15 ideas
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |
17744 | De Morgan started the study of relations and their properties [De Morgan, by Walicki] |
Full Idea: De Morgan started the sustained interest in the study of relations and their properties. | |
From: report of Augustus De Morgan (On the Syllogism IV [1859]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 |
13501 | De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD] |
Full Idea: There was a prejudice against relations (in favour of properties) but De Morgan and others that impeccable inferences turn on relations and elude Aristotle's syllogistic. Thus: All horses are animals. Hence, all heads of horses are heads of animals. | |
From: report of Augustus De Morgan (On the Syllogism IV [1859]) by William D. Hart - The Evolution of Logic 4 | |
A reaction: This is actually an early example of modern analytic philosophy in action. You start with the inferences, and then work back to the ontology and the definition of concepts. But in pinning down such concepts, do we miss their full meaning? |
4483 | If abstract terms are sets of tropes, 'being a unicorn' and 'being a griffin' turn out identical [Loux] |
Full Idea: If trope theorists say abstract singular terms name sets of tropes, what is the referent of 'is a unicorn'? The only candidate is the null set (with no members), but there is just one null set, so 'being a unicorn' and 'being a griffin' will be identical. | |
From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.86) | |
A reaction: Not crucial, I would think, given that a unicorn is just a horse with a horn. Hume explains how we do that, combining ideas which arose from actual tropes. |
4477 | Universals come in hierarchies of generality [Loux] |
Full Idea: Universals come in hierarchies of generality. | |
From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.24) | |
A reaction: If it is possible to state facts about universals, this obviously encourages a rather Platonic approach to them, as existent things with properties. But maybe the hierarchies are conventional, not natural. |
4481 | Austere nominalists insist that the realist's universals lack the requisite independent identifiability [Loux] |
Full Idea: Austere nominalists insist that the realist's universals lack the requisite independent identifiability. | |
From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.60) | |
A reaction: Plato's view seems to be that we don't identify universals independently. We ascend The Line, or think about the shadows in The Cave, and infer the universals from an array of particulars (by dialectic). |
4482 | Austere nominalism has to take a host of things (like being red, or human) as primitive [Loux] |
Full Idea: In return for a one-category ontology (with particulars but no universals), the austere nominalist is forced to take a whole host of things (like being red, or triangular, or human) as unanalysable or primitive. | |
From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.68) | |
A reaction: I see that 'red' might have to be primitive, but being human can just be a collection of particulars. It is no ontologically worse to call them 'primitive' than to say they exist. |
4478 | Nominalism needs to account for abstract singular terms like 'circularity'. [Loux] |
Full Idea: Nominalists have been very concerned to provide an account of the role of abstract singular terms (such as 'circularity'). | |
From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.34) | |
A reaction: Whether this is a big problem depends on our view of abstraction. If it only consists of selecting one property of an object and reifying it, then we can give a nominalist account of properties, and the problem is solved. |
4480 | Times and places are identified by objects, so cannot be used in a theory of object-identity [Loux] |
Full Idea: Any account of the identity of material objects which turns on the identity of places and times must face the objection that the identity of places and times depends, in turn, on the identities of the objects located at them. | |
From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.56) | |
A reaction: This may be a benign circle, in which we concede that there are two basic interdependent concepts of objects and space-time. If you want to define identity - in terms of what? |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified. |
9342 | Understanding needs a priori commitment [Horwich] |
Full Idea: Understanding is itself based on a priori commitment. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional. |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it. |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge. |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9) | |
A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate. |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic. | |
From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11) | |
A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away. |