Medieval Latin logic developed through schools, universities, translations, textbooks, and disputations. Alongside the study of Aristotle, logicians constructed detailed theories of linguistic reference and inference.
Many of their questions remain recognizable: when does an expression refer to a thing rather than to a word? How does tense change the range of a term? What does a consequence preserve? How should a sentence that calls itself false be evaluated?
Their answers belong to their own intellectual settings. They are not adequately described as an interval between Aristotle and modern mathematical logic.
Texts and institutions
The earlier Latin curriculum relied heavily on Boethius's translations and commentaries, Aristotle's Categories and On Interpretation, and Porphyry's Isagoge.
The recovery and circulation of further Aristotelian works in the twelfth century enlarged this collection. The conventional distinction between the old and new logic concerns groups of texts and their availability, rather than a sudden replacement of one theory by another.
University teaching encouraged systematic exposition and organized dispute. Authors analyzed standard examples, proposed distinctions, and tested one another's rules through difficult cases.
Peter Abelard's twelfth-century work on language and dialectic helped shape questions about signification and inference. Thirteenth-century teaching traditions included William of Sherwood, Peter of Spain, and Lambert of Auxerre.
.jpg)
Sources and credit for Peter Abelard
Antoni Oleszczyński. Via Wikimedia Commons. Image source · Public domain · Biographical dates
The identity of the logical author called Peter of Spain should not simply be equated without qualification with Pope John XXI; the attribution is historically disputed.
Signification and supposition
Signification concerns what an expression means or signifies. Supposition concerns what a term stands for in a particular propositional use.
The distinction was developed differently by different authors. It cannot be mapped mechanically onto a single modern distinction between sense and reference.
Consider three English examples modeled on traditional discussions:
“Human is an animal.” “Human is a species.” “‘Human’ is a word.”
The first can use the term to stand for human beings. The second concerns a classificatory or conceptual item, according to the author's theory of universals. The third concerns a linguistic expression.
In Ockham's account, personal, simple, and material supposition distinguish important uses of this kind, with simple supposition analyzed through a mental concept rather than a separately existing universal.
Other authors classify or interpret the cases differently. The survey of medieval properties of terms documents these changes.
A reference shift that breaks an argument
Suppose someone argues:
Human is a species. Socrates is human. Therefore Socrates is a species.
The repeated term does not perform the same semantic role in the two premises. In the first, it concerns the species or concept; in the second, it is predicated of an individual.
Treating the two occurrences as interchangeable produces an invalid inference.
A modern type distinction between individuals and concepts can help explain the error. The medieval theory analyzes it through the properties of term occurrences within propositions.
This is a substantive theory of inference. It identifies a condition that a purely superficial match between words would miss.
Tense, modality, and restriction
The range of a term can change with its context. A statement about a former king may concern someone who is no longer a king. A modal statement may range over objects considered possible in the relevant interpretation.
Medieval theories of ampliation and restriction studied such changes.
From “A bridge once stood here,” one cannot infer “A bridge stands here now.” The subject's occurrence in the past-tense statement does not impose the same present-existence requirement.
Similarly, adding a qualifying adjective narrows which things a term can stand for. These apparently ordinary observations become important when constructing general rules of consequence.
The historical analysis links grammar with logical commitments while resisting the assumption that one fixed extension serves every occurrence of a word.
Syncategorematic expressions
Words such as “every,” “not,” “only,” and “except” contribute to logical structure without functioning as ordinary names for things.
The medieval study of syncategoremata examined their effect on propositions and inferences.
For example, “Only scholars entered” says that anyone who entered was a scholar. It does not say that every scholar entered.
The distinction can be reconstructed as
rather than
The modern formulas are explanatory aids. The historical achievement is the systematic analysis of particles whose position and force govern valid reasoning.
Ockham, Buridan, and consequence
William of Ockham's Summa logicae, written in the fourteenth century, integrates an account of terms, propositions, and arguments.
John Buridan developed extensive logical works, including a Treatise on Consequences. Consequence became a topic whose scope extended beyond the standard categorical syllogism.
Sources and credit for William of Ockham
self-created (Moscarlop). Via Wikimedia Commons. Image source · CC BY-SA 3.0 · Biographical dates
.jpg)
Sources and credit for John Buridan
Unknown photographer or artist. Via Wikimedia Commons. Image source · Public domain · Biographical dates
A basic question is whether the antecedent can be true while the consequent is false. Authors also distinguished kinds of consequence, including those grounded in form and those depending on the meanings or facts associated with particular terms.
Consider “Every human is an animal; therefore every human is an animal.” Its validity does not depend on the special content of the predicates.
By contrast, an inference involving a particular species and genus may depend on a substantive relationship between those terms unless that relationship is supplied as a premise.
The distinction connects with later concerns about logical form, but Buridan's theory includes its own treatment of propositions, time, and semantic conditions.
Insolubilia and the liar
Medieval discussions of insolubilia examined paradoxical statements, especially variants of the liar.
Take the schematic sentence : “This sentence is false.”
If is true, what it says appears to make it false. If it is false and says only that it is false, it seems to say something true.
Thomas Bradwardine's fourteenth-century treatment challenged the assumption that such a sentence signifies only its own falsity. His account of signification and its closure under consequence leads an insoluble to signify its own truth as well.
On a schematic reconstruction of this strategy, the sentence's full content cannot be true, because it includes incompatible claims. Judging it false does not make all of its content true: the falsity claim may be correct while the truth claim is not.
The solution therefore changes the semantic analysis that generated the simple two-way argument. It is not a modern Tarskian hierarchy imposed on the medieval text.
Other logicians proposed restrictions, alternative semantic accounts, or different responses to the setup. The historical survey of insolubles explains the disagreements and the surviving evidence.
Obligationes and disciplined disputation
Obligationes were rule-governed exercises in which a respondent accepted a posit and answered subsequent propositions according to specified conditions.
Suppose a respondent grants a false but possible proposition for the exercise. The task is not necessarily to report ordinary actual truth at every step. It is to maintain the prescribed relationship among the posit, relevant consequences, and other proposed claims.
The rules varied across authors and periods. A successful response depended on understanding the particular form of disputation.
These exercises investigated consistency, relevance, and the management of commitments. Their exact pedagogical and theoretical purposes remain subjects of historical interpretation.
They should not be identified without qualification with either modern games of logic or a general license to accept contradictions.
An active semantic tradition
The medieval Latin developments show sustained attention to the relationship between linguistic use and consequence.
The vocabulary differs from modern formal semantics, but the questions are precise. What is the range of a term here? Which assumptions does the inference require? What exactly does this proposition signify?
Later changes in mathematical notation and research aims altered the prominence of these theories. Their historical importance is not measured solely by whether a later mathematical logician directly adopted them.
The remaining companions turn to traditions whose histories should be examined without assuming a single route through the Latin curriculum.
Sources and further reading
- Peter Abelard, Dialectica and logical commentaries.
- William of Sherwood, Introduction to Logic; Peter of Spain, Tractatus.
- William of Ockham, Summa logicae.
- John Buridan, Treatise on Consequences and Summulae de dialectica.
- Thomas Bradwardine, Insolubilia, edited and translated by Stephen Read (2010).
- Properties of Terms, Medieval Theories of the Syllogism, and Insolubles, Stanford Encyclopedia of Philosophy.