A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
abstract 6.2.1
abstractor 6.2.1
Absurdity 1.2.4
accommodation 1.3.1
accumulated goals 7.7.4
accumulated resources 7.7.4
active for a term 7.5.4
Adams, Ernest W. (1926-) 5.1.3
Adjunction (see Adj under Rule Labels)
affirmative generalization 7.1.4
agreement (of interpretations) for a gap 7.7.2
alias set 6.3.2
alphabetic variant 6.2.2
alternatives 1.4.3
analysis 2.1.1
anaphoric pronoun 6.1.6
ancestor gap 2.3.3
and, logical (see ∧ under Symbols)
antecedent of a conditional 5.1.1
any 7.3.3
application 6.1.7
appropriate 1.3.4
argument 1.1.2
argument tree 2.2.5
Aristotle (384-322 BCE) 7.1.1
assumption 1.1.2
at least one 4.1.3
attachment rule 2.4.3
attribute of a generalization 7.1.4
attributive adjective 2.1.3
Austin 1.3.3
auxiliary resource 4.3.1
available resource 2.2.7
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
basic rule 3.5.1
basic system of derivations 3.5.1
Beth, Evert W. (1908-1964) 2.2.2
biconditional 5.2.2
body 6.2.1
Boole, George (1815-1864) 1.1.7
bound variable 6.2.2
bounding class 7.1.5
bounds indicator 7.1.5
branching conditional 5.1.4
Brouwer, L. E. J. (1881-1966) 3.1.3, 8.5.2
but-not form 3.1.4
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
case argument 4.2.1
categorical sentence 4.2.2
causal condition 5.2.2
Celarent 8.5.4
chain law 1.4.6
child gap 2.3.3
Chrysippus (280-207 BCE) 2.2.2
Church, Alonzo (1903-1995) 6.2.1, 7.7.1
claim of exemplification 8.1.1
class indicator 7.1.4
closed 6.2.2
co-alias 6.3.1
co-alias series 6.3.3
co-alias with respect to equations 6.3.2
complement 7.1.4
complementary generalization 7.1.4
complete expression 6.1.1
complete system of derivations 2.3.7, 7.7.1
compositionality 2.1.2, 3.1.2, 4.1.1, 5.1.2
compound sentence 2.1.1
compound term 6.1.7
conditional 5.1.1
conditional implication 5.3.1
conditional exhaustiveness 1.4.3
conditional inconsistency 1.1.6
conditionalization 5.3.1
confinement 8.1.4
conjunct 2.1.1
conjunction (connective) 2.1.1
conjunction (pattern of argument) 2.2.1 (see also Cnj under Rule labels)
consequent 5.1.1
consequentia mirabilis 4.3.1
conservative system 2.3.4
contingency, logical 1.4.4
constructive proof 8.5.2
contradictory sentences 1.2.6, 1.4.4
contraposition for generalizations 8.3.3
conversational implicature 4.1.2
conversion 8.1.3
counterexample, presentation of (see presenting a counterexample )
counterfactual conditional 5.1.3
Curry, Haskell (1900-1982) 5.1.2
cycle 7.7.3
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
Darii 8.5.4
dashes 7.2.1
dead-end gap 2.3.1
decisive system of derivations 2.3.6
decision procedure 2.3.6
deductive logic 1.1.4
deductive reasoning 1.1.4
definite description 1.3.7, 6.1.6 (see also 8.4)
deixis 1.3.2
delineation 1.3.6
De Morgan, Augustus (1806-1871) 4.2.4
descendant gap 2.3.3
description operator 8.4.3
detachment rule 4.3.1
development of a gap 2.2.2
Diodorus Cronus ( -c.284 BCE) 5.1.3
direct generalization 7.1.4
discharged assumption 2.4.1
disjunct 4.1.1
disjunction 4.1.1
divisible/indivisible 1.4.2, 2.3.2
domain 7.1.4
dots 7.2.1
double conditional 5.1.2
double negation 3.1.3
down tack (see ⊤ under Symbols)
dummy restriction 7.2.1
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
embedding 6.4.3
