusion cannot be deduced only from the facts
- Set is consistent
- No premise in set can be deduced from explanandum
- Deduction is slender
Problem with IN explanation
Problem: adding true sentence (penicillin example) can lead to negation of previous conclusions
Solution (carnap): add requirement of total relevant evidence (what is total relevant evidence?)
Causal explanation:
- Set of sentences describes how occurrence of n events are jointly sufficient for occurrence of explanandum
- Occurrence of every event is necessary for occurrence of explanandum
- Set of sentences is consistent
Functional explanation:
- Finite set of sentences Γ functionally explains E iff:
- Γ describes a function of the prime object or objects involved in E and shows how the functioning leads to E,
- And Γ is consistent.
Idea of unification-explanation:
to explain phenomena is to unify the phenomena
Unification-explanation:
- Consider some scientific theory, say T.
- Collect from the scientific literature accepted ‘explanations’ of the phenomena (collected in set Φ of saved phenomena) that T is supposed to save: this yields a set of sentences: KΦ.
- Find recurring deductive ‘argument-patterns’ in KΦ: deductions that have [principles, postulates, laws of T] among its premises and have as their conclusions [descriptions of the saved phenomena in Φ].
- Collect the different deductive ‘argument-patterns’ and call this rational reconstruction of KΦ: a systematization f T.
- Set KΦ under-determines any such systematization.
- Lay down some conditions for systematizations, and then find the best one: this best one is called the Unification of KΦ: U[KΦ].
- A rationally reconstructed deductive argument from U[KΦ] that concludes with a description of phenomenon ϕ in Φ is called: an explanation of ϕ.
Axiomatisation:
to find a limited number of sentences from which all sentences in KΦ deductively follow, and having a limited number of primitive concepts in terms of which all other concepts in KΦ can be defined
Unification
best systematisation = (i) the least number of argument patterns (which then are instantiated many times in KΦ); and has (ii) the most encompassing consequence class.
Parsimony
Systematisations containing less pure argument patterns have a larger parsimony factor: they are more parsimonious.
Stringency:
A systematisation intuitively becomes better whenever the number of patterns it instantiates decreases and the stringency of the patterns increases
Consequences:
some systematisations are more consequential than others, meaning they encompass more of the deductive consequences
What makes quality of unification? and how
Parsimony, stringency and consequentialism together make the quality of unification.
How does unification explanation avoid redundancy, tacking and symmetry problems?:
Redundant premises and reversed deductions are absent in scientific publications, hence are not in the set of sentences we start with: KΦ
Redundancy: addition of redundant sentences makes systematization less parsimonious and less stringent
Tacking: adding more disjunctions will make the generating set of any set of argument patterns less parsimonious
Contrast class:
: The ambiguity in questions can be eliminated by mentioning the so-called contrast class: by underlining different parts of the question and asking: why this and not something else? Contrast class is determined by context
Pluralism:
There are several types of explanations in science, which are not reducible to some single type of explanation.
