The Logic of Proportionality: Reasoning with Non-Numerical Magnitudes

German Law Journal, Forthcoming

32 Pages Posted: 23 Oct 2012 Last revised: 24 Dec 2013

See all articles by Giovanni Sartor

Giovanni Sartor

European University Institute Law Department

Date Written: October 22, 2012


This paper aims at explaining the basic logical structure of proportionality assessments, under the assumption that such assessments are based on quantitative reasoning, even when no numbers are explicitly given.

First an analysis of practical rationality is proposed, including the endorsement of values, the adoption of goals to be pursued, the selection of plans of actions to be executed, In particular it is argued that possible plans for action are to be assessed with regard to their impacts on all relevant values.

Then the way in which norms have an impact on practical rationality is considered, distinguishing two kinds of norms: value-norms and action-norms. Value norms determine what values an agent should consider, in what scale of importance, to assess the merits of its goal-directed choice; action norm determine what actions the agent should execute.

The reasoning involved in assessing the merits of an action with regard to a set of values is then considered, and a novel approach is proposed. The idea is that this assessment is performed by processing mental magnitudes, concerning the impact of the action on the realization of values, the proportional utilities so delivered, and the weights of the values. Even though this processing does not use symbolically expressed numbers, it still deals with quantities, and has to comply with the common laws of arithmetic. Relying on some work on cognitive and evolutionary psychology it is observed that processing non-symbolic approximate continuous magnitudes is a fundamental cognitive capacity. We share it with animals and it supports our understanding of numerical mathematics, and our ability to learn it.

Moving more specifically into the analysis of proportionality in constitutional adjudication, it is argued that it consists in examining the extent to which value-norms directed at the legislator have been complied with. The traditional standards of suitability, necessity and proportionality are examined and reformulated under the perspective of reasoning with non-numerical magnitudes.

Finally some specific issues are considered, such as how action-norms can be obtained on the basis of value assessments, and how proportionality assessments are constrained by the requirement of consistency with precedents.

Keywords: proportionality, legal reasoning, law

Suggested Citation

Sartor, Giovanni, The Logic of Proportionality: Reasoning with Non-Numerical Magnitudes (October 22, 2012). German Law Journal, Forthcoming. Available at SSRN: or

Giovanni Sartor (Contact Author)

European University Institute Law Department ( email )

Via Bolognese 156 (Villa Salviati)
50-139 Firenze

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