Term
| An argument vs. a valid vs. a sound argument |
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Definition
Argument- any set of sentences one of which is designated as the conclusion
Valid-it is impossible for the premises to be true and the conclusion false
Sound- a valid argument with true premises |
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Term
| A valid sentence vs. a valid argument |
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Definition
| A valid English sentence is true in all possible worlds |
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Term
| Deduction vs. induction vs. abduction |
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Definition
Deduction- to reach theorems from assumptions
Induction- truth of premises increases likelihood of conclusion being true w/o entailing it
Abduction- forming a hypothesis to fit the premise. what detectives do |
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Term
| Use vs. mention of an expression |
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Definition
Mention-talking about a sentence having a certain property. ‘my dog’ has 6 letters
Use-talking about a substance with a certain property. My dog has no letters |
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Term
| A particular of individual thing |
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Definition
| Anything picked out by a sortal |
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Term
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Definition
Numbers are one two three four etc, the actual representation. abstract
Numerals are what represents them 1, 2, 3, 4, I, II, III, IV. Concrete representations |
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Term
| The English alphabet (as understood here) |
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Definition
| Upper case, lower case , . ; : () +=-{}<>”’`?! numerals Greek alphabet |
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Term
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Definition
| Any expressions that function to refer to some one individual thing which can be described by a sortal |
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Term
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Definition
| Noun phrases that begin with `the’ or a possessive noun or pronoun the king of france, hers |
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Term
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Definition
| The Greek alphabet. When one wants to refer to some unknown linguistic object such as letters, phrases, sentences |
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Term
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Definition
| A sentence from which all indexicalities have been eliminated. All tokens of a single eternal sentence have the same truth value |
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Term
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Definition
Concrete-has a place in space and time. X is red
Abstract-no place in space or time redness. numbers |
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Term
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Definition
Sortal term-how many (fingers)
Mass term-how much (tarragon |
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Term
| Type vs. token expressions |
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Definition
| Type-a set containing a token and all of its replicas, not in space and time |
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Term
| Object language vs. meta language |
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Definition
Object language-language we are talking about=L
Meta-language-language we are talking in when talking about object language=English |
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Term
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Definition
| Any sequence of letters of the English alphabet that conforms to he grammatical rules for forming indicative sentences |
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Term
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Definition
| Any sentence into which one or more variables has been substituted for one or more tokens of singular terms |
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Term
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Definition
| `u’ `v’ `w’ `x’ `y’ `z’ standing alone with or without numbers, genderless pronouns, expressions that can be used to refer to something that at some particular time is “unknown” |
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Term
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Definition
| Any type expression different tokens of which have different references. `this’ `that’ `I’ `you’ `she’ `here’ `now’ |
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Term
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Definition
| Something that satisfies the predicate |
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Term
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Definition
| A connective or quanitfier |
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Term
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Definition
| The shortest wff containing it |
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Term
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Definition
| The operator of widest scope (in a wff) |
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Term
| A complete interpretation |
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Definition
(i) Specification of a domain, or universe of discourse: any non-null set, D;
(ii) Assignment of one or more names to every element of D, and to every name exactly one element;
(iii) Assignment of a (possibly null) set of n-tuples of elements of D to every n-place predicate;
(iv) Assignment of a truth-value, T or F, to every sentential letter. |
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Term
| Difference b/w practically, physically and logically possible |
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Definition
Practically-at the present time
Physically-abiding by the laws of nature and physics
Logically-conceivable in a certain world |
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Term
| Corresponding conditional |
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Definition
the conditional that consists of the conjunction of the premises of the argument as antecedent and the conclusion of the argument as consequent.
This is useful because one can then say that an argument is valid iff its corresponding conditional is valid.
