RM2 Lecture 3

Why science?

• Describes and explains causal relationships
  

• Builds theories from data
  

• Solves problems and predicts outcomes (applied science)

what is science?

• No simple definition: science seeks truth through a rational method, using empirical tools to update beliefs.

• Seeks to:

  1. Describe

  2. Predict

  3. Explain

  4. Control
     
     

Demarcation problem

How do we distinguish science from non-science or pseudoscience?

• Examples of non-science: opinion, religion, art, pseudoscience

  • They all have the same “goals” as science, describe, predict, explain

    • But this doesn’t make them a science, hence the complexity 

So… Science evolves and involves the willingness to doubt yourself and to be proven wrong, (AKA updating beliefs)

doubt in science

• Doubt is not weakness — it's a strength!

• Scientists should be willing to change their views

Famous quotes by Feynman and Carl Sagan: Embrace not knowing

science is NOT

• Absolute/ final

• Free from bias or values

• Guaranteed to be true

• Meant to "prove" theories

how does one update beliefs in science?

through rational (deduction) and empirical (induction) means

deduction

Logical reasoning from premises

• If premises are true, conclusion must be true

• Can give valid arguments, but only as good as the premises

Modus ponens: affirming the antecedent

• if P then Q. P, therefore Q.

  • When it rains, things get wet. It is raining right now, so my phone is getting wet.

Modus tollens: denying the consequent

• if P then Q. Not Q, therefore not P.

  • If it rains I stay at home. I do not stay at home, therefore it is not raining. 

But how do we know the premises are true?

• You should always distinguish whether the argument is valid. The conclusion can still be wrong, even if the argument is valid, which means one of the premises is wrong. 

how do we know what is true?

epistemology, the philosophy of knowledge

Empiricists vs Rationalists

• Empiricists: all we know comes from observations / the senses

• Rationalists: the main source of truth is not sensory but intellectual and deductive

e.g. • Statement: “There can be an infinite number of numbers.” True or false?

• Empiricist: False, you cannot know that until you counted until infinity, which is impossible.

• Rationalist: Yes, that is true. You can always add another number. Therefore, an infinite number of numbers must exist. We can generalize from the rule that you can always add another number.

Induction

reasoning based on regularity/ patterns

• generalises based on repeated observations

e.g. "The sun has risen every day so far → it will rise tomorrow"

• absolute truth cannot be established through inductions

but inductive reasoning cannot be rationally justified (Hume)

• observing X repeatedly doesn’t prove it will always be true

induction relies on assumptions like uniformity of nature, which can’t be proven

• you cannot derive a law from past observations

• absolute truth cannot be established through inductions

Logical Positivism & the Vienna Circle

• Early 20th-century movement

The verification principle: only statements that can be verified through direct observation are meaningful

Logical positivists attempted to find a way to establish truth only based on observation

• But there is no way of establishing truth of statements beyond the current observation

They couldn’t get induction to be logical

• Verification is never complete, future observations might contradict the current theory

• Induction also doesn't account for scientific theories that go beyond current observation (e.g. atoms, gravity)

Popper’s critique of Logical Positivism & Solution

Wanted to solve the problem of induction by replacing it with deduction: falsification

• You can never be sure a hypothesis is correct enough through observation (as the logical positivists wanted). But you can determine with certainty whether a hypothesis is incorrect

if a theory is not falsifiable, it’s pseudoscientific

induction into deduction

confirmation (requires induction) into falsification (is deductive)

Hypothetic-deductive method (Popper)

a form of scientific enquiry

1. Form falsifiable hypothesis

2. deduce predictions (If H is true, we should observe X)

3. test predictions with data

   1. if prediction fails, hypothesis is falsified

   2. if prediction holds, you generate falsifiable predictions

Null- hypothesis significance testing (Popper)

NHST is more inductive

NHST does not equal strict falsification

• it doesn’t prove H0 is false

  • A small p-value tells you your data are unlikely under H0, not that it’s definitely false

    • There’s always a chance that you reject H0 even when it’s true. 

NHST doesn’t prove H1 is true either

• H1 is not even there in NHST, it’s just the alternative, if H0 is falsified

• A small p-value doesn’t “disprove” H₀ with certainty

• Rejecting H₀ is not rejecting a theory in Popper’s sense

• NHST is inductive, not deductive

You might reject H0 due to chance (Type 1 error), or support H1 without directly testing it

but NHST still helps in practice

• repeated evidence against H0 builds support for alternatives

  • NHST provides a way to revise theory, even if not deductively pure

empirical cycle

• Phenomenon → Theory → Prediction → Test → Evaluation

  • Theory revised or rejected based on evidence

Hypothesis best practices

• make hypotheses falsifiable

• sketch out what different data patterns would mean

• Ask:

  • what does falsification imply?

  • should we modify the experiment? or maybe the theory?