empty reference value 1.3.7
entailment 1.1.6
entity 6.1.6
epistemic condition 5.2.2
equation 6.1.4
equivalence (logical) 1.2.3
equivalence class 6.3.2
equivalence relation 1.2.3
ex falso quodlibet 2.2.6 (see also EFQ under Rule labels)
ex nihilo verum 2.2.6 (see also ENV under Rule labels)
exception class 7.1.5
exception indicator 7.1.5
exclusion 1.1.6, 1.4.4 (see also inconsistency, conditional)
exclusion, mutual (see mutually exclusive)
exclusive disjunction 4.1.2
exclusive disjunction form 4.1.2
exemplify 8.1.1
exhaustive, jointly (see jointly exhaustive )
exhaustiveness, conditional 1.4.3
existence (requirement for a definite description to refer) 8.4.1
existential 8.1.1
existential claim 8.1.1
existential commitment 8.1.5
existential generalization 8.5.2
expansion by a range 7.5.1
exploitable 7.7.3
exploitation 2.2.3
extension (of a rule) for equations 6.3.3
extensional interpretation 2.1.8, 6.4.1
extensional operation 6.1.3
extraction 2.2.1 (see also Ext under Rule labels)
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
Ferio 8.5.4
first-order logic 1.1.7, 8.5.4
Fitch, Frederic (1908-1987) 2.2.2
flag 7.5.5
formal logic 1.1.7
formal validity 2.3.8
formula 6.2.2
free variable 6.2.2
Frege, Gottlob (1848-1925) 1.1.7, 4.1.3, 6.1.3, 6.2.1, 7.1.1, 7.1.1, 7.4.1, 8.4.3, 8.5.4
fully developing path 7.7.1
function 6.1.7
functor 6.1.7
functor abstract 6.2.1
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
gap 2.2.2
general argument 7.5.3
general exemplification 8.2.1
general term 6.1.6
generalization 7.5.3
generalization over pairs 7.4.1
Gentzen, Gerhard (1909-1945) 2.2.2
goal 2.2.2
Gödel, Kurt (1906-1978) 7.7.1, 8.5.4
grade (of a resource or goal) 3.4.1
grammatical predicate 6.1.1
grammatical subject 6.1.1
Grice, H. Paul (1913-1988) 1.3.4, 4.1.2, 5.1.3
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
higher-order logic 8.5.4
hypothetical 4.2.2
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
ID of a reference value 6.4.1
identity 6.1.4
if-conditional 5.1.1
immediate component 2.1.7
immediate inference 1.1.2
implication 1.2.3
implication, conditional (see conditional implication )
inclusive disjunction 4.1.2
inclusive disjunction form 4.1.2
inconsistency, conditional 1.1.6, 1.4.4 (see also exclusion)
inconsistent with (see inconsistency, conditional )
indefinite article 7.3.1
independence, logical 1.2.6, 1.4.4
indicated class 7.1.4
indicative conditional 5.1.3
indirect proof 3.3.1 (see also the rule Indirect Proof under Rule Labels)
individual 6.1.6
inductive inference 1.1.4
inference 1.1.2
inference, immediate (see immediate inference )
inference ticket 5.3.2
instance 7.5.1
intensional entity 6.3.1
intensional interpretation 2.1.8, 6.4.1
intensional property 6.3.1
interpretation of a gap 7.7.2
intersection 7.1.5
intuitionism 3.1.3
intuitionistic negation 3.1.3
irreflexivity 7.8.2
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
Jaskowski, Stanislaw (1906-1965) 2.2.2
jointly exhaustive 1.2.6, 1.4.4
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
lambda abstraction 6.2.1
law (see the list of laws )
tilde equal (see ≃ under Symbols)
Leibniz, G. W. (1646-1716) 1.1.7, 1.2.1
lemma 1.4.6
Lemma (the rule—see Lem under Rule Labels)
