LFE #3 – A fortiori arguments

In this short lesson, part of the Legal Fundamentals Explained (LFE) series, Gonçalo Fabião (University of Lisbon) examines the structure and use of a fortiori arguments in legal reasoning. He clarifies that a fortiori arguments should not be understood as a method of legal interpretation, nor as a tool for interpreting legal provisions. Furthermore, he argues that a fortiori arguments are not logically valid in the strict sense, as they do not ensure truth-preserving inferences.

Below, you can find the full transcription corresponding to this video lesson*.

Gonçalo Fabião

Hello everyone. My name is Gonçalo Fabião. I am currently a guest lecturer at the University of Lisbon in its School of Law, and I’m also a member of the Lisbon Public Law and Lisbon Legal Theory Group.

In this short video, I would like to briefly outline the a fortiori arguments. A fortiori arguments intend to draw conclusions from propositions deemed stronger. There are two types of a fortiori arguments, usually named as a maiori ad minus and a minori ad maius, translated from Latin. The first one means “from greater to less,” and the second one means “from lesser to greater.”

What I would like to address in this video is the following:

1. I will outline the structure of the a fortiori arguments;

2. I will claim that a fortiori arguments are not an interpretative method or argument for interpreting legal dispositions;

3. I will claim that the a fortiori argument is not a logically valid argument because it does not guarantee truth-preserving inferences.

Now, let’s begin with the structure of a fortiori arguments.

A fortiori arguments presuppose a relation of comparison between two objects within a scale. This scale is what an author, Luís Duarte d’Almeida, refers to as a scalar property. This relation has two main features:

• The first feature is that it is a transitive relation. This means that two objects share one property through a connector—the scalar property.

• The second feature is that the relation is asymmetric. This means that the compared objects are not identical—one is stronger than the other.

This relation is accompanied by an implicit proposition, and this implicit proposition is called the hereditary proposition. It represents that a property of one object (the source) is inherited by another object (the target).

So, a legal a fortiori argument needs a five-stage method:

1. One needs to find a relevant property of an object. In the legal domain, the object is a human action, and the relevant property is whether that human action is permitted, forbidden, or obligatory.

2. One needs to find a different object to be compared with the first object.

3. One needs to find the reason for the state of affairs regarding the first object. This reason will allow us to draw the scalar property.

4. The first object and the second object should be compared within the scalar property to determine whether there is a transitive relation between the two.

5. One will infer according to the hereditary proposition.

An a fortiori argument of the type a maiori ad minus applies to permissive norms, like so:

1. There is a criterion X scale according to which human action Y is permitted until a threshold Z.

2. According to the criterion X scale, human action 1 ranks below threshold Z and is therefore permitted.

3. Human action 2 ranks lower than human action 1 in the criterion X scale.

4. Having the hereditary proposition, one is able to conclude that human action 2 is permitted as well.

Let’s see this with a simple example:

Suppose that a child’s parents say the child is allowed to ride their bicycle to their school located within 5 kilometres from the child’s home. Action 1—riding a bicycle to school—is permitted within the criterion “distance scale,” which means that the school distance ranks below the threshold of distance the child’s parents allow them to ride their bicycle.

There is no information as to whether the child’s parents allow them to ride their bicycle to the park, which is 2 kilometres away from their home. But according to the scalar property of distance, this action ranks lower than riding a bicycle to school. Therefore, a maiori ad minus—riding to the park is also permitted.

Now for the a fortiori arguments of the type a minori ad maius. This applies to obligation norms in the following way:

1. There is a criterion X scale according to which human action 1 is forbidden from threshold Z.

2. According to the criterion X scale, human action 1 ranks above threshold Z and is therefore forbidden.

3. Human action 2 ranks higher than human action 1 in the criterion X scale.

4. Adding the hereditary proposition, one is able to conclude that human action 2 is forbidden as well.

Let’s see this with a very similar example:

If the same parents from the previous example, instead of permitting their child to ride their bicycle to school, instead only said that their child is forbidden to ride their bicycle to the park—which, as we know, is 2 kilometres away from their home—then, using the same scalar property of distance, one could conclude a minori ad maius that the child is also forbidden to ride their bicycle to school, because the school is farther away from home than the park.

Okay. So why is the a fortiori argument not an interpretative method?

Interpretation serves the purpose of identifying legal norms. It deals with an empirical issue. Only after interpretation is it possible to ascertain whether the legal system raises logical issues such as normative conflicts or legal gaps.

The a fortiori arguments serve the purpose of solving the problem of legal gaps, since it is only necessary because there is a case for which no relevant norm applies.

In the example of the prohibition of riding the bicycle to the park, there is a legal gap concerning riding the bicycle to school. The a fortiori argument serves the purpose of solving the legal gap.

And how is this done?

The method consists of comparing the case that is expressly regulated by a legal norm with another case that is not expressly regulated, using the already mentioned scalar property. The expressly regulated case is the source of the solution, and the not expressly regulated case is the target that will receive the same solution as the source.

Finally, why is the a fortiori argument not a logically valid argument?

In order to work with the a fortiori argument, one needs to define a scalar property that will serve for comparison between objects. In other words, one needs to determine the reason an action is forbidden or permitted. This amounts to determining the purpose of the norm issuer.

But this task is by no means simple, and may very well be impossible.

Let’s just think about a legislative collective body, like a parliament, where each member may have a different reason to enact a legal norm. So, if it is possible to have different accounts of a legal norm’s ratio legis, then it is not possible to have a true and singular scalar property. Which means that the conclusions obtained through a fortiori arguments are not truth-preserving.

Let’s suppose that the parents in the previous examples did not allow their child to ride their bicycle to school because of a distance criterion, but because of a function criterion. So, the purpose of allowing their child to ride their bicycle to school was to provide a means of transportation to school, and not to define an area of free bicycle riding.

If this was the case, then the conclusions drawn above are not truth-preserving.

With this, I do not intend to claim that a fortiori arguments are not useful in legal argumentation. They indeed are. But they should be questioned and should not be seen as conversation stoppers.

I hope this video proved to be useful to whatever purpose you might have. Thank you very much for your attention.

(*some minor grammatical and changes have been introduced in order to make the reading more fluid, but in no way altering the content or the format of each speaker’s interventions).

The LFE video series is powered by the EU Horizon Twinning project “Advancing Cooperation on The Foundations of Law – ALF” (project no. 101079177). This project is financed by the European Union.