Lecture 8 - Models

Question 1

Classification of models

Answer 1

• Representation models: represent something in the world: data models, mathematical models, concrete models, simulation models
• Theory models: model that makes theory true

Question 2

Data model

Answer 2

experimental experience reduced to a simple entity ready for comparison with a model or theory

Combiniation of data structure (data set) and specification story (what is the data actually)

Question 3

How do we justify the introduction of numbers and quantities?

Answer 3

As soon as we have established that a concept
is quantifiable, we are allowed to add a quantitative feature the concept, not to replace it with
numbers. Representational measurement theory provides conditions for when we can quantify.

Question 4

Some qualities from which we can determine if something is quantifiable

Answer 4

• Irreflexivity: more than itself
• Anti-symmetric: if 1 is more than 2, 2 is not more than 1
• Transitive: …
• Incomplete ..

Question 5

Mathematical structure

Answer 5

• a few sets called base sets (sets that contain mathematical entities)
  ✴ a few families of subsets of the base sets
  ✴ a few properties that some of the base-set members have and others not
  ✴ a few relations between base-set members
  ✴ a few operations on these base sets
  ✴ a few mappings, or functions, on these base sets
  ✴ a few special elements of the base sets, called constants

Question 6

Mathematical model

Answer 6

mathematical structure with a specification story of what in the mathematical structure
is supposed to represent which feature of the target in reality

Question 7

Concrete models

Answer 7

existing pieces of matter that have targets, f.e. scale model

Question 8

Simulation models

Answer 8

Simulate some process in reality: their target.
➡ Can be concrete or abstract
➡ Simulations are run.
➡ Simulations rely on some mathematical model.
➡ Simulations are used for prediction

Question 9

Taxinomy of idealisations / simplifications

Answer 9

✶ Aristotlean: truncations, discarding properties and relations of the target.
✶ Galilean : distortions, distorting properties and relations of the target.
✶ Newtonian: approximations in mathematical models

( All models are idealisations/simplifications)

Question 10

What is a theory according to structuralist conception?

Answer 10

A theory is a family of models, that is, of mathematical structures,
characterised by a predicate in axiomatic set-theory, plus a specification
story

Question 11

Two views are on the relation between models and theories

Answer 11

A. Models are Mediators between Theories and the Phenomena: Model M is an application of T to some target, but includes specifications about
the target that are not deducible from T.
B. Models are Building Blocks of Theories