Lewis, David K. (1941-2001) 1.3.1, 1.3.6, 5.1.3, 8.4.1
linked conditional 5.3.x
logical and (see ∧ under Symbols)
logical contingency (see contingency (logical) )
logical equivalence (see equivalence (logical) )
logical independence (see independence (logical) )
logical possibility 1.2.1
logical predicate (see predicate (logical) )
logical space 1.2.5
logical implication 5.1.1
logical vocabulary 6.1.4
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
main connective 2.1.5
main resource 4.3.1
thorough system of derivations 7.7.1
material implication 5.1.1
mathematical logic 1.1.7
meaning postulate (for a definite description) 8.6.3
meta-mathematics 1.1.7
minimal sentence 3.4.1
misleading sentence 1.3.4
modal logic 3.1.2
modus ponendo ponens 5.3.2 (see also modus ponendo ponens under Laws and also MPP under Rule labels)
modus ponendo tollens (see modus ponendo tollens under Laws and also MPT under Rule labels)
modus ponens (see modus ponendo ponens)
modus tollendo ponens (see modus tollendo ponens under Laws and also MTP under Rule labels)
modus tollendo tollens 5.3.2 (see also modus tollendo tollens under Laws and also MTT under Rule labels)
modus tollens (see modus tollendo tollens)
monotonic 1.4.6
Morris, C. W. (1903-1979) 1.3.2
multiple ambiguity 7.1.1
multiple conjunction 2.1.5
multiple generality 7.4.1
mutually exclusive 1.2.6, 1.4.4
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
natural deduction system 2.2.2
necessary condition 5.2.2
negation 3.1.1
negative form (of a definition) 1.4.1
negative generalization 7.1.4
neither-nor form 4.1.4
Nil 8.6.1
the nil 8.4.3
non-constructive proof 8.5.2
non-deductive reasoning 1.1.4
non-empty extension 8.1.1
non-logical vocabulary 6.1.4, 6.4.1
non-monotonic inference 1.4.6
non-restrictive relative clause 6.1.8
not-and-not form 3.1.4
not-but form 3.1.4
not-both form 3.1.4
not-without form 3.1.4
numerical quantifier phrase 8.3.2
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
object 6.1.6
obversion 8.1.2
only-if conditional 5.2.1
open term 6.2.2
operation 6.1.1
ordered pair 6.4.2
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
parent gap 2.3.3
path 7.7.1
performative verb 1.3.3
Philo (c. 300 BCE) 5.1.3
place of a predicate 6.1.2
planning for a goal 2.2.3
positive form (of a definition) 1.4.1
possible world 1.2.1
pragmatics 1.3.2
predicate (logical) 6.1.1 6.1.2
predicate, zero-place 6.2.2
predicate abstract 6.2.1
predication 6.1.2
premise 1.1.2
presenting a counterexample 2.3.5
presupposition, semantic 1.3.2, 1.3.7
presupposition of a question 1.3.7
progressive rule 2.3.6
proof by cases 4.2.1 (see also PC under Rule labels)
proof by choice 8.5.1
property 6.1.3
property in intension 6.3.1
proposition 1.2.2
proximate argument of a gap 2.2.5
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
quantified formula 7.2.1
quantified predicate 7.1.4, 7.2.1, 8.1.1
quantifier 7.2.1
quantifier distribution 7.3.2
quantifier interchange 7.4.1
quantifier phrase 6.1.6, 7.1.1
quod erat demonstrandum 2.2.3 (see also QED under Rule labels)
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
range 6.4.1
reductio argument 2.4.2
reference function 6.1.7
reference value 1.3.7
referential opacity 6.1.3
referential transparency 6.1.3
reject (a conditional) 5.4.1
