Metaphysics
Explanation is a variety of description, because to explain something is to render it intelligible in light of something else. Explanation can only refer in the light of other facts, and as such we remain in the realm of description.
If we speak of logic we should speak of descriptive language, like propositions.
Propositions are bearers of truth values.
We want to search for true propositions and eliminate the false ones.
One very basic requirement is the principle of non-contradiction -(p^-p).
In the fourth book of metaphysics, Aristotle argues that this is the only presupposition of any science. We don’t want to presuppose too much because we do not want to be arbitrary, but according to aristotle it is necessary. However, it cannot itself be proven, and must itself be assumed from self-evidence. You are a vegetable if you don’t believe it.
eg. ”I exist, I don’t exist” – meaningless.
Descartes relies on a similar principle in the cogito. If I deny my own existence in speech it seems like nonsense.
People use their language in two different senses. Knowledge is often used in slightly different senses, and as such we will often run into pseudocontradictions based on natural language. People are not always aware of this, though Aristotle was quite aware in discussing the sophist’s use of contradictions. The same goes for Heraclitus, who Aristotle argues creates contradictory statements to seem dark and profound.
This kind of sophistry is alive and well today too. John Caputo argues that we cannot tell truth from falsity, we cannot tell a genuine contradiciton from a mere ambiguity, because the boundaries have been blurred for us. There is ofcourse a difference between vague and precise language, but most often we can find a way to render it preciser.
Aristotle argues that the PNC is a purely formal requirement, and it doesn’t commit us to one thought or the other.
For Aristotle the PNC goes along with the principle of the excluded middle (pv-p). This is not something everyone agrees with. A lot of people think they are not necessary for one another.
Aristotle admits that there may be cases in which we cannot determine the inherent truth value, like the problem of the future contingents. There are facts about the future that are not contingent, like mathematically true statements – which tend to stay the same even in the future.
Aristotle has the example of the sea battle: assume somone utters the statement that ’tomorrow there will be a sea battle’. This is either true or false according to the PNC. But we may not know which of them is true or not. Predictions are essentially fallible.
Thomas Aquinas adds that we may not be omniscient ourselves, but God is, and as such the contingent statements still have a truth value. It is a different kind of category of knowledge therefore, rather than a limit of logic.
If we think of propositions of truth values is that they need a kind of infrastructure.
Plato discovered this already. Imperatives do not bear truth values, because they are not descriptive.
In cases of statements we have truth and falsity.
A statement is successful if it describes an existing reality accurately.
What we have here is predication. Plato points that what we need for a proposition is at least a noun and a verb. More generally, it is rather a verbal phrase (Chomsky) like a copula plus a further expression.
eg. S is P or F(a).
Aristotle says this is a saying something about something. This is the order of predication.
One subject term, a particular and a predicate are the building blocks of propositions.
F(a), F(b) → F(a)^F(b)
T(s, p) → Socrates is the teacher of Plato
Semantic holism: the claim that the link between a proposition and the reality that it is about is a holistic affair, ie. that there is no exact and context independent relation between the parts of a proposition and the parts of reality that it describes.
The idea is that somehow you understand a proposition holophrastically, by putting everything together and then project it onto reality.
If you think of someone like Quine, then there is no clear analysis of propositions that allows us to read the structure of reality through propositions.
Quine has the famous example: suppose you come to a foreign country and have to learn an exotic language, so you hear certain words in certain environments, and as such you have a pretty natural inclination to link the words to perceivable reality. Now imagine if someone says ’gavogai’, and you are the one learning the language in question and you see a rabbit, and then apply the working hypothesis that gavogai means rabbit. (Aristotelians would argue that this model of referring to whole things is the most natural) Now this language may not be referring to the entire rabbit because they do not speak of whole animals, but something else in relation to it. So basically you have to gradually learn how it is employed. How language hooks onto reality is purely conventional, without a 1 to 1 form attached to it.
Robert Brandon translates this into the language of committments and entitlements that we have to learn, that is, what certain propositions commit us to and what we are entitled to do with them. Mistakes in the language game is a mistake in overstretching ones committments and entitlements.
Quine is also a nominalist, there are only particulars and no universals. Since he is not a metaphysician, he presents it simply as his view. He also accepts modern set theory, which require universals. Damn it. Ultimately numbers are an abnormality in Quine’s doctrine.
The warning from the professor about this: that language use is only a matter of convention, and there is no general form in which thought and language hook onto reality, then there is no metaphysics. Semantic holism is necessarily antimetaphysical.
This basically means to block the possibility of metaphysics at a very early stage. If we want to do metaphysics we have to ignore semantic holism. We cannot however say that metaphysics is simply linguistics, we cannot learn everything about reality through some kind of chomskean mission.
Semantic atomism refers to the idea that propositions are true or false in relation to the general structure of reality. A proposition is true IFF its parts correspond to reality in a meaningful way.
Alfred Tarski’s definition of truth, proposition snow is white is true iff snow is white.
This holds for any proposition whatsoever, as correspondence theory of truth.
Aristotle’s doctrine of categories.
