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 Rule labels
abstract 6.1.4
Absurdity 1.2.2
accommodation 1.3.3
accumulated goals 7.7.4
accumulated resources 7.7.4
active for a term 7.5.3
Adams, Ernest W. (1926-) 5.1.2
Adjunction (see Adj under Rule Labels)
affirmative generalization 7.1.4
agreement (of interpretations) for a gap 7.7.2
aleph-null (see ℵ0 under Symbols)
alias set 6.3.2
alphabetic variant 6.1.4
alternative (from a relatively exhaustive set) 1.4.5
analysis 2.1.1
analysis tree 2.2.1
anaphoric pronoun 6.2.1
and, logical (see ∧ under Symbols)
antecedent of a conditional 5.1.1
any 7.3.3
application 6.2.2
appropriate 1.3.3
argument 1.1.2
Aristotle (384-322 BCE) 7.1.1
assumption 1.1.2
at least one 4.1.3
attachment rule 2.4.3
attribute 6.1.2
attribute of a generalization 7.1.4
attributive adjective 2.1.2
auxiliary resource 4.3.1
available resource 2.2.6
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 Rule labels
bar notation 4.2.2
basic rule 3.5.1
basic system of derivations 3.5.1
basic law for equivalence (see basic, for equivalence under Laws)
Beth, Evert W. (1908-1964) 2.2.2
biconditional 5.2.2
body 6.1.4
Boole, George (1815-1864) 1.1.5
bound variable 6.1.4
bounding class 7.1.5
bounds indicator 7.1.5
branching conditional 5.1.3
Brouwer, L. E. J. (1881-1966) 3.1.3, 8.5.1
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 Rule labels
case argument 4.2.1
categorical sentence 4.2.2
causal condition 5.2.2
chain law 1.4.2
Chrysippus (280-207 BCE) 2.2.2
Church, Alonzo (1903-1995) 6.1.4, 7.7.1
claim of exemplification 8.1.1
class indicator 7.1.4
closed 7.2.1
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 2.3.4, 7.7.1
compound sentence 2.1.1
compound term 6.2.2
conclusion 1.1.2
conclusion covariance 1.4.2, 1.4.3
conclusion replacement 1.4.3
conditional 5.1.1
conditionalization 5.3.1
conditioned instance 7.6.1
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 2.3.2
contingency, logical 1.4.6
constructive proof 8.5.1
contradictory sentences 1.4.5
contraposition for generalizations 8.3.3
conversational implicature 4.1.2
conversion 8.1.3
counterexample 1.4.1, 2.3.1, 7.1.4
counterexample, presentation of (see presenting a counterexample )
counterfactual conditional 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 Rule labels
dashes 7.2.1
dead-end gap 2.3.1
decisive system of derivations 2.3.4
decision procedure 2.3.4
deductive logic 1.1.3
deductive reasoning 1.1.3
definite description 1.3.4, 6.2.1 (see also 8.4)
deixis 1.3.1
De Morgan, Augustus (1806-1871) 4.2.4
De Morgan's laws 4.2.4
description operator 8.4.2
detachment rule 4.3.1
development of a gap 2.2.2
Diodorus Cronus ( -c.284 BCE) 5.1.2
direct generalization 7.1.4
direct rule 2.3.4
disjunct 4.1.1
disjunction 4.1.1
division 1.4.1, 1.4.5, 2.3.1, 7.7.1
domain 7.1.4
dots 7.2.1
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 Rule labels
embedding 6.4.3
empty reference value 1.3.4, 6.2.1
entailment 1.1.4
entity 6.2.1
epistemic condition 5.2.2
equation 6.1.3
equivalence (logical) 1.2.2, 1.4.3
equivalence class 6.3.2
equivalence relation 6.3.1
ex falso quodlibet 2.2.1 (see also EFQ under Rule labels)
ex nihilo verum 2.2.1 (see also ENV under Rule labels)
exception class 7.1.5
exception indicator 7.1.5
exclusion 1.4.4
exclusive disjunction 4.1.2
exclusive disjunction form 4.1.2
exemplify 8.1.1
exhaustive (jointly) 1.4.5, 3.1.2
exhaustiveness, relative 1.4.5
existence (requirement for a definite description to refer) 6.2.1
existential 8.1.1
existential claim 8.1.1
existential commitment 8.1.5