(x)Fx
(x)(Fx only if Gx) |
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Term
| “redundancy” definition of truth and 3 reasons for accepting it |
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Definition
| The sentence ‘p’ is true iff p. It is not circular and can be made as simple as possible. It can be understood by anyone who knows rudimentary English. Captures ordinary use of the English |
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Term
| 2 reasons why the redundancy theory is incoherent |
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Definition
| Not grammatically correct. P is not remotely an English sentence. Contradictory (17) “Sentence #17 is not true” iff Sentence #17 is not true |
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Term
| Provide and explain 2 reasons any argument with inconsistent premises is automatically valid |
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Definition
| Definition and addition plus disjunctive syllogism |
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Term
| Distinguish realism from relativism about a domain, citing prima facie clear and contrasting examples, as well as examples that are problematic and not clear one way or the other and why |
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Definition
Realism is that a domain can be the way it is independent of human thought (such as physics and cosmology, regardless of what we figure out the truth about these shall always be the same)
Relativism is the view that some domain d, the truth of sentences in that domain depend upon what some person or set of people think is true. (Traffic laws)
Ambiguous are ethics and aesthetics |
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Term
| Distinguish implication from implicature w/ examples |
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Definition
Implication is a study in logic, conditionals lead to the conclusion
Implicature has to do with conversation. The idea that you will give someone the maximum relevant information |
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Term
| Convention for using corner quotes |
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Definition
| Used with meta-linguistic variables. Stipulate that any Greek letter occurring within corner quotes is always used and never mentioned |
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Term
| Identify English names of greek alphabet |
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Definition
| α:alpha ß:beta Φφ:phi ,Δδ:delta ε:epsilon μ:mu Γ:gamma ψΨ:psi Σ,σ:sigma τ:tau |
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Term
| Explain how ‘p iff q’ is short for ‘if p then q’ and its converse |
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Definition
If x then y = x only if y
If y then x = x if y
If x then y, and if y then x
X only if y, and x if y
X if y, and x only if y
X if and only if y |
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Term
| State full syntatics rules for language l and explain all the syntactic terminology underlined in the text (e.g logical constant, n-ary predicate, well-formed formula, free vs bound variable, sentence, operator, scope, general vs molecular formula, conjunction, disjunction, conditional, biconditional) |
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Definition
| WFF- well-formed formula = no ambiguities? recursive definition = if sigma is a wff so is the negation, universal quantification and existential quantification of sigma; as well as the conjunction, disjunction, conditional and biconditional of sigma and psi (if psi is also a wff) |
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Term
| Provide all the clauses of the tarski recursive definition of “true in language L” |
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Definition
Base Clauses:
- Sentential letter is true under I iff I assigns T to it
- an n-ary predicate followed by n names is true under I iff the objects I assigns to those n names form an n-tuple in the set I assigns to that predicate
Recursive Clauses:
- conjunct = when both parts are true
- disjunct = when at least one part is true
- conditional = when the antecedent and consequent are true or the antecedent is false and the consequent can either be true or false
- biconditional = when the antecedent and the consequent are either both true or both false
- existential quantifier = at least one object in the domain that makes this true
- universal quantifier = every object in the domain makes this true |
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Term
| Construct n-domain expansions of quantified sentences |
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Definition
Domain <1,2> a=1 b=2
(∃y)(x)L2xy = ((x)L2xa v (x)L2 xb)
((L2 aa & L2 ba) v (L2 ab & L2 bb)) |
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Term
| Provide revised technical definitions of ‘valid’, ‘invalid’, ‘consistent’, inconsistent, contingent in terms of formal interpretations |
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Definition
Provide revised technical definitions of ‘valid’, ‘invalid’, ‘consistent’, inconsistent, contingent in terms of formal interpretations Provide revised technical definitions of ‘valid’, ‘invalid’, ‘consistent’, inconsistent, contingent in terms of formal interpretationsSENTENCES:
VALID: A sentence is valid iff it is true under ALL interpretations of L
INVALID: A sentence is invalid iff it is not valid, i.e. there is at least one interpretation that makes it false
CONSISTENT: A sentence is consistent iff it is true under at least one interpretation. (it may be true under all interpretations; all valid sentences are a fortiori consistent
INCONSISTENT: A sentence is inconsistent iff it is not consistent, i.e. it is true under no interpretation
CONTINGENT: A sentence is contingent iff there is at least one interpretation that makes it true and at least one that makes it false
ARGUMENTS:
VALID: An argument is valid iff there is no interpretation that makes the premises true and the conclusion false
INVALID: an argument is invalid iff it is not valid, i.e. iff there is at least one interpretation that makes the premises true and the conclusion false |
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Term
| Explain the “decision” or “student’s” problem for language L |
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Definition
| In tarski’s definition, since the interpretation needed to render a given sentence true requires various assignments of the domain, names and truth values of sentential letters, the student’s problem is that there is no set procedure for going through all the possible interpretations to find one that makes some sentence true. |
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Term
| Difference between “implies” and “only if” and the relation between them |
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Definition
| One sentence implies another when the corresponding conditional is valid. One should not say that the antecedent of a conditional implies the consequent because this would be grammatically improper and cause a run-on sentence. |
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Term
| Explain the problem of negative existentials, the problems with McX’s and Wyman’s solutions to it, and how Russel’s Theory of descriptions combined with the (Tarskian) model theory we’ve discussed afford at least a satisfactory answer |
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Definition
Wyman-unactualized possible
McX-can’t deny the existence of pegasus b/c then you would be talking about nothing. pegasus is an idea in your head.
Russel’s theory of descriptions-that all names (columbus, pegasus) can be paired down to definite descriptions that start the. The man that discovered america, the winged horse captured by Bellerophon.