relation 6.1.3
relative complement 7.1.4
relative scope 2.1.5
render exhaustive (see conditional exhaustiveness )
resource 2.2.2
restricted existential 8.1.1
restricted universal 7.2.1
restricting formula 7.2.1
restricting predicate 7.2.1, 8.1.1
restriction by a relation 7.4.1
restrictive relative clause 6.1.8
double right turnstile (see ⊨ under Symbols)
run-on conjunction 2.1.5
run-on disjunction 4.1.3
Russell, Bertrand (1872-1970) 8.4.2, 8.5.4
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
safe rule 2.3.4
salience 8.4.1
scope 2.1.5
scope ambiguity 7.1.1
scope line 2.2.2
second-order logic 8.5.4
securing a compound term 7.8.1
securing a definite description 8.6.2
semantic presupposition (see presupposition, semantic)
semantics 1.3.2
sentence 6.2.2
sequent 2.2.1
sequent proof 2.2.1
serial conjunction 2.1.5
serial disjunction 4.1.3
setentailment 1.4.6
Sextus Empiricus (2nd cent.) 5.1.3
singular term 6.1.6
sorites argument 1.3.6
sorites paradox 1.3.6
sound system of derivations 2.3.7, 7.7.1
Stalnaker, Robert C. (1940-) 5.1.3
statement 1.3.5
stronger claim 1.2.3
structure 6.4.1
subjunctive conditional 5.1.3
substantive existential commitment 8.1.5
subtraction 7.1.4
sufficient system of derivations 2.3.2
sufficient condition 5.2.2
super-valuation 1.3.7
syllogism 1.1.2, 7.1.1, 7.5.6, 8.5.4
symbolic logic 1.1.7
synthesis 2.1.8
system of derivations 2.2.2
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
Tautology 1.2.4
tautology 1.2.4
tense logic 3.1.2
term 6.1.6
there-is existential 8.1.3
thing 6.1.6
effectual system of derivations 7.7.1
tree-form proof 2.2.1
true of 6.4.2
truth conditions 1.2.2
truth function 2.1.2
truth-functional completeness 3.1.4
truth-functional connective 3.1.2
truth-functional logic 1.1.7, 3.1.2
truth table 2.1.2
truth value 1.2.1
type 6.1.7
type theory 8.5.4
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
ultimate argument of a derivation 2.3.1
ultimate component 2.1.7
ultimate resources 7.7.4
unanalyzed component 2.1.7
undefined term 1.3.7
uniformly general exemplification 8.2.1
union (of sets) 1.1.3
uniqueness (requirement for a definite description to refer) 8.4.1
universal instantiation 7.5.2
universal predicate 7.2.1
universal quantifier 7.2.1
universal sentence 7.2.1
unless conditional 5.2.3
unrestricted existential 8.1.1
unrestricted universal 7.2.1
up tack (see ⊥ under Symbols)
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
vacuous abstraction 6.2.1
valid conclusion 1.1.6
validity of an argument 1.1.6
validity, formal or in virtue of form (see formal validity )
van Fraassen, Bas (1941-) 1.3.7
veil of ignorance 7.5.5
virgule (see / under Symbols)
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
weakening 4.3.2, 5.4.2 (see also Wk under Rule labels)
weaker claim 1.2.3
Wittgenstein, Ludwig (1889-1951) 1.2.5
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
yes-but answer 1.3.4
yes-no question 1.3.4
zero-place predicate (see predicate, zero-place)
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
/ (virgule—U+002F) 1.1.2
{a1, …, an} (list notation for sets) 1.1.3
∪ (union—U+222A) 1.1.3
∅ (empty set—U+2205) 1.4.2
⊨ (double right turnstile—U+22A8) 1.1.6
≃ (tilde equal—U+2243) 1.2.3
