Logic Syllabus • Discussion 1
• https://inquiryintoinquiry.com/2023/06/02/logic-syllabus-discussion-1/

Re: Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
Re: Laws of Form ( https://groups.io/g/lawsofform/topic/logic_syllabus/99218507 )
❝_❞ John Mingers ( https://groups.io/g/lawsofform/message/2326 )

❝In a previous post you mentioned the minimal negation operator. Is there also the converse of this, i.e. an operator which is true when exactly one of its arguments is true? Or is this just XOR?❞

Yes, the “just one true” operator is a very handy tool. We discussed it earlier under the headings of “genus and species relations” or “radio button logic”. Viewed as a venn diagram it describes a partition of the universe of discourse into mutually exclusive and exhaustive regions.

Reading \(\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_m \texttt{)}\) to mean just one of \(x_1, \ldots, x_m\) is false, the form \(\texttt{((} x_1 \texttt{),} \ldots \texttt{,(} x_m \texttt{))}\) means just one of \(x_1, \ldots, x_m\) is true.

For two logical variables, though, the cases “condense” or “degenerate” and saying “just one true” is the same thing as saying “just one false”.

\[\texttt{((} x_1 \texttt{),(} x_2 \texttt{))} = \texttt{(} x_1 \texttt{,} x_2 \texttt{)} = x_1 + x_2 = \textsc{xor} (x_1, x_2).\]

There's more information on the following pages.

Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator

Related Truth Tables
• https://oeis.org/wiki/Minimal_negation_operator#Truth_tables

Genus, Species, Pie Charts, Radio Buttons
• https://inquiryintoinquiry.com/2021/11/10/genus-species-pie-charts-radio-buttons-1/

Related Discussions
• https://inquiryintoinquiry.com/?s=Radio+Buttons

#Logic #LogicSyllabus #BooleanDomain #BooleanFunction #BooleanValuedFunction
#Peirce #LogicalGraph #MinimalNegationOperator #ExclusiveDisjunction #XOR
#CactusLanguage #PropositionalCalculus #RadioButtonLogic #TruthTable

Logic Syllabus • 3
• https://inquiryintoinquiry.com/logic-syllabus/

Logical Concepts
• https://oeis.org/wiki/Logic_Syllabus#Logical_concepts

Ampheck • https://oeis.org/wiki/Ampheck
Boolean Domain • https://oeis.org/wiki/Boolean_domain
Boolean Function • https://oeis.org/wiki/Boolean_function
Boolean-Valued Function • https://oeis.org/wiki/Boolean-valued_function
Differential Logic • https://oeis.org/wiki/Differential_logic
Logical Graph • https://oeis.org/wiki/Logical_Graphs
Minimal Negation Operator • https://oeis.org/wiki/Minimal_negation_operator
Multigrade Operator • https://oeis.org/wiki/Multigrade_operator
Parametric Operator • https://oeis.org/wiki/Parametric_operator
Peirce's Law • https://oeis.org/wiki/Peirce%27s_law
Propositional Calculus • https://oeis.org/wiki/Propositional_calculus
Sole Sufficient Operator • https://oeis.org/wiki/Sole_sufficient_operator
Truth Table • https://oeis.org/wiki/Truth_table
Universe of Discourse • https://oeis.org/wiki/Universe_of_discourse
Zeroth Order Logic • https://oeis.org/wiki/Zeroth_order_logic

#Logic #LogicSyllabus #Ampheck #BooleanDomain #BooleanFunction #BooleanValuedFunction
#DifferentialLogic #LogicalGraph #MinimalNegationOperator #MultigradeOperator
#ParametricOperator #PeircesLaw #PropositionalCalculus #SoleSufficientOperator
#TruthTable #UniverseOfDiscourse #ZerothOrderLogic

"it's not just physical"
...
"so, let's make things physical"

okay, Tegan a/o Sara, let's just see if that checks out...
...
{uhh, does this check out?}

[song: "Closer (PROFF Bootleg)" specifically, bc omg]

thx, https://truthtablemaker.com/

#Logic #TruthTable #Philosophy #Lyrics #TeganAndSara #PROFF #Demisexual

Nothing is Sacred
Everything is Nothing
Everything is Sacred

here's the truth table to prove it, thx https://truthtablemaker.com/

#writing #Logic #TruthTable #Philosophy

Nothing is Sacred
Everything is Nothing
Everything is Sacred

here's the truth table to prove it, thx https://truthtablemaker.com/

#writing #Logic #TruthTable #Philosophy

#ThemeOneProgram • #JetsAndSharks 2.1
• https://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks-2/

Our #CactusGraph bears a vocabulary of \(41\) #LogicalTerms, each denoting a #BooleanVariable, so our proposition, call it \(``q",\) is a #BooleanFunction \(q:\mathbb{B}^{41}\to\mathbb{B}.\) Since \(2^{41}=2,199,023,255,552,\) its #TruthTable has \(>\) 2 trillion rows and its #VennDiagram has that many cells. There are \(2^{2^{41}}\) functions \(f:\mathbb{B}^{41}\to\mathbb{B},\) among which \(q\) is just one.

#Logic #LogicalGraphs