What is an Argument? Validity vs. Soundess of Arguments
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1 What is an Argument? An argument consists of a set of statements called premises that support a conclusion. Example: An argument for Cartesian Substance Dualism: 1. My essential nature is to be a thinking thing. 2. My body's essential nature is to be an extended thing in space. 3. My essential nature does not include being an extended thing in space. 4. Therefore, I am not identical with my body. 5. And since I am a thinking thing (namely a mind), my mind is not identical with my body. 1 Validity vs. Soundess of Arguments An argument is valid IFF it is logically impossible for all of its premises to be true while its conclusion is false. An Argument is sound IFF it is valid and all of its premises to be true Example of a valid but unsound argument: 1. All cats are dogs 2. All dogs are cows Thus: 3. All cats are cows 2 1
2 Use/Mention Distinction The so-called use/mention distinction is a linguistic distinction about when we use words to talk about things in the world as opposed to when we mention them to talk about the words themselves. Examples: Paris is a beautiful city Paris has six letters Paris is the capitol of France is a grammatical sentence That Paris is the capital of France is an interesting fact 3 Type/Token Distinction Properties and their Instances There can be different tokens of a type. Linguistic example: Paris Paris London Non-linguistic example: Colors/shapes/colored shaped 4 2
3 Numerical/Qualitative Identity Sameness/Difference Paris Paris London Here we have three numerically distinct words; but the first two words are of the same type (=type-identical) Here are three numerically distinct figures only the first two are qualitatively identical 5 Leibniz Law Leibniz Law is the conjunction of the following two principles: The Indiscernibility of Identicals: If two things are identical, then they share all their attributes (metaphysical truth) The Identity of Indiscernibles is the converse of this: If two things share all their properties then they are identicals (controversial claim) 6 3
4 Epistemology/Metaphysics/Semantics Epistemology is the investigation about what knowledge is and how we acquire it. Metaphysics investigates the nature of things in their most basic and general forms (ontology is the study of what are the most fundamental/real/nonreducible existents) Semantics investigates the meaning/ reference/truth of symbolic structures (language, anything that forms a representational system) 7 Propositions/Statements/Sentences/etc 1. The president of US in 1995 was a democrat 2. Bill Clinton in 1995 was a democrat 3. Le président des Etats-Units en 1995 était un Démocrate These are three different sentences (different sentence-types) (1) and (3) have the same meaning which is different than the meaning of (2) All three sentences have the same truth-conditions. A proposition is typically identified with either the meaning of a sentence or its truth-conditions Propositions are abstract entities that are essentially true or false. A sentence is true or false in virtue of expressing a proposition A fact is a true proposition The word statement is usually synonymous with proposition (but is used sometimes deliberately ambiguously to mean either a proposition or a sentence) 8 4
5 Reference/meaning of subsentential expressions: Singular terms (or, singularly referring expressions) A singular term (e.g., names, definite descriptions, pronouns, demonstratives, etc.) has a referent (or refers to whatever it is that we use the term to talk about) Many think that most or all singular terms have also a meaning. Two different singular terms (a definite description and a proper name, respectively): The president of US in 1995 Bill Clinton They have the same person as their referent (same reference), but they differ in their meaning. 9 Extension/Intension of subsentential expressions: Predicates Predicates are linguistic expressions that are used to attribute a property or relation to things/objects/events/etc. Examples: is red, is circular, is a tiger, is bigger than, etc. Like the reference/meaning of singular terms, they have an extension and intension: The extension of a predicate is the set of all the actual objects that fall under it. So the extension of tiger is the set of all actual tigers. The intension of a predicate is the property that it expresses/ represents. So the intension of tiger is the property of being a tiger. 10 5
6 Predicate/Concept/Property These are intimately related notions. A predicate is a linguistic entity (a publicly observable symbolic device used to communicate) A property is a metaphysical or ontological category, it s part of the furniture of the world. A concept is a mental representation, idea, or a psychological notion, but not public, rather private to minds APPLE #APPLE# 11 Possible Worlds A possible world is a way our world might have been. It is what we express when we use subjunctive conditionals (counterfactual statements) like: If Al Gore had been elected as president in 2000, the overall federal funding for scientific research would not have decreased What makes this conditional true or false is not facts about the actual world, but rather what happens in a possible world where everything had been the same except in 2000 Al Gore wins the election and the events that follow afterwards. In the infinite space of all possible worlds, some are more similar to the actual world than others. 12 6
7 Modalities: Possible/Necessary/ Contingent A statement is possible IFF there is at least one possible world in which is true A statement is necessary IFF it is true in all possible worlds A statement is contingent IFF there is at least one possible world in which it is true and one possible world in which it is false A statement is impossible IFF there is no world in which it is true Necessary Contingent Impossible Possible 13 A priori/necessary/analytic Analytic VS. Synthetic (semantic) A priori VS. A posteriori (epistemological) Necessary VS. Contingent (metaphysical) A sentence is analytic IFF it is true solely in virtue of the meanings of the words that make up the sentence, synthetic otherwise. A statement is a priori IFF it can be known to be true (false) without consulting how the world is, a posteriori otherwise. A statement is necessary (impossible) IFF it is true (false) in every logically possible world. 14 7
8 Kinds of possibility/necessity Technologically/technically possible Nomologically/physically/empirically possible Logically/metaphysically possible Epistemically/conceptually possible Goldbach's conjecture: Every even integer n greater than 2 is the sum of two primes 15 Supervenience Local Mind-Body Supervenience I. The mental supervenes on the physical in that things (objects, events, organisms, persons, and so on) that are exactly alike in all physical properties cannot differ with respect to mental properties. That is, physical indiscernability entails psychological indiscernability. Local Mind-Body Supervenience II. The mental supervenes on the physical just in case if anything x has a mental property M, there is a physical property P such that x has P, and necessarily any object that has P has M. Global Mind-Body Supervenience III. The mental supervenes on the physical in that worlds that are alike in all physical respects are alike in all mental respects; in fact, worlds that are physically alike are exactly alike overall
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