The basic idea is that both the subject and the predicates fall into categories. They cover categories, which means they are universal concepts.
Johnathan Lowe, Durham, took this basic insight of Aristotle that to say something meaningful is to say something of something; which he calls the four category ontology.
So you have for example a
struct right-angled figure
{
lower left = particular objects;
upper left = object kinds;
lower right = particular properties;
upper right = property kinds;
};
Ultimately universal terms are proxies. Ultimately, Socrates’ wisdom is unlike any wisdom other than Socrates’. For competent speakers of a language this isn’t really a problem to figure out.
It is a huge provocation to argue that every universal is a property. The standard models of predicate logic treats being human as a property. Lowe would argue that this is an object kind, not a property kind. The human kind as such means the totality of human beings, not a property.
If you mix up these levels you can easily commit category mistakes, like Gilbert Ryle argues. If you link a particular object to a property kind, and the same with a particular property and an object kind.
Aristotle says that there are in things that are predicated of them etc. there are 4 them based on being predicated and being in them.
In a different sense, we can say that kind membership is in something, but this is somehow different, and Lowe distinguishes these. We can say predicate universals to other universals, like predicating rationality to human beings. Socrates is an example of rationality, as such it is rationality that is in socrates but which is also said of him.
There is also the mysterious category which are neither said of something, nor is in something, and these are particulars. Being Socrates is not in Socrates, not is being Socrates predicated of Socrates, because Socrates is the subject of predication.
If you identify someone as something, you are not predicating that thing.
Aristotle himself distinguishes between 10 different categories. Aristotle was authoritative for basically 2000 years, but now alternative suggestions have come up, like the Kantian table of categories, which has 12 items rather than 10. For Kant, some of the Aristotelian categories are not categories in the Kantian sense, necessity for example is not a category according to Aristotle. If you read Hegel’s science of logic the list becomes a lot longer, the entire doctrine of Being is an extended list of categories that are both Kantian and non-Kantian. Then later on you have phenomenological cateogorical systems in both Brentano and Husserl. One of the basic jobs in the school of Husserl was category research, the discipline aimed at metaphysics, and it was supposed to come up with a system of metaphysical categories – but they were to be discovered by logical and epistemological analysis.
There are substances, and substance kinds. Either particular substances or the kinds that they belong to. The first can be primary and secondary.
Aristotle does not think that property is a category. We treat it as a category in the simplified system by Lowe, but property for Aristotle is an umbrella term that covers a whole lot of shit that has nothing in common except for depending on the substance. The substances are independent entities that ground the properties. Properties don’t exist independently.
Aristotle distinguishes quantity. This is done by highlighting how we ask about certain properties and what answers we have. So quantity then is about ’how many?’.
This is why mathematics is about reality according to Aristotle, because reality is quantifiable and mathematics is the study of reality insofar as it is quantifiable. And quantity is one of the 9 accidental cateogories, they are the changing and mutable parts of substances.
Qualities come in oppositions. A property change in regards to quantity means one going from the other. It is a dipolar category basically.
Relation, this is something that relates a substance to something else. Relation is the weakest category; because relations depend on every substance. Relations are constantly produced by something else, they are not self-grounding.
There is place and time, space is the totality of all possible places. Everything that exists is ultimately a particular that can be situated at a specific place. God is in whatever place doesn’t exclude other places. All other substances can be localised.
All substances are either active or passive. This is irreducible for Aristotle. Substances are ultimately agents that do certain things, or they are patients who have certain things done to them.
There is no activity without passivity.
For Aristotle, having is a very peculiar category. Some substances have something that is not a substance, like wearing shoes.
Position is also its own category. Then there are positions like sitting upright or lying down.
These two are often discussed as categories we can probbly reduce to other categories.
Aristotle did not insist on all the 9 accidental categories. There are certain core categories that he always mentions.
Franz Brentano wrote about the notion of being in Aristotle, and Aristotle’s use of the categories. He goes through all the places Aristotle mentions being and distinguishes several meanings of the word, and says that when it comes to categories, we (aristotelians) are confronted by the necessity of a proof for why these are complete. Brentano decided to provide the proof: he removed the having and the position, and then a bunch of other shit to show that these are complete. It basically shows that Aristotle is internally coherent.
This is a piece of formal ontology. It represents how we formally divide reality into kinds and their instantiations, but it does not inform us about what can count. Just by this we don’t really know what a substance is. This is the question that metaphysics hinges upon. Aristotle argues that if we get substance right, all accidents will be done correctly in virtue of that.
Substance is the basis of causation, and a kind of independent entity, that can be spoken of in virtue of itself, without other kinds.
Ideally metaphysics can reach a kind of deductive system. The first premises are principles, they are self-evidently true, and therefore guarantee the truth of every proposition derived from them. This is the general pattern of demonstration, and metaphysics is supposed to be a demonstrational science. This is in the order of presentation, in the order of discovery however we do induction from empirical observation, and careful generalisation – that is to more universal claims until we reach the principles. The principles are what comes first in the order of being but which come last in the order of knowledge.
Substance metaphysics is not a very particular method of theorising, it is rather just a logical model that most metaphysics seems to follow.