In the treatise of an unknown author, “On the Principles of Theology,” and other medieval works, we can find some statements attributed to William Ockham (1285-1349 AD), all of them formulating the principle of Ockham’s razor:
“Beings are not to be multiplied beyond necessity.”
“Plurality is not to be posited without necessity.”
“What can happen through fewer [principles] happens in vain through more.”
“When a proposition is verified of things, more [things] are superfluous if fewer suffice.”
Ockham himself uses two strategies for the elimination of redundant entities: he analyzes if there is a good reason for the existence of the entity; and if the existence of the entity leads to falsehood, as presented on the UML Activity Diagram below:
Analyze & understand the reasons and consequences of the ENTITY
Analyze & understand the reasons and consequences of the Entity
Is there a good reason for the ENTITY?
“Ockham has two main lines of attack against other people’s ontologies. One proceeds by arguing that the reasons others give for postulating certain entities are not good reasons, that everything that can be done with such entities can be done without them. This is the main strategy he uses, for example, to argue that real entities are not needed in most of Aristotle’s ten categories. Combined with Ockham’s Razor, this approach implies not only that such entities are unnecessary, but that therefore they should not be postulated.”
Is the existence of the ENTITY leading to a falsehood?
“Ockham has two main lines of attack against other people’s ontologies. […] The second main line of attack is different. It argues that certain other people’s ontological theories not only postulate unnecessary entities but lead to plain falsehood – either to self-contradiction or, at least, to claims that contradict established facts. This is one of the ways Ockham argues, for example, against realist theories of universals.”
Eliminate ENTITY from the theory – apply Ockam’s razor
All citations from: Spade, Paul Vincent, “Ockham’s Nominalist Metaphysics”, The Cambridge Companion to Ockham, ed. Paul Vincent Spade, Cambridge University Press, 2006
Spade, Paul Vincent and Claude Panaccio, “William of Ockham”, The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.)
William Ockham (1285-1349 AD), in Summa of Logic(SL), writes about the concepts of connotation:
Terms can be categorematic and syncategorematic. The former signifies (represents) something in themselves (e.g., man, Aristotle, a number, an object), the latter represents something connected with other concepts (e.g., non in nonhuman).
Categorematic terms can be absolute or connotative terms.
The absolute terms have only one (primary) signification, while the connotative terms have a primary and at least a secondary signification, the connotata.
Examples for absolute terms: ‘man,’ ‘horse,’ ‘animal,’ ‘tulip.’
Examples for the connotative term: ‘red’ has as primary signification ‘red’, but brings to the mind as connotata ‘redness’ also.
The following OntoUML diagram presents the main classes of Ockham’s logic:
“The immediate parts of syllogisms are sentences (propositiones), and these are resolved into what Ockham in the first chapter of SL calls ‘terms’. Terms, broadly speaking, come in two sorts: categorematic and syncategorematic.” (Normore)
“A categorematic term is one that has signification. […] Categorematic terms have a ‘fixed and definite signification.’ Ockham explains that, in the narrow sense, a term signifies whatever it is ‘verified’ of. A term is verified of a thing if it can be truly predicated of a proper name or demonstrative pronoun picking out that thing in a singular affirmative categorical sentence with the present tense and unmodified copula ‘is’ (est). Thus ‘human’ signifies, in the narrow sense, Socrates if and only if ‘Socrates is human’ is true. […] Ockham presents another, ‘wider’ sense of signification in which a term signifies a thing if it can be truly predicated of a proper name or demonstrative pronoun picking out that thing in an affirmative singular sentence with the copula ‘can be’ (potest). In this wide sense the term ‘green’ can be said to signify even the White House if that building can be green. It is often suggested that, in introducing this wider sense of signification, Ockham commits himself to an ontology of possibilia. The signification relation connects language to the world, and Ockham suggests that the signification of mental categorematic terms is natural. We encounter objects in the world, and these encounters produce (absolute and, if there are any, simple connotative) mental terms. Thus we acquire these terms but do not learn them in any sense requiring that we have already represented the world. But the signification relation does not enter directly into the truth conditions for sentences. For that we need another relation – that of supposition.” (Normore)
subkind of Term
Signification relates CategorematicTerm with Object.
mediates CategorematicTerm with Object
“Among categorematic terms, some have only a primary signification, whereas others, in addition, have a secondary signification, or connotation. The former Ockham calls absolute terms. They correspond, in modern philosophical terminology, to natural kind terms, such as ‘man,’ ‘horse,’ ‘animal,’ ‘tulip,’ ‘flower,’ and so forth. What characterizes them is that each one signifies all its significates in exactly the same way and can indifferently stand for any of them in propositions. Consider ‘horse,’ for example. According to Ockham, it signifies nothing but horses; and every horse it signifies equally: it can stand for any of them in propositions such as ‘Every horse is a mammal,’ ‘Some horses are white,’ or ‘Bucephalus is a horse.’” (Panoccio)
subkind of Term; signifies Object
“A connotative term, by contrast, has at least two series of significates. Like absolute terms, it has primary significates such as red things in the case of ‘red’ and horsemen in the case of ‘horseman’; but in addition it also refers the mind, in virtue of its very meaning, to some other singular beings in the world, for which it normally will not stand in propositions (e.g., rednesses in the case of ‘red’ and horses in the case of ‘horseman’). Those are said to be its secondary significates or connotata. In mental as well as in spoken languages, the class of connotative terms is very extensive for Ockham – much more than that of absolute ones. It includes all concrete qualitative terms such as ‘red,’ all relational terms (‘father,’ for instance, primarily signifies all fathers and connotes their children), many psychological, semantical, and moral terms such as ‘intellect,’ ‘will,’ ‘true,’ ‘good,’ and so forth, all quantitative and dimensional terms such as ‘figure,’ ‘length,’ ‘solid,’ and so on, and generally, Ockham says, “all the expressions in the categories other than substance and quality.” (Panoccio)
subkind of Term; signifies Object and Connotata
An object, a thing or state of affairs in the external world.
“Like absolute terms, it has primary significates such as red things in the case of ‘red’ and horsemen in the case of ‘horseman’; but in addition it also refers the mind, in virtue of its very meaning, to some other singular beings in the world, for which it normally will not stand in propositions (e.g., rednesses in the case of ‘red’ and horses in the case of ‘horseman’). Those are said to be its secondary significates or connotata.“ (Panoccio)
role of object
Panoccio, Claude, “Semantics and Mental Language”, The Cambridge Companion to Ockham, ed. Paul Vincent Spade, Cambridge University Press, 2006
Calvin, G. Normore, “Some Aspects of Ockham’s Logic”, The Cambridge Companion to Ockham, ed. Paul Vincent Spade, Cambridge University Press, 2006