existential generalization 8.5.1
expansion by a range 7.5.1
exploitable 7.7.3
exploitation 2.2.3
exploitation chain 2.2.1
extension (of a rule) for equations 6.3.3
extensional interpretation 2.1.7, 6.4.1
extensional operation 6.1.2
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 Rule labels
first-order logic 1.1.5, 8.5.3
Fitch, Frederic (1908-1987) 2.2.2
flag 7.5.3
formal logic 1.1.5
formal validity 2.3.1
formula 6.1.4
free variable 7.2.1
Frege, Gottlob (1848-1925) 1.1.5, 4.1.3, 6.1.2, 6.1.4, 7.1.1, 7.1.1, 7.4.1, 8.4.2, 8.5.3
fully developing path 7.7.1
function 6.2.2
functor 6.2.2
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 Rule labels
gap 2.2.2
general argument 7.5.2
general exemplification 8.2.1
general term 6.2.1
generalization 7.5.2
generalization over pairs 7.4.1
Gentzen, Gerhard (1909-1945) 2.2.2
goal 2.2.2
Gödel, Kurt (1906-1978) 7.7.1, 8.5.3
grade (of a resource or goal) 3.4.1
grammatical predicate 6.1.1
grammatical subject 6.1.1
Grice, H. Paul (1913-1988) 1.3.3, 4.1.2, 5.1.2
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 Rule labels
higher-order logic 8.5.3
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 Rule labels
ID of a reference value 6.4.1
identity 6.1.3
if-conditional 5.1.1
immediate component 2.1.6
implication 1.3.3
implication, relative (see relative implication )
implicature 1.3.3
inclusive disjunction 4.1.2
inclusive disjunction form 4.1.2
inconsistency, relative 1.4.4
inconsistent 1.4.4
inconsistent with (see inconsistency, relative )
indefinite article 7.3.1
independence, logical 1.4.6
indexicality 1.3.1
indicated class 7.1.4
indicative conditional 5.1.2
indirect proof 3.3.1 (see also the rule Indirect Proof under Rule Labels)
individual 6.2.1
individual term 6.1.1
inductive inference 1.1.3
inference 1.1.2
inference ticket 5.3.2
instance 7.5.1
intensional entity 6.3.1
intensional interpretation 2.1.7, 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 Rule labels
Jaskowski, Stanislaw (1906-1965) 2.2.2
jointly exhaustive 1.4.5
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 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 Rule labels
lambda abstraction 6.1.4
lambda operator 6.1.4
law (see the list of laws )
left right double arrow (see ⇔ under Symbols)
Leibniz, G. W. (1646-1716) 1.1.5, 1.2.1
lemma 1.4.2
Lemma (the rule--see Lem under Rule Labels)
Lewis, David K. (1941-2001) 5.1.2, 6.2.1
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 1.2.3
logical implication 5.1.1
logical vocabulary 6.1.3
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 Rule labels
main connective 2.1.4
main resource 4.3.1
thorough system of derivations 7.7.1
material implication 5.1.1
mathematical logic 1.1.5
meaning postulate (for a definite description) 8.6.2
meta-mathematics 1.1.5
minimal sentence 3.4.1
minimally sound rule 2.3.2, 7.7.2
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)
monotonicity 1.4.2
Morris, C. W. (1903-1979) 1.3.1
multiple ambiguity 7.1.1
multiple conjunction 2.1.4
multiple generality 7.4.1
mutually exclusive 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 Rule labels
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 8.4.2
non-constructive proof 8.5.1
non-deductive reasoning 1.1.3
non-empty extension 8.1.1
non-logical vocabulary 6.1.3, 6.4.1
non-monotonic inference 1.4.2
non-restrictive relative clause 6.2.3
normative discipline 1.1.1
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 Rule labels
object 6.2.1
obversion 8.1.2
only-if conditional 5.2.1
open term 7.2.1
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 Rule labels
