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Difficulty: Very hardInferences from the Text

The Quine-Putnam indispensability argument asserts that one ought to have ontological commitment to all and only the entities that are indispensable to our best scientific theories; since mathematical entities are indispensable to these theories, they must exist. The nominalist Hartry Field counters this not by rejecting the normative premise regarding ontological commitment, but by attempting to demonstrate that mathematics is merely a useful fiction. Field's strategy involves reformulating scientific theories without reference to mathematical entities, arguing that such "nominalized" models remain empirically equivalent to standard versions. However, certain anti-nominalists argue that even a comprehensively successful nominalization of all scientific models would not neutralize the indispensability argument. These critics maintain that the nominalized models inevitably sacrifice crucial explanatory depth, thereby demonstrating that mathematics is indispensable for providing the explanatory power characteristic of our best scientific theories.

Based on the passage, which one of the following can be most strongly inferred regarding the views of the "certain anti-nominalists"?

  1. A
    A scientific theory cannot be considered empirically equivalent to a standard mathematical model if it sacrifices crucial explanatory depth.
  2. B
    The primary purpose of scientific theories is to provide explanatory depth rather than to yield accurate empirical predictions.
  3. C
    Field attempts to neutralize the indispensability argument by rejecting its initial premise regarding ontological commitment.
  4. It is possible for a theoretical model to be empirically equivalent to our best scientific theories without itself qualifying as one of those best theories.Answer
  5. E
    Mathematical entities possess an objective reality that exists independently of the scientific theories that employ them.

Answer

The correct answer is the option stating that it is possible for a theoretical model to be empirically equivalent to our best scientific theories without itself qualifying as one of those best theories.
The correct answer accurately synthesizes the views of the anti-nominalists. The critics accept, for the sake of argument, that Field's nominalized theories can achieve empirical equivalence with standard mathematical theories. However, they conclude that these nominalized theories are NOT our "best scientific theories" because they lack explanatory depth (which is why math remains indispensable to the "best" theories). Therefore, according to the anti-nominalists, a theory can possess empirical equivalence to our best theories without qualifying as a "best" theory itself.

Step-by-Step Solution

1
Analyze the core criteria for the Quine-Putnam argument.
The argument dictates ontological commitment only to entities indispensable to our "best scientific theories."
Establishing the foundational definition that governs the entire debate in the passage.
2
Examine Field's counter-strategy.
Field attempts to prove mathematics is dispensable by creating "nominalized" theories that are "empirically equivalent" to standard mathematical theories.
Understanding the specific mechanism by which the nominalist claims to defeat the indispensability argument.
3
Evaluate the anti-nominalists' rebuttal to Field's strategy.
The anti-nominalists concede that nominalized models might achieve empirical equivalence, but they argue these models sacrifice "explanatory depth," meaning mathematics is still indispensable to our "best" theories.
Identifying the exact logical wedge the critics use to separate Field's models from the "best" models.
4
Synthesize the anti-nominalists' conclusion.
Because a nominalized model can be empirically equivalent but still lack the explanatory depth required of our "best" scientific theories, empirical equivalence alone is not sufficient to qualify a model as our "best" scientific theory.
Deriving the necessary logical inference that bridges empirical equivalence, explanatory depth, and the status of being a "best" theory.

Key Concept

Logical Deduction from Conceded Premises
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