-((∃x)Wx) & (y)(Wy |
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Term
| Identify what a “theory” is in terms of Language L, and set out the four axioms of the theory of identity |
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Definition
any set of sentences of L (called the theory’s axioms), and all their logical consequences
The Reflexivity of Identity
(x)x=x
The Symmetry of identity
(x)(y)(x=y
The Transitivity of Identity
(x)(y)(z)(x=y & y=z)
The Indiscernability of Identicals (“Leibniz’s Law”)
(x)(y)(x=yφx=φy))
What Prof. Rey stressed was interesting about the notion of IDENTITY is that it seems to have some prima facie value, but on contemplation it is entirely self-referential. “For all things, one thing is the same as itself”; “For all things, if a thing is identical to itself, then it is identical to itself”; etc.
The question arises: how do we find it so informative? Through application of mathematical principles? Other avenues of thought? |
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Term
| Explain why, according to Quine, efforts to extend a theory of meaning beyond an extensional semantics to include analyticities along with logical truths seem to confront a problem of circularity |
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Definition
Explain why, according to Quine, efforts to extend a theory of meaning beyond an extensional semantics to include analyticities along with logical truths seem to confront a problem of circularity This is in need of clarification. how is (∃x)(Mx & Bx) consistent?
Renate and Cordate have the same extension but not the same intension. Bachelor and unmarried male have the same intension and extension. If you try to narrow it down by substituting words and trying to save the truth value of sentences (salva veritate) it can still work for co-extensives (all cordates are cordates works as all cordates are renates).
Counterargument is that it does not work in modal contexts (necessary, possible, could)
“Necessarily, all cordates are cordates” is not the same as “Necessarily, all cordates are renates” in a possible world there could be cordates that are not renates. But this works for bachelor and unmarried male.t
According to Quine (∃x)(Mx & Bx), where Mx stands for “is married” and Bx stands for “is a bachelor”, with {1} assigned to both M and B is thus true under at least one interpretation, which makes it logically consistent.
Kant argues that this cannot be done as bachelor is synonymous with unmarried male.
But what is the criterion for synonymy? It brings us back to the beginning |
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Term
| Explain the phenomenon of “referential opacity,” how it seems to raise a problem for a theory of identity, and a general strategy philosophers have proposed for dealing with it |
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Definition
Leibniz’s law (axiom 4) runs into problems with modal words and words expressing propositional attitudes.
Referentially opaque = the singular terms that occur in scope of modal or propositional attitude words don’t really refer in the way that they superficially appear to do.
example: MT = SC then John believes MT is witty iff John believes SC is witty
General Strategy for dealing: idea that thought involves a relation to a spelt representation that may be entokened in brain - what John believes is the sentence ‘MT is witty’
Now if the direct object of John’s thinking is not the man MT, but the man’s name MT, MT is covertly being mentioned not used.
therefore if MT=SC, then anything true of (the man) MT must also be true of (the man) SC. ***NOT that anything true of (the name) MT must also be true for (the name) SC |
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Term
| Explain briefly the “logicist” program initiated by Frege, and how Russell’s paradox (which you should be able to explain) raised a serious problem for it |
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Definition
Logicism program put forth math as an extension of logic - math reducible to logic
Russell’s Paradox exposes an inconsistency in “naive” set theory
- the predicate y is not a member of y
ex. nobody shaves all and only all those people who do not shave themselves
- if something is a member of itself it must satisfy the conditions on the set (not be a member of itself)
- **but if it isnt a member of itself then it does satisfy the conditions of the set and so it is a member of itself
Consequently there is not a set for every predicate |
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Term
| Explain why some infinities are larger than others, and the revision this fact requires “objectual” rather than “substitutional” clauses for the truth conditions for the quantified sentences |
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Definition
distinguish between ordinals and cardinals
Ordinals = members of a certain sequence or ordering
Cardinals = measures of size
Ordinals and cardinals same in case of finite numbers but diverge at infinite
Ex. infinity +1 and infinity + 2 have same cardinality but infinity + 2 occurs after infinity + 1 ordinally speaking
Denumerable number of objects leads to omega inconsistency
- a quantified sentence can be true but all substitutions false
To fix this we must resort to the objectual interpretation and a further notion of B-variant
- an interpretation I’ is a B-variant of an interpretation I iff I’ and I are either the same or differ only with respect to the object they assign to the name B |
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Term
| Explain Quine’s criterion of ontological commitment, and provide two philosophically interesting applications of it. |
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Definition
suppose we have the sentence (Fa & ~Fb) - sentence ontologically committed to the existence of at least two objects. Or we could say formula (Fx & Fy) requires two different objects as values of its variables.
Quine offers plausible evidence: go out in world come back with a theory you think is true, formulate theory in language L and see what needs to exist for the theory to be true. ie: see what are the values of your variables.
“to be is to be the value of a variable” |
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