Here is a handout for a presentation I gave on "Galilean Idealization" by Ernan McMullin. I tried to keep it as one, double-sided page for the sake of ease. As a result, much of the presentation was "off the paper." Thankly, this classic essay lends itself to a short summary of the distinctions the author makes. I might suggest reading the essay along with the handout, however, if you are struggling with either the essay or the handout.

I did take the WordDoc I wrote this in and dropped it into ChatGPT in order to format it for the blog. As a result, there's a couple odd formating choices that I am too lazy to fix now.

“Galilean Idealization,” Ernan McMullin

Bob’s question: How can models explain or be successful if they are false?

Idealization

Idealization involves simplifications for the goal of making a problem more computable or tractable.

Galilean idealizations can be understood in two ways:

The second sense expresses a distortion of the subject—a “departure from truth”—distinctive of the Galilean method.

Models

For McMullin, models are postulated structures of elements, relations, and properties. Every model must idealize—for example, by simplifying the phenomenon to be explained or by leaving out some physical detail.

McMullin aims to show us different methods of idealization and how they might nonetheless be getting something right.

1. Mathematical Idealization

Mathematical idealization uses mathematical formalisms to capture (i.e., represent) a physical situation, with the hope of capturing the “essentials” of that situation.

There is a distinction between physical semantics (meaning) and mathematical syntax (rules).

This raises the question: Is there a physicalization of mathematics?

2. Construct Idealization

Construct idealizations concern our conceptual representation of the object, whereas causal idealizations concern the problem situation itself. Construct idealizations focus on how we represent the objects relevant to explanation and prediction.

McMullin distinguishes two notions of construct idealization, which matters for how we might add features back into models.

2.1 Formal Idealization

Formal idealization removes features relevant to explanation, or simplifies the (possibly essential) structure of the object.

Example: Assuming an elliptic orbit is circular.

De-idealizing: Adding features back into formally idealized models may allow them to capture more of the phenomenon. If so, this supports a moderate version of scientific realism.

2.2 Material Idealization

Material idealization removes features deemed irrelevant to the explanation. While the construct could be further specified, this is unnecessary for explanatory purposes.

Example: Treating atomic nuclei as simple balls without internal structure.

De-idealizing: Adding features back into materially idealized models without changing their explanatory success suggests that the original model got something right.

3. Causal Idealization

Causal idealization operates on the problem situation itself by removing surrounding circumstances to simplify analysis.

McMullin highlights an important methodological insight in the history of thought:

“Complex causal situations can only be understood by first taking the causal lines separately and then combining them.” (p. 265)

Example: Vector decomposition. Other causes are treated as impediments.

De-idealizing: Adding causes back into the analysis.

3.1 Subjunctive vs. Non-Subjunctive Idealization

Some causal idealizations isolate causal lines through literal experiments (non-subjunctive).

Example: Galileo’s acceleration experiments.

Other causal idealizations isolate causal lines through thought experiments (subjunctive).

Example: Imagining Aristotelian substances tied together.

Some subjunctive idealizations are possible only in thought, while others are readily testable.

Examples: Tying Aristotelian substances together versus frictionless planes.

Response to Cartwright

Roughly: In experiments, causes can be isolated, and idealizing in the causal sense may generate laws. Since the composition of causes remains permissible, causal idealization remains a viable method. Cartwright needs to resist this composition of causes line.

Discussion Questions