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Adolf Rami (Göttingen) - Non‐Standard Neutral Free Logic, Empty Names and Negative Existentials
Weekly Research Seminar
Please note that this seminar commenced at 5:30pm with refreshments served from 5pm in room 005, 48/49 Old Elvet
Title: Non‐Standard Neutral Free Logic, Empty Names and Negative Existentials
There was no circulated abstract for this seminar.
Handout information (below)
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Non‐Standard Neutral Free Logic, Empty Names and Negative Existentials
by Dolf Rami, 23.02.2011
THE STRUCTURE OF THE PAPER
1 The Task: The Analysis of Singular Negative Existential Sentences
2 The Problem: An Inconsistent Set of Assumptions concerning SNES
3 Overview: Six Solution Strategies
4 Negative and Neutral Free Logic
5 Motivations for a Solution based on Neutral or Negative Free Logic
6 Objections against a Solution based on Neutral or Negative Free Logic
[1.0] The Task: The Analysis of Singular Negative Existential Sentences
(E1) Vulcan does not exist.
(E2) Pegasus does not exist.
(E3) Sherlock Holmes does not exist.
[2.0] The Problem: An Inconsistent Set of Assumptions concerning SNES
(The Truth‐Value Thesis)
Some sentences of the grammatical form 'n does not exist' are true.
(The Logical‐Form Thesis)
Every sentence of the grammatical form 'n does not exist' is a sentence of the logical form '¬E!a'.
(The Truth‐Condition Thesis)
Every sentences of the logical form '¬E!a' is true iff the object designated by ‘a' is not a member of
the extension of ‘E!'.
(The Connection Thesis)
Every instance of the schema '(x('n' designates x) n exists)' is true.
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[3.0] Overview: Six Solution Strategies
[3.1]‐[3.6] Strategies A‐F
[4.0] Negative and Neutral Free Logic
[5.0] Motivations for a Solution based on Neutral or Negative Free Logic
[5.1] Motivation 1: Methodological balance
[5.2] Motivation 2: Material Adequateness I - Empty Proper Names
[5.3] Motivation 3: Material Adequateness II - The Semantics of ‘exist'
(E4) Something exists.
(E5) Everything exists.
(E6) Every man exists.
(E7) Barack Obama exists.
(E8) Something is an F, but there are no F's.
(E9) There are things that do not exist.
(E9*) There are things that do not exist in space and time.
(E9**) There are things that do not exist (at all); namely Vulcan, Pegasus and Sherlock Holmes.
(E10) Every tiger exists.
(E11) Every unicorn exists.
(E12) Unicorns exist.
[6.0] Objections against a Solution based on Neutral or Negative Free Logic
[6.2] Objections against Negative Free Logic
(P1) x(x is an adult ↔ ¬(x is a minor))
(P2) xy(x is distinct from y ↔ ¬(x is identical with y))
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[6.2] Objections against Neutral Free Logic
Option I (Non‐Standard Neutral Free Logic I):
Treats ‘exist' as a primitive logical predicate with the following truth‐conditions:
V(E!t) = T iff I(t) is defined.
V(E!t) = F iff I(t) is not defined.
Option II (Non‐Standard Neutral Free Logic II):
Treats ‘exist' as a logical predicate that can be defined on the basis of logical expressions
only:
(LP) x(E!x =df y(x=y))
Assigns the following truth‐conditions to existential generalisations:
(EGT) V(xA) = T iff for at least one d D, V(t,d)(A(t/x)) = T
(EGF) V(xA) = F iff there is no d D, V(t,d)(A(t/x)) = T
[6.3] Objections against Negative and Neutral Free Logic
(E13) Every Peter is a Peter.
(E14) A curious Peter entered the room.
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