Testing the hypotheses

Mixed reasoning:

• inference from an hypotheses to a proposition is deductive
• inference from the truth of a proposition to the truth of hypothesis is inductive

The problem of auxiliary assumptions

The consequent doesn’t follow from the hypotheses alone: the role of auxiliary assumptions derives from the fact that if we have a proposition which is deductively inferred from an hypothesis H and an auxiliary condition A, by falsifying p we may either disconfirm A or H.
The test provides non conclusive grounds for rejecting H

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The Duhem-Quine problem

The Duhem–Quine thesis argues that no scientific hypothesis is by itself capable of making predictions. Instead, deriving predictions from the hypothesis typically requires background assumptions that several other hypotheses are correct — that an experiment works as predicted, or that previous scientific theory is accurate.

Duhem-Quine thesis on Wikipedia

The occurrence of an observation which refutes a prediction derived from the conjunction of a theory under test with a number of necessary auxiliary assumptions only shows

• that at least some one member of that conjunction is false
• that the false assumption is not necessarily the theory under test

The holistic view

We aren’t testing individual theories and hypotheses, but a whole set of ad-hoc assumptions, auxiliary hypotheses, etc.

H∧A -> p
!p
---- !(H∧A), where !(H∧A) ≈ !H ∨ !A

How can it be known if the falsity lies in H or A?

27^th November 2020

The raven Paradox

A video about the raven paradox.

A paradox of relevance, about using it for testing.

It comes from two main ideas:

• instance confirmation, Nicod’s principle:

  Consider the formula or the law: F entails G. How can a particular proposition, or more briefly, a fact affect its probability? If this fact consists of the presence of G in a case of F, it is favourable to the law […]; on the contrary, if it consists of the absence of G in a case of F, it is unfavourable to this law.

• equivalence condition: logically equivalent statements are confirmed by the same evidence

thus

1. all ravens are black, which is logically equivalent to
2. everything that is not black is not a raven

But in here it lies a contradiction: the more black ravens I see, the more I prove statement 1, but according to the equivalence condition, even collecting data which confirms the second statement would also confirm the first one, which is absurd.

We’re assuming a world where everything is either a black raven, or is not a raven.

The world is divided in

• not black ravens (disconfirms the hypothesie)
• black ravens (confirms the hypothesis)
• non ravens (confirms the hypothesis)
  • non-black non-ravens (confirms the hypothesis)

If we observe a green chair, it tells us nothing about ravens, it’s not relevant, nevertheless, it’s considered valuable for the equivalence condition.

From Goodman:

Taken by itself the statement that the given object is neither black nor a raven confirms that everything that is not a raven is not black as well as the hypothesis that everything that is not black is not a raven. We tend to ignore the former hypothesis because we know it to be false from abundant other evidence – from all the familiar things that are not ravens but are black.

Nelson Goodman, Fact, Fiction & Forecast, p.72

Back to the hypothetical- deductive model, summarizing Popper and Hempel’s views:

• a scientific hypotheses must be testable
• confirmation is not truth
• Hempel: disconfirmation doesn’t need to be falsity

does such approach describe how scientists conduct their work?

Ignaz Semmelweis

Inference to the Best Explanation

Inferring to the hypotheses: inference to the best explanation.

one infers, from the premise that a given hypothesis would provide a “better” explanation for the evidence than would any other hypothesis, to the conclusion that the given hypothesis is true.

Harman, G.H. (1965), The Inference to the Best Explanation, Philosophical Review, Vol.74, No.1

According to Lipton, Semmelweis reasoned in IBE, not H-D: underlying the idea of IBE is the logical move of trying to understand if we can infer to an hypotheses before inferring from an hypotheses.

Charles Sanders Peirce and the logic of Abduction

How did Kepler arrive to his first law?

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The H-D method accounts to the process pursued after having an hypotheses, how to “catch” it instead.

Criticisms of abduction

Abduction cannot be a logic of discovery, because the hyp is already included (or supposed to be known) in the premises

we can locate abduction between discovery and testing

Inference to the best hypotheses

3^rd December 2020

Two problematic areas:

• how to formulate scientific hypotheses
• how we come to postulate the entities we use in sci laws in order to explain what we observe at an empirical level

We often infer the existence of such entities +++

Looking at scientific theories in terms of postulates we’re not basing our theories of something not sure; nevertheless if these theories work they are a satisfactory result anyway.

How do we know what we call “electron” etc. is actually what we see in the world?

How do we explain that electrons and quarks are actually “natural kinds”?

Next topic: Natural kinds