The Rules of the Game

The park was unusually quiet for a Saturday afternoon. A few children chased one another through the grass beyond the fountain while an old man sat beneath an oak tree feeding birds with stale bread. Between them, on a weathered stone table, rested a wooden chessboard whose pieces had clearly seen years of use.

Lee had always liked playing here. Something about chess belonged outdoors.

He slid a pawn forward.

Alison answered almost immediately, hardly looking at the board.

"You've been distracted all afternoon."

Lee smiled.

"I've been thinking."

"That's usually dangerous."

"It usually is."

They played another few moves in silence.

Finally Lee looked up.

"Can I ask you something?"

Alison nodded.

"Do you think the laws of logic are true because we assume they're true?"

She looked at him curiously.

"You mean things like identity? Non-contradiction? Excluded middle?"

"Exactly."

"I've always thought of them as axioms," she said. "Every system has to begin somewhere."

Lee nodded.

"So did I."

He rotated the knight between his fingers before placing it carefully onto its new square.

"But lately I've started wondering whether they're really assumptions at all."

Alison rested her elbows on the table.

"What else would they be?"

"I'm beginning to think they're unavoidable."

Alison laughed softly.

"Everything sounds unavoidable until someone invents another logic."

"So let me ask a different question."

He gestured toward the board.

"Suppose I wanted to convince you that bishops don't move diagonally."

"You'd fail."

"Probably. But I could at least try."

"Sure."

"What if I wanted to argue that this chessboard doesn't exist?"

"You'd look ridiculous."

"But I could still make the attempt."

"I suppose."

Lee nodded.

"Now suppose I wanted to argue that the law of non-contradiction is false."

Alison frowned.

"Some philosophers have."

"Have they?"

She hesitated.

"They've written about it."

"That's different."

He leaned back.

"Think about what's required even to make that argument."

She waited.

"I have to distinguish what I'm saying from what I'm not saying."

"Yes."

"I have to intend my words to keep the same meaning from the beginning of the sentence to the end."

"Of course."

"I have to expect that if my conclusion is true, its negation isn't."

Alison remained quiet.

Lee continued.

"Every step of the argument already depends on the very thing I'm trying to reject."

"So you're saying denying logic requires logic."

"Not just denying it."

He shook his head.

"That's what I realized recently."

He picked up one of the captured pawns and rolled it absentmindedly between his fingers.

"Trying to prove the laws of logic has exactly the same problem."

Alison looked puzzled.

"How so?"

"A proof requires premises."

She nodded.

"It requires inference."

She nodded again.

"It requires that the symbols mean the same thing throughout the proof."

"Yes."

"It requires contradiction to actually matter."

"I see where you're going."

"So proving the laws already assumes them."

He placed the pawn back beside the board.

"But disproving them assumes them too."

Alison stared at the chessboard for several moments.

"So they can't be proven."

"Not in the ordinary sense."

"And they can't be disproven."

"Not in the ordinary sense either."

A breeze drifted through the trees, carrying the smell of fresh-cut grass.

Somewhere behind them a church bell marked the hour.

Alison finally spoke.

"That almost sounds like you're saying they're beyond evidence."

"I don't think they are."

"No?"

"I think they're beneath it."

She raised an eyebrow.

Lee smiled.

"Evidence already assumes logic."

He tapped the board gently.

"You don't use the rules of chess to justify the existence of the rules of chess."

Alison laughed.

"You also can't play chess without them."

"Exactly."

She became quiet again.

"So if you can't prove them..."

"...and you can't disprove them..."

"...what are they?"

Lee looked out across the park before answering.

"I think they're conditions."

"Conditions?"

"Conditions that make reasoning possible."

He paused.

"If affirming something requires it..."

"...and denying it requires it..."

"...then maybe it isn't another claim within the system."

He looked back at her.

"Maybe it's one of the things that allows there to be a system at all."

Alison considered that for a while.

"It reminds me of Descartes."

"The cogito?"

She nodded.

"You can't doubt your own existence without existing."

"Exactly."

"I used to think the laws of logic were accepted on faith."

"And now?"

"Now I think they're discovered the same way the cogito is."

"By failing to escape them."

Lee smiled.

"That's a much better way of putting it."

Several moves passed before Alison spoke again.

"If that's true..."

Lee waited.

"...what does it mean for God?"

He had expected the question.

"I don't know."

She laughed.

"That's not the answer you've been building toward."

"No."

He smiled.

"It's just the honest one."

He studied the board.

"But I do think it means something."

"I can argue that God exists."

Alison nodded.

"I can argue that God doesn't exist."

Another nod.

"I can suspend judgment entirely."

"Yes."

"But notice something."

She waited.

"None of those positions require God to already exist."

Alison looked down at the board.

"But every one of them requires logic."

Lee didn't interrupt the silence that followed.

"So you're saying..."

Alison spoke slowly now.

"...logic occupies a different category."

"I think so."

"It isn't competing with God."

"No."

"It comes before the question."

"That's exactly what I've been wondering."

She looked back toward the fountain where the children were still running in circles.

"Theists often say logic comes from God."

Lee nodded.

"I've heard that."

"Does your argument refute that?"

"I don't think it refutes God."

"What then?"

"I think it changes the burden."

He folded his hands.

"If someone says God grounds logic, they now have to explain how that's possible without already relying on logic to make the claim."

Alison smiled.

"So the explanation borrows the very thing it's trying to explain."

"That's what troubles me."

The game had entered its final stages.

Only a handful of pieces remained.

Alison studied the board much longer than before.

Finally she spoke.

"You know what strikes me?"

"What?"

"If you're right..."

She moved her rook.

"...then logic isn't the sort of thing you believe."

Lee looked at the board, then back at her.

"No."

"What is it then?"

He thought for a moment.

"It's what remains after every attempt to remove it fails."

Alison nodded almost imperceptibly.

Neither of them spoke again for several minutes.

The pieces continued to move according to rules neither of them had written, rules neither of them had justified, rules neither of them could ignore without ceasing to play the game altogether.

Lee looked at the board.

"Check."

Alison smiled.

"I suppose neither of us could argue otherwise."

The game ended a few moves later.

The conversation didn't.