path 7.7.1
performative verb 1.3.x
Philo (c. 300 BCE) 5.1.2
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 1.3.1
predicate (logical) 6.1.1 6.1.2
predicate, zero-place 6.1.4
predicate abstract 6.1.4
predication 6.1.2
premise 1.1.2
premise contravariance 1.4.2, 1.4.3
premise replacement 1.4.3
presenting a counterexample 2.3.3
presupposition 1.3.4
progressive rule 2.3.4
proof by cases 4.2.1 (see also PC under Rule labels)
proof by choice 8.5.1
property 6.1.2
property in intension 6.3.1
proposition 1.2.2
proximate argument of a gap 2.3.1
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 Rule labels
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 6.2.1, 7.1.1
quod erat demonstrandum 2.2.1 (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 Rule labels
range 6.4.1
reductio argument 2.4.2
reference function 6.2.2
referential opacity 6.1.2
referential transparency 6.1.2
reflexivity 1.4.2, 1.4.3, 6.3.1
reject (a conditional) 5.4.1
relation 6.1.2
relative complement 7.1.4
relative implication 5.3.1
relative exhaustiveness 1.4.5
relative inconsistency 1.4.4
relative scope 2.1.4
render exhaustive (see relative exhaustiveness )
resource 2.2.2
restricted existential 8.1.1
restricted existential generalization 8.5.1
restricted universal 7.2.1
restricted universal instantiation 7.6.1
restricting formula 7.2.1
restricting predicate 7.2.1, 8.1.1
restriction by a relation 7.4.1
restrictive relative clause 6.2.3
rightwards double arrow (see ⇒ under Symbols)
run-on conjunction 2.1.4
run-on disjunction 4.1.3
Russell, Bertrand (1872-1970) 8.4.1, 8.5.3
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 Rule labels
safe rule 2.3.2
salience 6.2.1
scope 2.1.4
scope ambiguity 7.1.1
scope line 2.2.2
second-order logic 8.5.3
securing a compound term 7.8.1
securing a definite description 8.6.2
semantic presupposition 1.3.4
semantics 1.3.1
serial conjunction 2.1.4
serial disjunction 4.1.3
Sextus Empiricus (2nd cent.) 5.1.2
singular Barbara 7.6.1 (see also SB under Rule labels)
singular Camestres 7.6.1 (see also SC under Rule labels)
singular term 6.2.1
solidus (see / under Symbols)
sound rule (see utterly sound rule and minimally sound rule )
sound system of derivations 2.3.4, 7.7.1
speech act 1.3.1
Stalnaker, Robert C. (1940-) 5.1.2
statement 1.3.2
structure 6.4.1
subject-predicate expansion 7.1.1
subjunctive conditional 5.1.2
substantive existential commitment 8.1.5
subtraction 7.1.4
sufficient system of derivations 2.3.1
sufficient condition 5.2.2
symbolic logic 1.1.5
synthesis 2.1.7
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 Rule labels
Tautology 1.2.2
tense logic 3.1.2
term 6.2.1
there-is existential 8.1.3
thing 6.2.1
effectual system of derivations 7.7.1
transitivity 1.4.2, 1.4.3, 6.3.1
true of 6.4.2
truth conditions 1.2.2
truth function 2.1.1
truth-functional completeness 3.1.4
truth-functional connective 3.1.2
truth-functional logic 1.1.5, 3.1.2
truth table 2.1.1
truth value 1.2.1
type 6.2.2
type theory 8.5.3
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 Rule labels
ultimate argument of a derivation 2.3.1
ultimate component 2.1.6
ultimate resources 7.7.4
unanalyzed component 2.1.6
undefined term 6.2.1
uniformly general exemplification 8.2.1
uniqueness (requirement for a definite description to refer) 6.2.1
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)
utterly sound rule 2.3.2, 7.7.2
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 Rule labels
vacuous abstract 7.2.1
vagueness 1.3.2
valid conclusion 1.1.4
validity of an argument 1.1.4
