(27) T/F: Justus shows that inductive inferences can include mathematical calculations, and models in conjunction with deductive reasoning.

Question

BlackTom AI · Accepted Answer

We start by restating the given statement to be evaluated: 'Justus shows that inductive inferences can include mathematical calculations, and models in conjunction with deductive reasoning.'

First, consider what inductive inference typically involves. Induction moves from specific observations to general conclusions, often relying on pattern recognition, empirical data, and probabilistic support. While induction can be aided by mathematical tools, the core idea of inductive reasoning is not fundamentally about performing formal mathematical deductions; it is about generalizing from observed instances.

Next, examine the claim that inductive inferences can include mathematical calculations. Mathematical calculations are usually associated with deductive reasoning, where conclusions follow necessarily from premises. Inductive inferences rely on evidence and probability, not guaranteed derivations. Therefore, counting routine mathematical calculations as a defining feature of induction is conceptually misleading.

Then, assess the part about 'models in conjunction with deductive reasoning.' Models themselves can be used in both inductive and deductive contexts. A model might be built to explain data (an inductive activity) or to derive predictions from axioms (a deductive activity). While models often accompany both forms of reasoning, asserting that inductive inferences inherently include models along with deductive reasoning overstates the role of models in induction.

Additionally, the inclusion of 'Justus' as the authority or source requires scrutiny. If the claim attributes this stance to a specific philosopher or scholar, one should verify whether that figure indeed argued that inductive inferences routinely incorporate mathematical calculations and models in tandem with deduction. Without that alignment, the statement risks misrepresenting the source.

In terms of logical structure, the statement blends distinct components (induction, mathematical calculation, modeling, and deduction) in a way that suggests a unified framework for induction that may not be universally accepted. Since induction, deduction, mathematics, and modeling are related but distinct tools in reasoning, the claim as stated is not accurate as a general rule.

Therefore, when evaluating the proposition, the combined emphasis on mathematical calculation and explicit modeling as integral parts of inductive inference, alongside deduction, does not align with standard characterization of induction. This mismatch explains why the statement is considered incorrect.

In summary, the core ideas of induction focus on generalizing from evidence and using probabilistic support rather than guaranteeing mathematical deductions, and while models can be used in both inductive and deductive contexts, their inclusion does not uniquely define inductive inference. Hence, the overall claim does not hold as a correct description of inductive reasoning.

HSH1000 Quiz 3 Xunzi (8.4%)

(27) T/F: Justus shows that inductive inferences can include mathematical calculations, and models in conjunction with deductive reasoning.

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