If the objects and properties aren't 'already' there, how do the facts give rise to them?
Jason Turner develops and defends a novel answer to this question: The facts are arranged in a quasi-geometric 'logical space', and objects and properties arise from different quasi-geometric structures in this space. In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure".
There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. Michael Potter presents a comprehensive new philosophical introduction to set theory.
Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels.
What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true.
Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. There is a long history of worrying about whether or not metaphysics is a legitimate philosophical discipline. Traditionally such worries center around issues of meaning and epistemological concerns.
Do the metaphysical questions have any meaning? Can metaphysical methodology lead to knowledge? But these questions are, in my opinion, not as serious as they have sometimes historically been taken to be. What is much more concerning is another set of worries about metaphysics, which I take to the greatest threat to metaphysics These worries, in effect, hold that the questions that metaphysics tries to answer have long been answered in other parts of inquiry, ones that have much greater authority.
The Facts in Logical Space: A Tractarian Ontology - Jason Turner - Google книги
What metaphysics tries to do has been or will be done by the sciences. There is nothing left to do for philosophy, or so the worry. Let me illustrate this with two examples, one of which is our main concern here. Michail Peramatzis presents a new interpretation of Aristotle's view of the priority relations between fundamental and derivative parts of reality, following The purpose of the book is to clarify the notion of existential dependence and cognate notions, such as supervenience and the notion of an internal relation.
- The Facts in Logical Space : A Tractarian Ontology - hiqukycona.tk.
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I defend the view that such notions are best understood in terms of the concept of metaphysical grounding, i. I first explore the notion of the world's being such that everything in it is a proper part. I then explore the notion of the world's being such that everything in it both is and has a proper part. Given two well recognized assumptions, I argue that both notions represent genuine metaphysical possibilities.
Finally I consider, but dismiss, some possible objections. A significant reorientation is currently under way in analytic metaphysics, away from an almost exclusive focus on questions of existence and towards a greater concentration on questions concerning the dependence of one type of phenomenon on another. Surprisingly, despite the central role dependence has played in philosophy since its inception, interest in a systematic study of this concept has only recently surged among contemporary metaphysicians.
In this paper, I focus on a promising account of ontological dependence in terms of a I argue that even this essentialist account is, as it stands, not fine-grained enough to recognize different varieties of dependence which ought to be distinguished even within the realm of ontology. Which, gives me the suspicion that Wittgenstein still held onto Kantian transcendentalism in some sense of the Tractatus. In that case, the totality of the world is the categories of my mind coming into contact with the various sense impressions.
I've long held the suspicion that Wittgenstein of the Tractatus was a monist or believed in modalism of atomic facts. What are some thoughts about this idea derived from Libenitz? Sam26 1. So early Wittgenstein actually thought reality consisted of atomic facts and not things like apples, trees, people, etc? Sam26 Options Share. Here's something I posted on Quora. This was written to answer the following question: What did Ludwig Wittgenstein mean by "the limits of my language are the limits of my world"?
Second, he assumes that the function of language is to describe the world, and he assumes that the structure of language is revealed by logic. Why did Wittgenstein think that logic would reveal the structure of language, and reveal how language is connected to the world? We have hints here and there, but it seems that not only did he believe that logic lay at the bottom of all science, but he also believed that there was something universal about logic his idea of logic has ontological implications , a peculiar depth PI Wittgenstein believed that if we can talk about the world, then propositions must be logically connected with the world.
In this way, the truth of a proposition is not connected with other propositions, but connected with the world. So you have propositions complex propositions , which are made up of simpler propositions called elementary propositions that are directly connected to the world. Two questions that naturally arise, how are elementary propositions related to complex propositions, and how are elementary propositions logically connected to the world? First, complex propositions are truth-functions of elementary propositions. Thus, if a complex proposition is broken down into elementary propositions, then the truth-value of the proposition is determined by the truth-value of its component parts seen in truth-tables , namely, the elementary propositions that make up the proposition.
Second, elementary propositions connect with the world in that they are pictures of atomic facts, which are the smallest constituent parts of facts. Once we have completely analyzed the proposition, that analysis will have the same complexity as its referent Nb p. The referent being facts in the world.
However, we are not done with propositions. Do not think of names like pencil, cup, chair, etc, these kinds of names are not what Wittgenstein had in mind. These names cannot be dissected any further. They are, in one sense, the end result of the analysis, in terms of the elementary proposition.
So how do propositions correspond to facts in the world? Facts are divided into atomic facts, just as complex propositions are divided into elementary propositions. There is a direct picturing correlation between an elementary proposition and an atomic fact. The arrangement of names in the elementary proposition must have the same logical structure as the arrangement of objects within the atomic fact. Propositions show their sense by their logical structure, and if that sense is correct or true, then it matches the facts in reality, or it mirrors reality.
So how does all of this answer your question? Well, for early Wittgenstein language is completely descriptive, that is, it attempts to describe the world, either truly or falsely. The limits of language, or what can be said, is the limit of our world. Things that have sense happen only within the limits of language. Senseless propositions attempt to say something about the limit of language; and attempts to go beyond the limits of what can be said, result in nonsense.
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