▵ (white up-pointing small triangle—U+25B5) 1.2.6
▿ (white up-pointing small triangle—U+25BF) 1.2.6
⧖ (hourglass—U+29D6) 1.2.6
⊤ (down tack—U+22A4) 1.2.4
⊥ (up tack—U+22A5) 1.2.4
∧ (logical and—U+2227) 2.1.1
○ (empty circle—U+25CB) 2.2.5
● (filled circle—U+25CF) 2.2.3
⊭ (negated double right turnstile—U+22AD) 2.3.1
¬ (not sign—U+00AC) 3.1.1
± (negation or de-negation) 4.2.2
∨ (logical or—U+2228) 4.1.1
→ (rightwards arrow—U+2192) 5.1.1
← (leftwards arrow—U+2190) 5.1.1
∀ (for all—U+2200) 7.2.1
∃ (there exists—U+2203) 8.1.1
∗ (asterisk operator—U+2217) 8.4.3
I (see description operator)
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
⊥ as an alternative, law for 1.4.7
⊥ as a premise, law for 1.4.7
aliases, law for 6.3.2
alternatives via assumptions 1.4.5, 1.4.6
the conditional as a conclusion, law for 5.3.1
the conditional as a premise, law for 5.4.1
congruence for a functor 6.3.1
congruence for a predicate 6.3.1
congruence for f 6.3.1
congruence for P 6.3.1
conjunction as a conclusion, law for 2.2.1
conjunction as a premise, law for 2.2.1
contravariance 3.1.2
covariance with the antecedent 5.1.2
covariance with the consequent 5.1.2
Curry’s law 5.1.2
cut law 1.4.6
De Morgan’s laws 4.2.4
descriptions, law for 8.6.1
disjunction as a conclusion, law for 4.2.2
disjunction as a premise, law for 4.2.1
inconsistency via Absurdity 1.4.5
inconsistency via absurdity 1.4.6
involution 3.1.2
lemmas, law for 1.4.6
modus ponendo ponens 5.3.2
modus ponendo tollens 4.3.1
modus tollendo ponens 4.3.1
modus tollendo tollens 5.3.2
monotonicity 1.4.6
negation as a conclusion, law for 3.2.1
negation as a premise, law for 3.2.1
non-contradiction, law of 3.2.2
premises, law for 1.4.6
repetition law 1.4.6
⊤ as a conclusion, law for 1.4.7
⊤ as an alternative, law for 1.4.7
⊤ as a premise, law for 1.4.7
unrestricted existential as a conclusion, law for 8.5.2
unrestricted existential as a premise, law for 8.5.1
unrestricted universal as a conclusion, law for 7.5.3
unrestricted universal as a premise, law for 7.5.2
A B C D E F G H I J K L M N O P Q R S T U V W XYZ Symbols Laws Rules
Adj (Adjunction) 2.4.3
CE (Co-alias Equation) 6.3.3
Cng (Congruence) 6.3.3
Cnj (Conjunction) 2.2.3
CP (Conditional Proof) 5.3.1
CR (Completing a Reductio) 3.3.2
DC (Distinguished Co-aliases) 6.3.3
EC (Equated Co-aliases) 6.3.3
EFQ (Ex Falso Quodlibet) 2.2.6
EG (Existential Generalization) 8.5.3
ENV (Ex Nihilo Verum) 2.2.6
Ext (Extraction) 2.2.3
IP (Indirect Proof) 3.3.1
Lem (Lemma) 2.4.1
LFR (Lemma for Reductio) 2.4.2
MPP (Modus Ponendo Ponens) 5.3.2
MPT (Modus Ponendo Tollens) 4.3.1
MTP (Modus Tollendo Ponens) 4.3.1
MTT (Modus Tollendo Tollens) 5.3.2
Nc (Non-contradiction) 3.2.2
Nc= (Non-contradiction given Equations) 6.3.3
NcP (Non-constructive Proof) 8.5.3
PC (Proof by Cases) 4.2.1
PCh (Proof by Choice) 8.5.3
PCh+ (Supplemented Proof by Choice) 8.5.3
PE (Proof of Exhaustion) 4.2.2
RC (Rejecting a Conditional) 5.4.1
QED (Quod Erat Demonstrandum) 2.2.3
QED= (QED given Equations) 6.3.3
RAA (Reductio ad Absurdum) 3.2.2
SD (Securing a Description) 8.6.2
SD+ (Securing a Description Supplemented) 8.6.3
ST (Securing a Term) 7.8.1
UG (Universal Generalization) 7.5.5
UG+ (Supplemented Universal Generalization) 7.8.1
UI (Universal Instantiation) 7.5.4