validity, formal or in virtue of form (see formal validity )
veil of ignorance 7.5.3
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 Rule labels
weakening 4.3.2, 5.4.2 (see also Wk under Rule labels)
Wittgenstein, Ludwig (1889-1951) 1.2.3
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 Rule labels
yes-but answer 1.3.3
yes-no question 1.3.3
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 Rule labels
/ (solidus--U+002F) 1.1.2
⇒ (rightwards double arrow--U+21D2) 1.1.4
⇔ (left right double arrow--U+21D4) 1.2.2
⊤ (down tack--U+22A4) 1.2.2
⊥ (up tack--U+22A5) 1.2.2
ℵ (alef symbol--U+2135) 1.2.3
ℵ0 (aleph-null) 1.2.3
2ℵ0 1.2.3
∧ (logical and--U+2227) 2.1.1
● (black circle--U+25CF) 2.2.3
○ (white circle--U+25CB) 2.3.1
⇏ (rightwards double arrow with stroke--U+21CF) 2.3.1
¬ (not sign--U+00AC) 3.1.1
∨ (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) 8.4.2
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 Rule labels
⊥ as a premise 1.4.4
basic, for contradictories 3.2.1
basic, for contradictoriness 1.4.5
basic, for equivalence 1.4.3
basic, for exclusion 1.4.4
basic, for inconsistency 1.4.4
basic, for relative exhaustiveness 1.4.6
law for aliases 6.3.2
conditional as a conclusion 5.3.1
conditional as a premise 5.4.1
conjunction as a conclusion 2.2.1
conjunction as a premise 2.2.1
cut 1.4.5
law for descriptions 8.6.1
disjunction as a conclusion 4.2.2
disjunction as a premise 4.2.1
law for lemmas 1.4.2
law for premises 1.4.2
modus ponendo ponens 5.3.2
modus ponendo tollens 4.3.1
modus tollendo ponens 4.3.1
modus tollendo tollens 5.3.2
negation as a conclusion 3.2.1
negation as a premise 3.2.1
non-contradiction 3.2.2
restricted existential as a conclusion 8.5.1
restricted existential as a premise 8.5.1
restricted universal as a conclusion 7.6.1
restricted universal as a premise 7.6.1
⊤ as a conclusion 1.4.3
⊤ as a premise 1.4.3
unrestricted existential as a conclusion 8.5.1
unrestricted existential as a premise 8.5.1
unrestricted universal as a conclusion 7.5.2
unrestricted universal as a premise 7.5.2
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
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 Rule labels
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) 2.2.5
EG (Existential Generalization) 8.5.2
ENV (Ex Nihilo Verum) 2.2.5
Ext (Extraction) 2.2.3
IP (Indirect Proof) 3.3.1
Lem (Lemma) 2.4.1
LFR (Lemma for Reductio) 2.4.2
MCR (Making a Counterexample for Reductio) 7.6.2
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) 8.5.2
PC (Proof by Cases) 4.2.1
PCh (Proof by Choice) 8.5.2
PCh+ (Supplemented Proof by Choice) 8.5.2
PE (Proof of Exhaustion) 4.2.2
PRCh (Proof by Restricted Choice) 8.5.2
PRCh+ (Supplemented Proof by Restricted Choice) 8.5.2
RC (Rejecting a Conditional) 5.4.1
REC (Restricted Existential Conclusion) 8.5.2
REG (Restricted Existential Generalization) 8.5.2
REP (Restricted Existential Premise) 8.5.2
QED (Quod Erat Demonstrandum) 2.2.3
QED= (QED given Equations) 6.3.3
RAA (Reductio ad Absurdum) 3.2.2
RNcP (Restricted Non-constructive Proof) 8.5.2
RUC (Restricted Universal Conclusion) 7.6.2
RUG (Restricted Universal Generalization) 7.6.2
RUG+ (Supplemented Restricted Universal Generalization) 7.8.1
RUP (Restricted Universal Premise) 7.6.2
SB (Singular Barbara) 7.6.2
SC (Singular Camestres) 7.6.2
SD (Securing a Description) 8.6.2
SD+ (Securing a Description Supplemented) 8.6.2
ST (Securing a Term) 7.8.1
UG (Universal Generalization) 7.5.3
UG+ (Supplemented Universal Generalization) 7.8.1
UI (Universal Instantiation) 7.5.3